MCQ(10) - Math Solution

Multiple Choice Questions (MCQ) On Mathematics

MCQ in Mathematics 

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Multiple Choice Questions (MCQ) in Mathematics for 9th, 10th, 11th and 12th standard and case study based questions with answers. Chapter-wise important MCQ in mathematics.

Multiple Choice Questions (MCQ) 
in Mathematics For Class 09

Multiple Choice Questions (MCQ) 
in Mathematics For Class 10

Multiple Choice Questions (MCQ)
in Mathematics For Class 11

 

Maths MCQ Class 10 Ch – 5 | Arithmetic Progression

 Mathematics

Multiple Choice Questions (MCQ)
MCQ | Class 10 | Chapter 5
ARITHMATIC PROGRESSION

  • MCQ Based on the general Arithmetic Progression.
  • MCQ  Based on the nth term of  Arithmetic Progression.
  • MCQ Based on the sum of n terms of  Arithmetic Progression.
  • MCQ Based on the word problems of Arithmetic Progression.
  • MCQ Based from the nth term from the end of the sequence.

Features

  • In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations. 
  • Solution Hints are also given to some difficult problems. 
  • Each MCQ contains four options from which one option is correct. 
  • On the right hand side column of the pdf Answer option is given.

Action Plan

  • First of all students should Learn and write all basic points and Formulas related to the Arithmetic Progression.
  • Start solving  the NCERT Problems with examples.
  • Solve the important assignments on the Arithmetic Progression.
  • Then start solving the following MCQ.

MCQ | CHAPTER 5 | CLASS 10

ARITHMETIC PROGRESSION

Q 1) In an Arithmetic Progression, if a = 28, d = – 4, n = 7, then an is:
a) 4
b) 5
c) 3
d) 7 

Ans: a
Q 2) If a = 10 and d = 10, then first four terms will be:
a) 10, 30, 50, 60
b) 10, 20, 30, 40
c) 10, 15, 20, 25
d) 10, 18, 20, 30
Ans: b

Q 3) 30th term of the A.P: 10, 7, 4, …, is
a) 97
b) 77
c) – 77
d) – 87
Ans: c

Q 4) 11th term of the A.P. – 3, -1/2, 2 …. Is
a) 28
b) 22
c) – 38
d) – 48 
Ans: b

Q 5) The missing terms in AP: __, 13, __, 3 are:
a) 11 and 9
b) 17 and 9
c) 18 and 8
d) 18 and 9 
Ans: c

Q 6) Which term of the A.P. 3, 8, 13, 18, … is 78?
a) 12th
b) 13th
c) 15th
d) 16th 
Ans: d

Q 7) The 21st term of AP whose first two terms are -3 and 4 is:
a) 17
b) 137
c) 143
d) -143 
Ans: b

Q 8) The number of multiples of 4 between 10 and 250 is:
a) 50
b) 40
c) 60
d) 30 
Ans: c

Q 9) 20th term from the last term of the A.P. 3, 8, 13, …, 253 is:
a) 147
b) 151
c) 154
d) 158 
Ans: d

Q 10) The sum of the first five multiples of 3 is:
a) 45
b) 55
c) 65
d) 75 
Ans: a

Q 11) In an AP, if d = – 4, n = 7, an = 4, then a is
a) 6
b) 7
c) 20
d) 28 
Ans: d

Q 12) The list of numbers –10, –6, –2, 2,… is
a) an AP with d = –16
b) an AP with d = 4
c) an AP with d = –4
d) not an AP 
Ans: b

Q 13) If the 2nd term of an AP is 13 and the 5th term is 25, then its 7th term is
a) 30
b) 33
c) 37
d) 38 
Ans: b

Q 14) Which term of the AP: 21, 42, 63, 84,… is 210?
a) 9th
b) 10th
c) 11th
d) 12th 
Ans: b

Q 15) What is the common difference of an AP in which a18 – a14 = 32?
a) 8
b) – 8
c) – 4
d) 4 
Ans: a

Q 16) The famous mathematician associated with finding the sum of the first 100 natural numbers is
a) Pythagoras
b) Newton
c) Gauss
d) Euclid 
Ans: c

Q 17) The sum of first 16 terms of the AP: 10, 6, 2,… is
a) –320
b) 320
c) –352
d) –400 
Ans: a

Q 18) The nth term of an A.P. is given by an = 3 + 4n. The common difference is
a) 7
b) 3
c) 4
d) 1 
Ans: c
Q 19) If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are
a) 2, 4, 6
b) 1, 5, 3
c) 2, 8, 4
d) 2, 3, 4 
Ans: d
Explanation: Reason: Let three numbers be a – d, a, a + d
∴ a – d + a + a + d = 9
⇒ 3a = 9 ⇒ a = 3
Also (a – d) . a . (a + d) = 24
⇒ (3 -d) .3(3 + d) = 24
⇒ 9 – d² = 8
⇒ d² = 9 – 8 = 1
∴ d = ± 1
Hence numbers are 2, 3, 4 or 4, 3, 2

Q 20)  The 10th term from the end of the A.P. -5, -10, -15,…, -1000 is
a) – 955
b) – 945
c) – 950
d) – 965 
Ans: a

Q 21) The sum of all two digit odd numbers is
a) 2575
b) 2475
c) 2524
d) 2425 

Ans: b

Q 22) Find the sum of 12 terms of an A.P. whose nth term is given by an = 3n + 4
(a) 262
(b) 272
(c) 282
(d) 292 
Ans: a
Q 23) The sum of first n odd natural numbers is
(a) 2n²
(b) 2n + 1
(c) 2n – 1
(d) n² 
Ans: d

Q 24) The sum of first n terms of the series a, 3a, 5a, …….. is
(a) na
(b) (2n – 1) a
(c) n²a
(d) n²a² 
Ans: c

Q 25) If 2x, x + 10, 3x + 2 are in A.P., then x is equal to
(a) 0
(b) 2
(c) 4
(d) 6 
Ans: d

Q 26) Which term of the AP: 27, 24, 21, ……… is zero?
(a) 8th
(b) 10th
(c) 9th
(d) 11th 
Ans: b

Q 27) If 7 times the 7th term of an A.P. is equal to 11 times its 11th term, then 18th term is
(a) 18
(b) 9
(c) 77
(d) 0 
Ans: d

Q 28) If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?
(a) 30
(b) 33
(c) 37
(d) 38 

Ans: b

Q 29) Next term of the AP √2, 3√2, 5√2, ……. is
(a) 2√7
(6) 6√2
(c) 9√2
(d) 7√2 
Ans: d
Q 30) If p, q, r and s are in A.P. then r – q is
(a) s – p
(b) s – q
(c) s – r
(d) none of these 
Ans: c

Q 31) If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are
(a) 2, 4, 6
(b) 1, 5, 3
(c) 2, 8, 4
(d) 2, 3, 4 

Ans: d

Q 32) If the sum of the first m terms of an AP is n and the sum of its n terms is m, then the sum of its (m + n) terms will be
(a) m + n
(b) -(m + n)
(c) m – n
(d) 0 

Ans: b
Q 33) The (n – 1)th term of an A.P. is given by 7,12,17, 22,… is
(a) 5n + 2
(b) 5n + 3
(c) 5n – 5
(d) 5n – 3 
Ans: d

Q 34) If a, b, c, d, e are in A.P., then the value of a – 4b + 6c – 4d + e is
(a) 0
(b) 1
(c) -1.
(d) 2
Ans: a 
Explanation : Let common difference of A.P. be d
∴ b = a + d, c = a + 2d, d = a + 3d and e = a + 4d
Given equation a-4b + 6c-4d + c
= a – 4(a + d) + 6(a + 2d) – 4(a + 3d) + (a + 4d)
= a – 4a – 4d + 6a + 12d – 4a – 12d + a + 4d = 8a – 8a + 16d – 16d = 0

Q 35) nth term of the sequence a, a + d, a + 2d,… is
(a) a + nd
(b) a – (n – 1)d
(c) a + (n – 1)d
(d) n + nd 
Ans: a

Q 36) If 2x, x + 10, 3x + 2 are in A.P., then x is equal to
(a) 0
(b) 2
(c) 4
(d) 6 
Ans: d
Q 37) The 10th term from the end of the A.P. 4, 9,14, …, 254 is
(a) 209
(b) 205
(c) 214
(d) 213 
Ans: a

Q 38) If the sum of first n terms of an AP is An + Bn² where A and B are constants. The common difference of AP will be
(a) A + B
(b) A – B
(c) 2A
(d) 2B 
Ans: d

Q 39) The sum of all odd integers between 2 and 100 divisible by 3 is
(a) 17
(b) 867
(c) 876
(d) 786 
Ans: b

Q 40) The sum of the first 15 multiples of 8 is
(a) 920
(b) 860
(c) 900
(d) 960 
Ans: d

Q 41) The 21st term of the AP whose first two terms are –3 and 4 is
(a) 17
(b) 137
(c) 143
(d) –143 
Ans: b

Q 42) If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?
(a) 30
(b) 33
(c) 37 

(d) 38
Ans: b

Maths MCQ Class 10 Ch-4 | Quadratic Equations

 

Mathematics

Multiple Choice Questions (MCQ)
MCQ | Class 10 | Chapter 4
QUADRATIC EQUATIONS

  • MCQ Based on the general quadratic equations.
  • MCQ  Based on the different methods of solving Quadratic Equations.
  • MCQ Based on the Nature of roots of Quadratic Equations.
  • MCQ Based on the Discriminant.
  • MCQ Based from the Quadratic Formula.

Features

  • In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations. 
  • Solution Hints are also given to some difficult problems. 
  • Each MCQ contains four options from which one option is correct. 
  • On the right hand side column of the pdf Answer option is given.

Action Plan

  • First of all students should Learn and write all basic points and Formulas related to the Quadratic Equations.
  • Start solving  the NCERT Problems with examples.
  • Solve the important assignments on the Quadratic Equations.
  • Then start solving the following MCQ.


MCQ | CHAPTER 4 | CLASS 10

QUADRATIC EQUATIONS

Q 1) Which one of the following is not a quadratic equation?
(a) (x + 2)22 = 2(x + 3)
(b) x22 + 3x = (–1) (1 – 3x)22

(c) (x + 2) (x – 1) = x2 – 2x – 3
(d) x3 – x2 + 2x + 1 = (x + 1)3 
Ans: c
Q 2) The sum of two numbers is 27 and product is 182. The numbers are:
(a) 12 and 13
(b) 13 and 14
(c) 12 and 15
(d) 13 and 24 
Ans: b
Q 3) The quadratic equation x2 + 7x – 60 has
(a) two equal roots
(b) two real and unequal roots
(b) no real roots
(c) two equal complex roots 
Ans: b
Q 4) A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
(a) 30 km/hr
(b) 40 km/hr
(c) 50 km/hr
(d) 60 km/hr 
Ans: b
Q 5) The quadratic equation 2x2 – √5x + 1 = 0 has
(a) two distinct real roots
(b) two equal real roots
(c) no real roots
(d) more than 2 real roots 
Ans: c
Q 6) The quadratic equation has degree
(a) 0
(b) 1
(c) 2
(d) 3 
Ans: c
Q 7) A bi-quadratic equation has degree
(a) 1
(b) 2
(c) 3
(d) 4 
Ans: d
Q 8) The polynomial equation x (x + 1) + 8 = (x + 2) (x – 2) is
(a) linear equation
(b) quadratic equation
(c) cubic equation
(d) bi-quadratic equation 
Ans: a
Q 9) The roots of the quadratic equation 6x² – x – 2 = 0 are

Ans: c

Q 10) The quadratic equation whose roots are 1 and -1/2 is

(a) 2x² + x – 1 = 0
(b) 2x² – x – 1 = 0
(c) 2x² + x + 1 = 0
(d) 2x² – x + 1 = 0 

Ans: b
Q 11) 

(a) 4

(b) 3

(c) 3.5

(d) -3 

Ans: b
Q 12)  The roots of the quadratic equation   

Ans: c

Q 13) The sum of the roots of the quadratic equation 3x2 – 9x + 5 = 0 is
(a) 3
(b) 6
(c) – 3
(d) 2 

Ans: a
Q 14) If one root of the equation x² + px + 12 = 0 is 4, while the equation x² + px + q = 0 has equal roots, the value of q is
a)   49 / 4
b)  4 / 49
c)  4
d)  49
Ans: a
Q 15) The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, the other two sides of the triangle are equal to:
(a) Base = 10cm and Altitude = 5cm
(b) Base = 12cm and Altitude = 5cm
(c) Base = 14cm and Altitude = 10cm
(d) Base = 12cm and Altitude = 10cm 
Ans: b
Q 16) If α and β are the roots of the equation 2x2 – 3x – 6 = 0. Then the equation whose roots are and is
(a) 6x² – 3x + 2 = 0
(b) 6x² + 3x – 2 = 0
(c) 6x² – 3x – 2 = 0
(d) x² + 3x – 2 = 0 
Ans: b
Q 17) The sum of the squares of two consecutive natural numbers is 313. The numbers are
(a) 12, 13
(b) 13,14
(c) 11,12
(d) 14,15 
Ans: a
Q 18) If one root of the quadratic equation 2x² + kx – 6 = 0 is 2, the value of k is
(a) 1
(b) -1
(c) 2
(d) -2 
Ans: b
Q 19) If – 5 is a root of the quadratic equation 2x² + px – 15 = 0, then
(a) p = 3
(b) p = 5
(c) p = 7
(d) p = 1 
Ans: c
Q 20) One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son’s age. Their present ages are
(a) 7 years, 49 years
(b) 5 years, 25 years
(c) 1 years, 50 years
(d) 6 years, 49 years 
Ans: a

Q 21) Equation of (x + 1)2 – x2 = 0 has number of real roots equal to:

(a) 1
(b) 2
(c) 3
(d) 4 
Ans: a
Q 22) The roots of 100x2 – 20x + 1 = 0 is:
(a) 1/20 and 1/20
(b) 1/10 and 1/20
(c) 1/10 and 1/10
(d) None of the above 
Ans: c
Q 23) If 1/ 2  is a root of the quadratic equation x2 – mx – 5/4 = 0, then value of m is:
(a) 2
(b) -2
(c) -3
(d) 3 
Ans: b
Q 24) If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then
(a) P = 0
(b) p = – 2
(c) p = ± 2
(d) p = 2 
Ans: d
Q 25) The roots of quadratic equation 2x2 + x + 4 = 0 are:
(a) Positive and negative
(b) Both Positive
(c) Both Negative
(d) No real roots 
Ans: d
Q 26) If α and β are the roots of 4x2 + 3x + 7 = 0, then the value of is  
a)   -3/4
b)   -3/7
c)   3/7
d)   7/4
Ans: b
Q 27) The sum of the reciprocals of Rehman’s ages 3 years ago and 5 years from now is 1/3. The present age of Rehman is:
(a) 7
(b) 10
(c) 5
(d) 6 
Ans: a
Q 28) If one root of equation 4x2 – 2x + k – 4 = 0 is reciprocal of the other. The value of k is:
(a) – 8
(b) 8
(c) – 4
(d) 4 
Ans: b

Q 29) The equation 2x² + kx + 3 = 0 has two equal roots, then the value of k is
(a)   ± √6
(b)   ± 4
(c)   ± 3√2
(d)   ± 2√6 

Ans: d
Q 30) Which of the following equations has 2 as a root?
(a) x2 – 4x + 5 = 0
(b) x2 + 3x – 12 = 0
(c) 2x2 – 7x + 6 = 0
(d) 3x2 – 6x – 2 = 0 
Ans: c

Q 31) A quadratic equation ax2 + bx + c = 0 has no real roots, if
(a) b2 – 4ac > 0
(b) b2 – 4ac = 0
(c) b2 – 4ac < 0
(d) b2 – ac < 0 

Ans: c
Q 32) The equation which has the sum of its roots as 3 is
(a) 2x2 – 3x + 6 = 0
(b) –x2 + 3x – 3 = 0

(d) 3x2 – 3x + 3 = 0 
Ans: b

Q 33) The roots of 100x2 – 20x + 1 = 0 is:
(a) 1/20 and 1/20
(b) 1/10 and 1/20
(c) 1/10 and 1/10
(d) None of the above 
Ans: c
Q 34) The equation (x + 1)2 – 2(x + 1) = 0 has
(a) two real roots
(b) no real roots
(c) one real root
(d) two equal roots 
Ans: a
Q 35) Which of the following is not a quadratic equation
(a) x² + 3x – 5 = 0
(b) x² + x3 + 2 = 0
(c) 3 + x + x² = 0
(d) x² – 9 = 0 
Ans: b
Q 36) The maximum number of roots for a quadratic equation is equal to
(a) 1
(b) 2
(c) 3
(d) 4 
Ans: b
Q 37) Values of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is
(a) 0 only
(b) 4
(c) 8 only
(d) 0, 8 

Maths MCQ Ch-15 Class 10 | Probability

  

Mathematics

Multiple Choice Questions (MCQ)
MCQ | Class 10 | Chapter 15
PROBABILITY

  • MCQ Based on the tossing of one coin, two coins and three coins.
  • MCQ  Based on the Tossing of one die and two die.
  • MCQ Based on the Playing cards
  • MCQ Based on the general problems of probability.
  • MCQ Based from the CBSE Sample Questions

Features

  • In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations. 
  • Solution Hints are also given to some difficult problems. 
  • Each MCQ contains four options from which one option is correct.

Action Plan

  • First of all students should Learn and write all basic points and Formulas related to the Probability.
  • Start solving  the NCERT Problems with examples.
  • Solve the important assignments on the Probability.
  • Then start solving the following MCQ.

MCQ | CHAPTER 15 | CLASS 10
PROBABILITY

Q 1) The probability of event equal to zero is called;
(a) Certain event
(b) Sure Event
(c) Impossible event
(d) Independent event 

Ans: c

Q 2) What is the probability of a sure event?
a) 0
b) 1
c) 2
d) 3 

Ans: b

Q 3) The probability that cannot exist among the following:
(a) 2 / 3
(b) -1.5
(c) 15%
(d) 0.7 

Ans: b
Q 4) The probability of getting a spade card from a well shuffled deck of 52 cards is
a) 1/ 34
b) 1/ 4
c) 12/ 13
d) 3/ 4 
Ans: b

Q 5) If P(E) = 0.07, then what is the probability of ‘not E’?
(a) 0.93
(b) 0.95
(c) 0.89
(d) 0.90
Ans: a

Explanation: 

P(E) + P(not E) = 1
Since, P(E) = 0.05 
 So, P(not E) = 1 – P(E) 
Or, P(not E) = 1 – 0.07 
 ∴ P(not E) = 0.93

Q 6) The total number of events of throwing 10 coins simultaneously is
(a) 1024
(b) 512
(c) 100
(d) 10
Ans: a Explanation :
 Total events 210 = 1024
Q 7) A bag has 3 red balls and 5 green balls. If we take a ball from the bag, then what is the probability of getting red balls only?
(a) 3
(b) 8
(c) 3/8
(d) 8/3 
Ans: c
Q 8) A bag has 5 white marbles, 8 red marbles and 4 purple marbles. If we take a marble randomly, then what is the probability of not getting purple marble?
(a) 0.5
(b) 0.66
(c) 0.08
(d) 0.77 
Ans: d
Q 9) A dice is thrown in the air. The probability of getting odd numbers is
(a) 1/2
(b) 3/2
(c) 3
(d) 4 
Ans: a
Q 10) Three coins are tossed simultaneously. The probability of getting all heads is
a) 1
b) 1/ 2
c) 1/ 4
d) 1/ 8
Ans: d 
Explanation: Here S = [HHH, HHT, HTH, THH, HTT, THT, TTH, TTT] = 8
∴ P(all heads) =1/8
Q 11) If two dice are thrown in the air, the probability of getting sum as 3 will be
(a) 2/18
(b) 3/18
(c) 1/18
(d) 1/36
Ans: c
Explanation: When two dice are thrown in the air:
Total number of outcome = 6 x 6 = 36
Sum 3 is possible if we get (1,2) or (2,1) in the dices. 
Hence, the probability will be = 2/36 = 1/18

Q 12) A card is drawn from the set of 52 cards. Find the probability of getting a queen card.
(a) 1/26
(b) 1/13
(c) 4/53
(d) 4/13 
Ans: b
Q 13) One card is drawn from a well shuffled deck of 52 cards. The probability of getting a king of red color is
a) 1/ 26
b) 1/ 13
c) 1/ 4
d) 1/ 2
Ans: a 
Explanation: Total cards = 52
Total events (S) = 52
a king of red color = 2
P(a king of red color) = 2/52 = 1/26
Q 14) The sum of the probabilities of all the elementary events of an experiment is
(a) 0.5
(b) 1
(c) 2
(d) 1.5 
Ans: b

Q 15) A card is selected at random from a well shuffled deck of 52 playing cards. The probability of its being a face card is
(a) 3/13
(b) 4/13
(c) 6/13
(d) 9/13 
Ans: a

Q 16) One card is drawn from a well shuffled deck of 52 playing cards. The probability of getting a non-face card is
a) 3/ 13
b) 10/ 13
c) 7/ 13
d) 4/ 13
Ans: b 
Explanation: Total cards = 52,
Total face cards = 12
∴ Non-face cards = 52 – 12 = 40
∴ P(a non-face card)= 40/52 = 10/13

Q 17) If an event cannot occur, then its probability is
(a) 1
(b) 3/4
(c) 1/2
(d) 0 
Ans: d

Q 18) If P(A) denotes the probability of an event A, then
(a) P(A) < 0
(b) P(A) > 1
(c) 0 ≤ P(A) ≤ 1
(d) –1 ≤ P(A) ≤ 1 
Ans: c

Q 19)A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favorable to E is
(a) 4
(b) 13
(c) 48
(d) 51
Ans: d
Explanation
In a deck of 52 cards, there are 13 cards of heart and 1 is ace of heart.
Given that the event E is that card is not an ace of hearts.
Hence, the number of outcomes favorable to E = 52 – 1 = 51
Q 20) If the probability of an event is p, the probability of its complementary event will be
(a) p – 1
(b) p
(c) 1 – p
(d) 1 – 1/p 
Ans: c

Q 21) The probability that a non leap year selected at random will contain 53 Sundays is
(a) 1/7
(b) 2/7
(c) 3/7
(d) 5/7
Ans: a
Explanation:
Non-leap year = 365 days
365 days = 52 weeks + 1 day
For 52 weeks, number of Sundays = 52
1 remaining day can be Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.
Total possible outcomes = 7
The number of favorable outcomes = 1 Thus, the probability of getting 53 Sundays = 1/7

Q 22) In a leap year what is the probability of getting 53 Friday
(a) 1/7
(b) 2/7
(c) 3/7
(d) 5/7 
Ans: b

Q 23) In an ordinary year, what is the probability of getting 52 Tuesday
(a) 1/7
(b) 2/7
(c) 4/7
(d) 6/7
Ans: d
Solution Hint
In an ordinary year probability of getting 53 Tuesday is = 
In an ordinary year probability of not getting 53 Tuesday is = 1-  =  
In an ordinary year probability of getting 52 Tuesday is = 
Q 24) The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is
(a) 7
(b) 14
(c) 21
(d) 28
Ans: b
Explanation:
Total number of eggs = 400

Q 25) Two players, Ram and Shyam, play a tennis match. It is known that the probability of Ram winning the match is 0.62. The probability of Shyam winning the match is
(a) 0.62
(b) 0.38
(c) 0.58
(d) 0.42 
Ans: b

Q 26) The probability of getting exactly one head in tossing a pair of coins is
(a) 0
(b) 1
(c) 1/3
(d)1/2
Ans: d
Explanation: Reason: S = [HH, HT, TH, TT] = 4 

Q 27) The letters of the word SOCIETY are placed at random in a row. The probability of getting a vowel is
a) 1/ 7
b) 2/ 7
c) 3/ 7
d) 4/ 7
Ans: c 
Explanation: Total letters = 7
No. of vowel = 3 [∵ Vowel are O, I, E]
∴ P(a vowel) = 3/7

Q 28) Cards bearing numbers 3 to 20 are placed in a bag and mixed thoroughly. A card is taken out from the bag at random. The probability that the number on the card taken out is an even number, is
a) 1/ 20
b) 1/ 4
c) 1/ 3
d) 1/ 2 
Ans: d
Q 29) The total events to throw three dice simultaneously is
(a) 6
(b) 18
(c) 81
(d) 216
Ans: d 
Explanation: 
Total cards = (6)3= 216

Q 30) The probability of getting a consonant from the word MAHIR is
a) 2/ 5
b) 3/ 5
c) 4/5
d) 1 
Ans: b
Q 31) One card is drawn from a well-shuffled deck of 52 cards. The probability that the card will not be an ace is
a) 1/ 13
b) 4/ 13
c) 12/ 13
d) 3/ 13 
Ans: c
Q 32) A girl calculates that the probability of her winning the first prize in a lottery is 8/100 . If 6,000 tickets are sold, how many tickets has she bought?
(a) 400
(b) 750
(c) 480
(d) 240
Ans: c 
Explanation: 
No. of tickets sold = (8/100) × 6000 = 8 × 60 = 480

Q 33)
A man is known to speak truth 3 out of 4 times. He throws a die and a number other than six comes up. Find the probability that he reports it is a six.
a) 3/ 4
b) 1/ 4
c) 1/ 2
d) 1
Ans: b
Explanation:
Probability of telling a truth = 3/4 

Probability of telling a lie = 1- 3/4 = 1/4
When a number other than six appears and man reports it is a six, it means man is telling a lie.
Required Probability = 1/ 4

Q 34) Which of the following cannot be the probability of an event?
(a) 1.5
(b) 3 / 5
(c) 25%
(d) 0.3 
Ans: a

Q 35) An integer is chosen at random from 1 to 100, Find the probability that it is divisible by 4 and 6
a) 4/ 25
b) 8/ 25
c) 7/ 25
d) 2/ 25 
Ans: d

Q 36) An integer is chosen at random from 1 to 100, Find the probability that it is a prime number
a) 4/ 25
b) 8/ 25
c) 1/ 4
d) 2/ 5 

Ans: c

Q 37) A jar contains 24 marbles, some are green and some others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/ 3. Find the number of blue marbles.
a) 12
b) 10
c) 8
d) 16 

Ans: c

Q 38) Three coins are tossed together. Find the probability of getting at most 2 tails.
a) 7/ 8
b) 3/ 4
c) 1/ 8
d) 5/ 8
Ans: a
Solution Hint
When 3 coins are tossed then possible outcomes are as follows
{HHH, HHT, HTH, THH, HTT, THT, TTH, TTH}
P(Getting at most 2 tail) = P(≤ two tails) = P(2 tail) + P(1 tail) + P(no tail) 

Questions From CBSE Sample Papers (2021-22)
Basic Maths (241)

Q 39) A box contains cards numbered 6 to 50. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square like 4,9….is

(a) 1/45
(b) 2/15
c) 4/45
(d) 1/9 

Ans: d
Q 40) If the letters of the word RAMANUJAN are put in a box and one letter is drawn at random. The probability that the letter is A is
(a) 3/5
(b) 1/2
(c) 3/7
(d) 1/3 
Ans: d

Q 41) A fair die is thrown once. The probability of even composite number is
(a) 0
(b) 1/3
c) 3/4
(d) 1 
Ans: b
Q 42) If P (E) denotes the probability of an event E, then 
(a) 0< P(E) ⩽1
(b) 0 < P(E) < 1
c) 0 ≤ P(E) ≤1
(d) 0 ⩽P(E) <1 
Ans: c

Q 43) In a throw of a pair of dice, the probability of the same number on each die is
(a) 1/6
(b) 1/3
c) 1/ 2
(d) 5/6 
Ans: a

Standard Maths SP (041)

Q 44) Two fair coins are tossed. What is the probability of getting at the most one head?
(a) 3 ⁄ 4
(b) 1 ⁄ 4
(c) 1 ⁄ 2
(d) 3 / 8
Ans: a
Solution Hint
Possible outcomes are (HH), (HT), (TH), (TT)
Favorable outcomes(at the most one head) are (HT), (TH), (TT) So probability of getting at the most one head =3/4

Q 45) A letter of English alphabets is chosen at random. What is the probability that it is a letter of the word ‘MATHEMATICS’?
(a) 4/13
(b) 9/26
(c) 5/13
(d) 11/26
Ans: a

Solution Hint
Number of Possible outcomes are 26
Favorable outcomes are M, A, T, H, E, I, C, S probability = 8/26 = 4/13

Q 46) A card is drawn from a well shuffled deck of cards. What is the probability that the card drawn is neither a king nor a queen?
(a) 11/13
(b) 12/13
(c) 11/26
(d) 11/52 
Ans: a
Q 47) Two fair dice are rolled simultaneously. The probability that 5 will come up at least once is
(a) 5/36
(b) 11/36
(c) 12/36
(d) 23/36
Ans: b
Solution Hint
Outcomes when 5 will come up at least once are-
(1,5), (2,5), (3,5), (4,5), (5,5), (6,5), (5,1), (5,2), (5,3), (5,4) and (5,6) Probability that 5 will come up at least once = 11/36

Q 48) Which of the following cannot be the probability of an event.
a) 1/3
b) 0.1
c) 3 %
d) 17/16 
Ans: d
Q 49) If the probability of an event is m. then the probability of its complimentary event is :
a) m – 1
b) m
c) 1 – m
d) 1 + m
Ans: c

Q 50) A dice is thrown once. The probability of getting an even prime number is :
a) 2/3
b) 1/ 2
c) 1/6
d) 0 
Ans: c

Q 51) A letter is drawn at random from the letters of the word MIRROR. Which are the letters that have equal probabilities of being drawn ?
a) I and O
b) M, I, R
c) M, I, O
d) M, I, O, R 
Ans: c

Q 52) In a single through of a pair of dice, the probability of getting the sum a perfect square is :
a)  1/18
b)  7/36
c)  1/36
d)  2/9
Ans: b

Questions from CBSE Final Question Paper 2021-22 (Standard)

Q 53) The probability of getting two heads when two fair coins are tossed together is
a) 1/3
b) 1/4
c) 1/2
d) 1 
Ans: b
Q 54) In a single through of a dice, the probability of getting a composite number is
a) 1/3
b) 1/2
c) 2/3
d) 5/6 
Ans: a
Q 55) The probability that a non-leap year has 53 Wednesday, is:
a) 1/7
b) 2/7
c) 5/7
d) 6/7 
Ans: a

Q 56) From the letters of the word ‘MANGO’ a letter is selected at random. The probability that the letter is a vowel is :
a) 1/5
b) 3/5
c) 2/5
d) 4/5 
Ans: c


Maths MCQ Ch-12 Class 10 | Area Related to Circle

  MATHEMATICS

MCQ | CHAPTER 12 | CLASS 10

Area Related to the Circles

Q 1) What is the formula for the circumference of a circle?
a) C = 2πd
b) C = 2πr
c) C = 2πa
d) C = 2πs 

Ans: b
Q 2) What is the formula for the area of a circle?
a) A = πd2
b) A = πs2
c) A = πr2
d) A = πa2
Ans: c
Q 3) The circumference of the circle having diameter 8.4 cm is
a) 25.2 cm
b) 26.4 cm
c) 28 cm
d) 27.6 
Ans: b
Q 4) The perimeter of a circle having radius 5cm is equal to:
(a) 30 cm
(b) 3.14 cm
(c) 31.4 cm
(d) 40 cm 
Ans: c
Q 5) What is the circumference of a circle if the radius is 7 m?
a) 8 m
b) 2 m
c) 44 m
d) 22 m 
Ans: c
Q 6) Area of the circle with radius 5cm is equal to:
(a) 60 sq.cm
(b) 75.5 sq.cm
(c) 78.5 sq.cm
(d) 10.5 sq.cm 
Ans: c
Q 7) Find the area of the circle whose circumference is 44 cm.
a) 154 cm2
b) 308 cm2
c) 77 cm2
d) 231 cm2 
Ans: a
Q 8) Find the area of a semicircle if the radius is 6 cm.
a) 1.35 m
b) 6.54 m
c) 18.00 m
d) 8.05 m 
Ans: b
Q 9) Find the radius of the circle if the circumference is 12 m.
a) 1.90 m
b) 1.09 m
c) 7.90 m
d) 1.40 m
Ans: a

Q 10) The largest triangle inscribed in a semi-circle of radius r, then the area of that triangle is;

(a) r2

(b) 1/2r2

(c) 2r2

(d) √2r2
Ans: a

  Q 11) Find the radius of a circle if 2 m is the area of the circle.
a) √0.83 m
b) 5 m
c) √0.63 m
d) √38 m 
Ans: c
Q 12) If the perimeter of the circle and square are equal, then the ratio of their areas will be equal to:
(a) 14:11
(b) 22:7
(c) 7:22
(d) 11:14 
Ans: a
Q 13) The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameter 36 cm and 20 cm is
a) 28 cm
b) 42 cm
c) 56 cm
d) 16 cm 
Ans: a
Q 14) The area of the circle that can be inscribed in a square of side 8 cm is
(a) 36 π cm2
(b) 16 π cm2
(c) 12 π cm2
(d) 9 π cm2
Ans: b
Solution Hint
Given, Side of square = 8 cm
Diameter of a circle = side of square = 8 cm
Therefore, Radius of circle = 4 cm Area of circle = π(4)2  = 16π cm2

Q 15) The area of the square that can be inscribed in a circle of radius 8 cm is

(a) 256 cm2

(b) 128 cm2

(c) 642 cm2

(d) 64 cm2

Ans: b

Solution Hint

Radius of circle = 8 cm

Diameter of circle = 16 cm = diagonal of the square

Let “a” be the triangle side, and the hypotenuse is 16 cm

Using Pythagoras theorem, we can write

162 = a2 + a2 ⇒ 256 = 2a2 ⇒ a2 = 256/2 ⇒ a2 = 128 = Area of a Square

Q 16) The area of a sector of a circle with radius 6 cm if the angle of the sector is 60°.
(a) 142/7
(b) 152/7
(c) 132/7
(d) 122/7
Ans: c
Solution Hint
Angle of the sector is 60°
Area of sector = (θ/360°) × π r2
∴ Area of the sector with angle 60° = (60°/360°) × π r2 cm2= (36/6) π cm2 = 6 × (22/7) cm2 = 132/7 cm2
Q 17) What is the name of the sector with a larger area?
a) Large
b) Major
c) Big
d) Wide 
Ans: b
Q 18) What is the name of the sector with a smaller area?
a) Small
b) Narrow
c) Minor
d) Tiny 
Ans: c
Q 19) Number of sectors in a circle are ____
a) 2
b) 3
c) 4
d) 1
Ans: a
Solution Hint 
A circle contains two sectors. The sector having a larger area is called a major sector and the sector having a smaller area is called a minor sector.
Q 20) In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The length of the arc is;
(a) 20cm
(b) 21cm
(c) 22cm
(d) 25cm 
Ans: c

Q 21) Find the radius of the wheel if the wheel rotates 100 times to cover 500 m.
a) 0.07 m
b) 0.47 cm
c) 0.79 m
d) 0.57 cm 

Ans: c
Q 22) In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The area of the sector formed by the arc is:
(a) 200 cm2
(b) 220 cm2
(c) 231 cm2
(d) 250 cm2
Ans: c

Q 23) Area of a sector of angle p (in degrees) of a circle with radius R is
(a) p/180 × 2πR
(b) p/180 × π R2
(c) p/360 × 2πR
(d) p/720 × 2πR2
Ans: d
 
Q 24) If the area of a circle is 154 cm2, then its perimeter is
(a) 11 cm
(b) 22 cm
(c) 44 cm
(d) 55 cm
Ans: c
Solution Hint
Given, Area of a circle = 154 cm2
πr2 = 154   ⇒ (22/7) × r2 = 154
r2 = (154 × 7)/22 ⇒ r2 = 7 × 7 ⇒ r = 7 cm Perimeter of circle = 2πr = 2 × (22/7) × 7 = 44 cm
Q 25) If θ is the angle (in degrees) of a sector of a circle of radius r, then the length of arc is
(a) (πr2θ)/360
(b) (πr2θ)/180
(c) (2πrθ)/360
(d) (2πrθ)/180 
Ans: c
Q 26) It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be
(a) 10 m
(b) 15 m
(c) 20 m
(d) 24 m
Ans: a

Q 27) The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is
(a) 56 cm
(b) 42 cm
(c) 28 cm
(d) 16 cm 
Ans: c
Q 28) Find the area of a sector of circle of radius 21 cm and central angle 120°.
(a) 441 cm2

(b) 462 cm2

(c) 386 cm2

(d) 512 cm2
Ans: b

 
Q 29) The wheel of a motorcycle is of radius 35 cm. The number of revolutions per minute must the wheel make so as to keep a speed of 66 km/hr will be
(a) 50
(b) 100
(c) 500
(d) 1000
Ans: c
Solution Hint
Circumference of the wheel = 2πr = 2 × (22/7) × 35 = 220 cm
Speed of the wheel = 66 km/hr = (66 × 1000)/60 m/min
= 1100 × 100 cm/min = 110000 cm/min 
Number of revolutions in 1 min = 110000/220 = 500
Q 30) If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(a) 2 units
(b) π units
(c) 4 units
(d) 7 units 
Ans: a
Q 31) The area of a quadrant of a circle with circumference of 22 cm is
(a) 77 cm2
(b) 77/8 cm2
(b) 35.5 cm2
(c) 77/2 cm2 
Ans: b
Q 32) A chord of a circle of radius 10 cm subtends a right at the centre. Find length of the arc.
a) 16.7 cm
b) 15.7 cm
c) 15.2 cm
d) 14.7 cm 
Ans: b

Q 33) In a circle of radius 14 cm, an arc subtends an angle of 30° at the centre, the length of the arc is
(a) 44 cm
(b) 28 cm
(c) 11 cm
(d) 22/3 cm 
Ans: d

Q 34) An arc of a circle is of length 6π cm and the area of the sector is 21π cm2. Find the diameter.
a) 14 cm

b) 7 cm

c) 21 cm

d) 10.5 cm

Ans: a

Solution Hint Find the radius by using the relation :

Q 35) The difference between circumference and diameter of a ring is 10 cm. Find the radius of the ring.
a) 3.07 cm
b) 0.37 cm
c) 2.33 cm
d) 4.57 cm
Ans: c

Solution Hint Circumference – Diameter = 10 cm (∵ Diameter = 2 × radius)
2πr – 2r = 10 cm ⇒ 2r(π – 1) = 10 cm
Q 36) The difference between the circumference and radius of a circle is 37 cm then area of the circle is
a) 111 cm2
b) 184 cm2
c) 154 cm2
d) 259 cm2 

Ans: c
Q 37) Find the diameter of the circle if the area of the circle is 6 m.
a) 3.07 m
b) 2.74 m
c) 2.33 m
d) 4.57 m 
Ans: b

Q 38) If the diameter of the semi-circular plot is 21 cm, then its perimeter is
a) 54 m
b) 27m
c) 42 m
d) 56 m
Ans: a

Solution Hint 

Perimeter of semi- circle is : πr + 2r
Q 39) Ratio of areas of two circles is 9 : 16. Find the ratio of their circumferences.
a) 9 : 16
b) 3 : 4
c) 16 : 9
d) 4 : 3 
Ans: b
Q 40) If radius of a circle is increased by 20 % then its area will be increased by
a) 40 %
b) 42 %
c) 44 %
d) 45 %
Ans: c
Solution Hint
Find area by taking radius r
Find new area by taking radius = r + 20% of r
Find the difference of two areas
Required Percentage  = 
Q 41)  If
diameter of a circle is decreased by 10 % 
then its area will be decreased by

a)
20 %                                                      

b)
18 %

c)
19 %                                                      

d)
11 %

Ans:
c

Solution Hint

Take diameter = 2r and radius = r

Find area by taking radius r

Find new area by taking radius = (2r + 20% of 2r)

Find the difference of two areas

Required
Percentage  = 

Q 42)  Find
the area swept by minute hand of length 12 cm in 20 minutes.

  

  

  

Ans: b

Q 43)  Find
the area of the shaded part





a)
42 cm
2     

b)
48  cm2         

c)
38.5 cm2          

d)
77 cm2

Ans: c

Q 44)  Find
shaded area if ABCD is a square of side 14 cm and APD and BPC are semi circle 





a)
54 cm2                                                         

b)
42  cm2         

c)
48 cm2                                                         

d)
36 cm2

Ans: b

Q 45)  A
square of diagonal   8 cm is inscribed in
a circle. Find the shaded area.






a)
16.3 cm2                                                         

b)
17.3  cm2         

c)
18.8 cm2                                                         

d)
18.3 cm2

Ans: d

Q 46)  Arcs
have been drawn with radii 14 cm each and with centre P, Q, R. Find the shaded
region.
a)
154 cm
2                                                           

b)
231  cm2         

c)
308 cm2                                                           

d)
316 cm2

Ans: c

Q 47)  In
a square of side 14 cm, four equal circles are 
drawn. Find the area of the shaded region.

a) 54 cm2 

b)
42  cm2         

c)
56 cm2

d)
48 cm2

Ans: b

Q 48)  ABCD
is a quadrilateral, arcs have been drawn of radii 21 cm each with vertices A,
B, C, D. Find the shaded area.
a)
1396 cm
2                                                          

b)
1416  cm2         

c)
1308 cm2                                                          

d)
1386 cm2

Ans: d

Q 49)  In
a rectangle 22 cm X 14 cm, a semi circle is drawn with 14 cm as diameter. Find
the shaded area.

a)
231 cm
2                                                        

b)
154  cm2         

c)
308 cm2                                                        

d)
77 cm2

Ans: a

Q 50)  Find
the area of the circle that can be inscribed in a square of side 6 cm

a)
36 
 cm2                                                      

b)
18 
 cm2         

c)
12
 cm2                                                      

d)
9
 cm2

Ans: d

Q 51)  Find
the area of the square that can be inscribed in a circle  of radius 8 cm

a)
256 cm2                                                        

b)
128  cm2         

c)
64 cm2                                                           

d)
77 cm2

Ans: b


Questions
from CBSE Sample paper 2021-22
Basic
Mathematics (241)

Q 52) In a circle of diameter 42cm ,if an arc subtends an angle of 60 ̊ at the centre where 𝜋 = 22/7,then the length of the arc is
(a) 22/7 cm
(b) 11cm
(c) 22 cm

(d) 44 cm
Ans: c

Q 53) If the circumference of a circle increases from 2𝜋 to 4𝜋 then its area _____ the original area
(a) Half
(b) Double
(c) Three times
(d) Four times
Ans: d

Q 54) If the difference between the circumference and the radius of a circle is 37cm , 𝜋 = 22/7, the circumference (in cm) of the circle is
(a) 154
(b) 44
(c) 14
(d) 7
Ans: b

Q 55) The perimeter of a semicircular protractor whose radius is ‘r’ is
(a) 𝜋 + 2r
(b) 𝜋 + r
(c) 𝜋 r
(d) 𝜋 r + 2r
Ans: d

Solution Hint
Perimeter of protractor = Circumference of semi-circle + 2 x radius = 𝜋 r + 2r

Q 56)  Area
of a sector of a circle is 1/6 to the area of circle. Find the degree measure
of its minor arc.

(a)
90 ̊                                           

(b)
60 ̊

(c)
45 ̊                                           

(d)
30 ̊

Ans: b

Standard Maths SPQ (041)

Q 57)  The
number of revolutions made by a circular wheel of radius 0.7m in rolling a
distance of 176m is

(a)
22                                                 

(b)
24

(c)
75                                                 

(d)
40

Ans: d
Q 58)  In
the figure given below, ABCD is a square of side 14 cm with E, F, G and H as
the mid points of sides AB, BC, CD and DA respectively. The area of the shaded
portion is

(a) 44cm2                                           

(b)
49 cm2

(c)
98 cm2                                          

(d)
49π/2 cm2

Ans:
c

Solution Hint

Shaded area = Area of semicircle + (Area of half square – Area
of two quadrants)

                      =
Area of semicircle + (Area of half square – Area of semicircle)

                      = Area of half square =  x 14 x14 = 98cm2


Q 59)  Given
below is the picture of the Olympic rings made by taking five congruent circles
of radius 1cm each, intersecting in such a way that the chord formed by joining
the point of intersection of two circles is also of length 1cm. Total area of
all the dotted regions assuming the thickness of the rings to be negligible is

(a) 4(π/12-√3/4) cm2                          

(b)
(π/6 – √3/4) cm2

(c)
4(π/6 – √3/4) cm2                          

(d)
8(π/6 – √3/4) cm2

Ans: d

Solution Hint

Let O be the  center of
the circle. OA = OB = AB = 1cm.

So ∆OAB is an equilateral triangle and AOB = 60°

Required Area= 8x Area of
one segment with r = 1cm, θ = 60°


Q 60)  The
circumference of a circle is 100 cm. The side of a square inscribed in the
circle is

(a)
50√2 cm                                     
 

(b)
100/π cm

(c)
50√2/π cm                                   

(d)
100√2/π cm

Ans: c

Maths MCQ Ch-8 Class 10 | Trigonometry

MATHEMATICS  MCQ | Class 10 | Chapter 8 
TRIGONOMETRY

Q 1) Trigonometric ratios are only applicable to which kind of triangles?

a) Right-angled triangles                           b) Any type of triangles
c) Acute angled triangles                           d) Obtuse angled triangles 

Ans a
Q 2) The value of equals to
a) tan θ                b) cot θ                   c) cosec θ                    d) sec θ 
Ans: a

Q 3) Trigonometric ratios are
a) sine, cosine and cotangent
b) sine, tangent, cotangent and secant
c) sine, cosine, tangent, cotangent, secant and cosecant
d) tangent, cotangent and secant 
Ans: c

Q 4) Choose the correct reciprocal ratios.
a) Tan θ, Sec θ                                     b) Cosec θ, Sec θ
c) Sec θ, Sin θ                                      d) Tan θ, Cot θ 
Ans: d

Q 5) What is the value of sec θ when θ is 45°?
a) √3                        b) 1                       c) 0                     d) √2 
Ans: d

Q 6) What is the value of sin 0° + cos 0° ?
a) 0                        b) 2                            c) 1                    d) ∞ 
Ans: c

Q 7) Evaluate cos 30° sin 60° + cos 60° sin 30°.
a) 2                        b) 0                            c) 1                        d) ∞ 
Ans: c

Q 8) The value of Cosec 0° is
a) Not defined        b) 1                            c) 0                        d) 2 
Ans: a

Q 9) The value of sin 90° + cos 0° + √2 cos 45° is
a) 2                        b) 1                             c) 4                        d) 3 
Ans: d

Q 10) The value of Cosec 90° is
a) 0                        b) 2                             c) 1                        d) √3 
Ans: c

Q 11) If sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A.
(a) 45°                    (b) 30°                       (c) 29°                    (d) 52°
 Ans: c

Q 12) Evaluate sin2 30.
a) 2                          b) 0                            c) 1/ 4                      d) ∞ 
Ans: c

Q 13) In ∆ ABC, right – angled at B, AB = 24 cm, BC = 7 cm. The value of tan C is:
(a) 12/ 7                    (b) 24/ 7                    (c) 20/ 7                     (d) 7/ 24
Ans: b

Q 14) The value of sin2 90° + √2 cos 45° + √3 cot 30° is
a) 2                            b) 0                            c) 4                            d) 5 
Ans: d

Q 15) The product of sec 30° and cos 60° is
a) 0                            b) 2                            c) 1                         
Ans: d

Q 16) Which among these are complementary angles?
a) ∠A + ∠B = 90°                                    b) ∠A + ∠B = 180°
c) ∠A + ∠B = 60°                                    d) ∠A + ∠B = 45° 
Ans: a

Q 17) Evaluate tan 75° + cot 65°.
a) Cot 25° + Tan 15°                                b) Cot 25° – Tan 15°
c) Cot 15° + Tan 25°                                d) Cot 15° – Tan 25° 
Ans: c

Q 18) Evaluate sec 65° + cosec 75°.
a) Cosec 25° + Sec 15°                            b) Cosec 25° – Sec 15°
c) Cosec 15° + Sec 25°                            d) Cosec 15° – Sec 25° 
Ans: a

Q 19) If in ΔABC, ∠C = 90°, then sin (A + B) =
(a) 0                            (b) 1/2                            (c) 2                            (d) 1 
Ans: d

Q 20) Find the correct trigonometric identity.
a) tan2θ = sec2θ – 1                                b) tan2θ + sec2θ = 1
c) tan2θ – sec2θ = 1                                d) tan2θ = sec2θ + 1 
Ans: a

Q 21) Evaluate (cosec θ – cot θ) (cosec θ + cot θ).
a) 0                        b) 1                        c) 2                        d) 3 

Ans: b

Q 22) Evaluate cosec θ sec θ.
a) cos θ + tan θ                                        b) cos θ – tan θ
c) tan θ – cot θ                                        d) cot θ + tan θ 

Ans: d

Q 23) (Sin 30° + cos 60°) – (sin 60° + cos 30°) is equal to:
(a) 0
(b) 1 + 2√3
(c) 1-√3
(d) 1+√3 

Ans: c

Q 24) If 3 cot θ = 2, then the value of tan θ



 
Ans: b

Q 25) Evaluate sec2 A + (1 + tan A) (1 – tan A).

a) 3
b) 0
c) 2
d) 1 
Ans: c

Q 26) (1 + cosec θ) (1 – cosec θ) + cot2θ is
a) Cot ⁡θ
b) 0
c) 1
d) Tan θ 
Ans: b
Q 27) The value of       is equal to:
(a) 0
(b) 1
(c) 2
(d) 3 
Ans: b

Q 28) The value of (Cos θ + sin θ)2 + (Cos θ – sin θ)2  is
a) -2
b) 0
c) 1
d) 2 

Ans: d

Q 29) 1 – cos2A is equal to:
(a) sin2A
(b) tan2A
(c) 1 – sin2A
(d) sec2
Ans: a

Q 30) Value of sin (90° – A) =
(a) sin A
(b) tan A
(c) cos A
(d) cosec A 
Ans: c

Q 31) sin (90° – A) and cos A are:
(a) Different
(b) Same
(c) Not related
(d) None of the above 

Ans: b
Q 32) Find the value of
(a) sin60°
(b) cos60°
(c) tan60°
(d) sin30° 
Ans: c

Q 33) The value of sin 60° cos 30° + sin 30° cos 60° is:
(a) 0
(b) 1
(c) 2
(d) 4 
Ans: b
Q 34) Evaluate
(a) 0
(b) 1
(c) 1 / 2
(d) 2 
Ans: b

Q 35) sin 2A = 2 sin A is true when A =
(a) 30°
(b) 45°
(c) 0°
(d) 60° 
Ans: c

Q 36) The value of (sin 45° + cos 45°) is
(a) 1/√2
(b) 1
(c) √3/2
(d) √2 
Ans: d

Q 37) If sin A = 1/2 , then the value of cot A is
(a) √3
(b) 1/√3
(c) √3/2
(d) 1 
Ans: a

Q 38) If A, B and C are interior angles of a ΔABC then Cos(B+C)/2 is equal to

 

Ans: a

Q 39) If ∆ABC is right angled at C, then the value of cos(A + B) is
(a) 1/2
(b) 1
(c) 0
(d) √3/2 
Ans: c

Q 40) If x tan 45° sin 30° = cos 30° tan 30°, then x is equal to
(a) √3
(b) √3/2
(c) 1/2
(d) 1 
Ans: d

Q 41)

 

Ans: b

Q 42) The value of (tan 1° tan 2° tan 3° … tan 89°) is
(a) 0
(b) 1
(c) 2
(d) ½
Ans: b

Explanation:
tan 1° tan 2° tan 3°…tan 89°
= [tan 1° tan 2°…tan 44°] tan 45° [tan (90° – 44°) tan (90° – 43°)…tan (90° – 1°)]
= [tan 1° tan 2°…tan 44°] [cot 44° cot 43°…cot 1°] × [tan 45°]
= [(tan 1°× cot 1°) (tan 2°× cot 2°)…(tan 44°× cot 44°)] × [tan 45°]
= 1 × 1 × 1 × 1 × …× 1 {since tan A × cot A = 1 and tan 45° = 1} = 1

Q 43)  The
value of sin² 30° – cos² 30° is

  

  


  


Ans:  a

 Q 44)  If sin
A = 8/ 17  what will be the value of cos
A sec A ?


a) 2                              

b) -1                          

c) 1                               

d) 0

Ans:  c

Q 45)  If tan
α = √3 and cosec β = 1, then the value of α – β ?


a) -30°                         

b) 30°                       

c) 90°                             

d) 60°

Ans:  a


Q 46)   In
triangle ABC, right angled at C, then the value of cosec (A + B) is


a) 2                        

b) 0                                 

c) 1                                

d) ∞

Ans:  c


Q 47)  What is
the value of cos A sec A + sin A cosec A – tan A cot A?


a) 0                          

b) 2                               

c) 1                                 

d) 3

Ans:  c


Q 48)  Which
of the following is true ?

a) sin
2A = 2sinA                                  

b) tan
A

c)
sin(A + B) = sin A + sin B                

d) (sin
A)2 = sin2 A

Ans:  d


Q 49)  If  15 cot A = 8 then cos A =

  

  


   


Ans:  c

Q 50)  If     ,  then find   


  

  


  



Ans:  d
Q 51)  If   tanθ = 3 sin θ, then the value of secθ is

a)   

b)    

c)   

d)    

Ans: a

Q 52)  If 3
cot 
θ  = 4, then the value of    is

  

  




Ans: b

Q 53)  Evaluate:   

a)  tan 60o                      

b)  cos 30o                      

c)  tan 30o                    

d)  sin 30o

Ans: c

Q 54)  If  tan (2A + B) =   and  cot (3A – B ) = 

a)  24o, 18o              

b)  18o, 24o

c)  24o, 28o         

d)  20o, 24o    

Ans: b

Q 55)  If  cos (2A – B) =   sin (A + 2B ) =  

a)  24o, 18o                                           

b)  18o, 26o

c)  28o, 24o                                           

d)  24o, 30o    

Ans: a

Q 56)  Sin a =  ,  cos b =   , then  (a + b) =

a) 0o                   

b)  30o                            

c)  60o                         

d)  90o 

Ans: d

Q 57)  If  θ  is an acute angle and  tanθ + cot θ  = 2, find  tan10 θ + cot 10 θ

a)  210                   

b)
2                                

c) 25                           

d) 1

Ans: b

Solution
Hint

tanθ + 1/ tanθ = 2   ⇒ tan2 θ – 2tan θ + 1 = 0

Factorise
this equation and then solving it we get  
θ = 45o

Using this value
of  
θ and find the required value

Q 58)  If  θ  is an acute angle and  sinθ + cosecθ  = 2, find  sin15 θ + cosec 15 θ

a)  215                  

b)
1                                

c)
2                           

d) 0

Ans: c

Solution
Hint

sinθ + cosecθ = 2 = 1 + 1

sinθ = 1 and cosecθ = 1

sin15 θ + cosec 15 θ = (sinθ) 15 + (cosec θ) 15 = (1)15 + (1)15 = 1 + 1 = 2

Q 59)  If  1 + sin2 θ= 3 sinθ cosθ, then θ =

a) 45o                       

b)  30o                            

c)  60o                         

d)  90o

Ans: a

Solution
Hint

Dividing
both side by cos2
 θ we get

Sec2 θ + tan2 θ = 3 tan θ

1 + tan2 θ + tan2 θ = 3 tan θ

2 tan2 θ – 3 tanθ + 1 = 0

Factorise
this equation we get tan 
θ = 1  or  1/2

tanθ = 1  ⇒  θ = 45o

Q 60)  If 5
sin 
θ = 12 cos θ , then find the value of  (secθ – tan θ)(secθ + tanθ)

a)  1                         

b)  – 1                          

c)  2                         

d) 3

Ans: a

Solution
Hint:

(sec θ – tan θ)(sec θ+ tan θ ) = sec2 θ – tan2 θ = 1

 
Q 61)  If sin θ + cos θ = 1 then what is the value of 3 sin θ cos θ

a)  3          
              

b)  3/ 2          
               

c) 2/
3                      

d) 0

Ans: d

Solution
Hint

sin θ +
cos θ = 1

Squaring
on both side and find the value of  sin θ
cos θ

We get  sin θ cos θ = 0        ⇒        3 x sin θ cos θ = 0

Questions From CBSE Sample Paper 2021-22
Basic Mathematics SP (241)

Q 62) If sinθ = x and secθ = y , then tanθ is

(a)
xy      

(b)
x/y

(c)
y/x                                           

(d)
1/xy

Ans: a

Q 63) What
is the value of (tan
θ cosecθ)2 – (sinθ secθ)2

(a)
-1                                              

(b)
0

(c)
1                                                

(d)
2

Ans: c

Q 64) Given
that sin
θ = a/b ,then tanθ is equal to

 

  


 



Ans: d

Q 65) If
x = 2sin2
θand y = 2cos2θ+ 1 then x + y is

(a)
3                                                

(b)
2

(c)
1                                                

(d)
1/2

Ans: a

Q 66) If
cos
θ + cos2θ= 1,the value of sin2θ+ sin4θ is

(a)
-1                                               

(b)
0

(c)
1                                                

(d)
2

Ans: c

Q 67 In
the figure given below, AD = 4cm, BD = 3cm and CB = 12 cm, then cot
θ  equals

(a)
3/4                                            

(b)
5/12

(c)
4/3                                            

(d)
12/5

Ans: d

Standard
Mathematics SP(041)

Q 68 In
∆ABC right angled at B, if tan A= √3, then cos A cos C- sin A sin C =

(a)
-1                                              

(b)
0

(c)
1                                               

(d)
√3/2

Ans:
b

Solution Hint

tan A = √3 = tan 60° so A = 60°, Hence C = 30°.

 cos A cos C – sin A sin C = (1/2)x (√3/2) –
(√3/2)x (1/2) = 0

Q 69 If
the angles of ∆ABC are in ratio 1 : 1 : 2, respectively (the largest angle being
angle C), then the value of   
   is

(a)
0                                                 

(b)
1/2

(c)
1                                                 

(d)
√3/2

Ans:
a

Solution Hint

1x + 1x + 2x = 180°, x = 45°.

A , B and C are 45°, 45° and
90°resp.

Using these values to find
the value of the given function.

Q 70 If
4 tanβ = 3, then




















 

(a)
0                                                   

(b)
1/3

(c)
2/3                                                

(d)
3 ⁄ 4

Ans: a

Q 71 If
 tan α + cot α = 2, then tan20α
+ cot20α =

(a)
0                                                  

(b)
2

(c)
20                                                

(d)
220

Ans:
b

Solution Hint

tan α + cot α = 2 gives α = 45°. So tan α = cot α = 1

tan20α + cot 20α
= 120 + 120 = 1 + 1 = 2

Q 72 If
1+ sin2α = 3 sinα cosα, then values of cot α are

(a)
-1, 1  

(b)
0, 1

(c)1,
2    

(d)
-1, -1

Ans:
c

Solution Hint

1+ sin2α = 3 sinα cos α

sin2α + cos2α + sin2α = 3 sinα
cos α

2 sin2α – 3sinα cos α + cos2α = 0

(2sinα – cos α)( sinα – cosα) =0

cotα
= 2 or cotα = 1

Q 73 If
2sin2β – cos2β = 2, then β is

(a)
0o  

(b)
90o

(c)
45o

(d)
30o

Ans: b

Q 74 In
the given figure, D is the mid-point of BC, then the value of  
 is








(a)
2                                                   

(b)
1/2

(c)
1/3                                                 

(d)
1/4

Ans: b

Maths MCQ Ch-6 Class 10 | Triangle

Mathematics
Multiple Choice Questions (MCQ)
Class 10 | Chapter 6 | Triangles

MCQ Based on Basic Proportionality Theorem or Thales Theorem(BPT)
MCQ  Based on the Similarity of Triangles
MCQ Based on the Ratio of Areas of two similar Triangles
MCQ Based on the Pythagoras Theorem and its Converse.
MCQ Based from the CBSE Sample Questions

In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations. Solution Hints are also given to some difficult problems. Each MCQ contains four options from which one option is correct. On the right hand side column of the pdf Answer option is given.

Action Plan
First of all students should Learn and write all basic points and Formulas related to the Triangles
Start solving  the NCERT Problems with examples.
Solve the important assignments on the Similarity of Triangles.
Then start solving the following MCQ.

MCQ | CHAPTER 6 | TRIANGLES

Q 1) Which of the following triangles have the same side lengths?
(a) Scalene
(b) Isosceles
(c) Equilateral
(d) None of these 

Ans: c

Q 2) Two congruent figures are similar when two similar figures are congruent.
a) True
b) False
Ans: a
Explanation: Two geometric figures are said to be similar if they are of same shape but different sizes and congruent if they have same shape and size.

Q 3) The figure shown is congruent.
    
a) True
b) False
Ans: a
Explanation The stars in the given figure are congruent because they are same shape and same size. Congruent figures have same shape and size

Q 4) Two geometric figures which have same shape and size are known as congruent.
a) False
b) True 
Ans: b
Q 5) If ∠A = ∠P, ∠B = ∠Q, ∠C = ∠R then, ∆ABC & ∆PQR are similar according to which test?
a) AAA test
b) AA test
c) SAS test
d) SSS test 
Ans: a

Q 6) The figure shown below is similar.
     

a) True
b) False
Ans: a
Explanation The two figures shown are similar because they have same shape but are different in sizes. The second pentagon is smaller in size as compared to a pentagon, but the basic structure of both the figures is same i.e. both are pentagon.

Q 7) In the given figure DE || BC, if AD = 5.9cm, DB = 4cm and AE = 7cm then, what will be the value of AC?

a) 2.3 cm
b) 5.1 cm
c) 11.74 cm
d) 10.9 cm 
Ans: c

Q 8) D and E are the midpoints of side AB and AC of a triangle ABC, respectively and BC = 6 cm. If DE || BC, then the length (in cm) of DE is:
(a) 2.5
(b) 3
(c) 5
(d) 6 
Ans: b

Q 9) A man goes 10 m west and 24 m north. Find his distance from the starting point.
a) 34 m
b) 28 m
c) 30 m
d) 26 m 
Ans: d

Q 10) What is the value of x id DE || BC ?

a) 0
b) 1
c) 2
d) 3 
Ans: b
Q 11) The diagonals of a rhombus are 16 cm and 12 cm, in length. The side of rhombus in length is:
(a) 20 cm
(b) 8 cm
(c) 10 cm
(d) 9 cm
Ans: c
Solution Hint
Since diagonals of a rhombus bisects each other at right angle
By Pythagoras theorem,
(16/2)2 + (12/2)2 = side2
82 + 62 = side2
64 + 36 = side2 
 Side = 10 cm
Q 12) The perimeters of two similar triangles ABC, PQR is 64 cm and 24 cm respectively. If PQ is 12 cm what will be the length of AB?
a) 30 cm
b) 32 cm
c) 12 cm
d) 16 cm
Ans: b
Solution Hint perimeters of similar triangles is the same as the ratio of their corresponding sides.

Q 13) If ∠D = ∠L, ∠E = ∠M then, ∆DEF & ∆LMN are similar according to which test?
a) AAA test
b) AA test
c) SAS test
d) SSS test 
Ans: b

Q 14) In the given figure, LM || PQ, what will be the relation between x, a, b and c?

a) a = c / b
b) ab = cx
c) bx = ac
d) cb = ax 
Ans: c

Q 15) Corresponding sides of two similar triangles are in the ratio of 2:3. If the area of small triangle is 48 sq.cm, then the area of large triangle is:
(a) 230 sq.cm.
(b) 106 sq.cm
(c) 107 sq.cm.
(d) 108 sq.cm 
Ans: d

Q 16) If DE || BC, AD = 4cm, BD = 7.5cm, AE = 6.4 cm & DE = 5cm then what will be the lengths of BC?

a) 11.23 cm
b) 15.24 cm
c) 14.375 cm
d) 14.275 cm 
Ans: c

Q 17) In ∆ ABC, DE || BC, AD = 4 cm, BD = 5 CM, DE = 8 CM Then BC =
a) 12 cm
b) 16 cm
c) 18 cm
d) 20 cm 
Ans: c

Q 18) Area of an equilateral triangle with side length a is equal to:
(a) √3/2 a
(b) √3/2 a2
(c) √3/4 a2
(d) √3/4 a
Ans: c

Q 19) If the areas of two similar triangles are in the ratio 361 : 529. What would be the ratio of the corresponding sides?
a) 19 : 23
b) 23 : 19
c) 361 : 529
d) 15 : 23 
Ans: a

Q 20) If perimeter of a triangle is 100 cm and the length of two sides are 30 cm and 40 cm, the length of third side will be:
(a) 30 cm
(b) 40 cm
(c) 50 cm
(d) 60 cm 
Ans: a

Q 21) In two similar triangles ∆ABC and ∆DEF, AB = 15cm, DE = 5cm. If AL and DM are the altitudes of the triangles ABC, DEF respectively, then what will be the ratio of their altitudes?
 

a) 3 : 1
b) 1 : 3
c) 1 : 2
d) 2 : 1 
Ans: a

Q 22) The perimeter of two similar triangles are 50 cm and 30 cm respectively. If one side of first triangle is 9 cm, then find the corresponding side of the other triangle.
a) 4.8 cm
b) 5.6 cm
c) 3.8 cm
d) 5.4 cm 
Ans: d

Q 23) In ∆ ABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm. The angle B is
(a) 120°
(b) 60°
(c) 90°
(d) 45° 
Ans: c

Maths MCQ Ch-7 Class 10 | Co-ordinate Geometry

Mathematics

Multiple Choice Questions (MCQ)
MCQ | Class 10 | Chapter 7 
Co-ordinate Geometry

  • MCQ Based on Cartesian Coordinate System
  • MCQ  Based on the Distance Formula.
  • MCQ Based on the Section Formula.
  • MCQ Based on the Point on the x-axis and Point on the y-axis
  • MCQ Based from the CBSE Sample Questions

Features

  • In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations. 
  • Solution Hints are also given to some difficult problems. 
  • Each MCQ contains four options from which one option is correct. 
  • On the right hand side column of the pdf Answer option is given.

Action Plan

  • First of all students should Learn and write all basic points and Formulas related to the Coordinate Geometry.
  • Start solving  the NCERT Problems with examples.
  • Solve the important assignments on the Coordinate Geometry.
  • Then start solving the following MCQ.

MCQ | CHAPTER 7 | CLASS 10
CO-ORDINATE GEOMETRY

Q 1) The distance of the point P(2, 3) from the x-axis is
(a) 2
(b) 3
(c) 1
(d) 5 
Ans: b
Q 2) The distance between the point P(1, 4) and Q(4, 0) is
(a) 4
(b) 6
(c) 5
(d) 3√3 
Ans: c

Q 3) Point of intersection of x – axis and y – axis is
a) (x, y)
b) (0, 0)
c) (x, 0)
d) (0, y) 
 Ans: b

Q 4) Find the distance between (-3, 0) and (5, 0)
a) 8
b) 2
c) -2
d) -8 
Ans: a

Q 5) Any point on the x – axis is of the form
a) (0, x)
b) (x, y)
c) (y, 0)
d) (x, x) 
 Ans: c

Q 6) Any point on the y – axis is of the form
a) (0, x)
b) (x, y)
c) (y, 0)
d) (y, y) 
 Ans: a

Q 7) Find the distance between (0, 3) and (0, -4)
a) -1
b) 1
c) 7
d) -7 
Ans: c

Q 8) Find the distance of (-2, 4) from y – axis
a) -2
b) 2
c) 4
d) -4 
Ans: b

Q 9) Find the distance of (4, -5) from x – axis
a) -5
b) 4
c) -4
d) 5 
Ans: d

Q 10) Find the distance of (-3, 2) from origin
a) 3
b) 2

 
Ans: c

Q 11) Find the distance between (1, 4) and (2, 3)

  b)     2

 
Ans: 

Maths MCQ Ch-3 Class 10 | Pair of Linear Equations

Mathematics

Multiple Choice Questions (MCQ)
MCQ | Chapter 3 | Class X

Pair of Linear Equations in Two Variables

MCQ Based on Pair of linear equations in two variables
MCQ  Based on the Unique solution or intersecting lines.
MCQ Based on the Infinitely many solutions or coincident lines.
MCQ Based on the No solution or Parallel lines.
MCQ Based on the consistency or inconsistency of pair of linear equations.
MCQ Based from the CBSE Sample Questions

In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations. Solution Hints are also given to some difficult problems. Each MCQ contains four options from which one option is correct. On the right hand side column of the pdf Answer option is given.

Action Plan
First of all students should Learn and write all basic points and Formulas of Pair of Linear Equations in two variables.
Start solving  the NCERT Problems with examples.
Solve the important assignments on the Pair of Linear Equations in Two Variables.
Then start solving the following MCQ.

MCQ | CHAPTER 3 | CLASS 10

PAIR OF LINEAR EUATIONS IN TWO VARIABLES

Q 1)What will be the nature of the graph lines of the equations 5x – 2y = 9 and 15x – 6y = 1 ?
a) Parallel
b) Coincident
c) Intersecting
d) Perpendicular to each other
Ans: a

Q 2)The equations 2x – 3y = 5 and 4x + 6y = 10 has
a) Unique sol.
b) No Sol.
c) Infinitely many sol
d) Inconsistent 
Ans: a
Q 3)What will be the nature of the graph lines of the equations x + 3y – 2 = 0 and 2x – y + 5 = 0 ?
a) Parallel
b) Coincident
c) Intersecting
d) Perpendicular to each other 
Ans: c
Q 4) If a pair of linear equations is consistent, then the lines will be
(a) always coincident
(b) parallel
(c) always intersecting
(d) intersecting or coincident 
Ans: d
Q 5) What will be the nature of the graph lines of the equations 2x + 5y + 15 = 0 and 6x + 15y + 45 = 0 ? 
a) Parallel
b) Coincident
c) Intersecting
d) Perpendicular to each other 
Ans: b
Q 6) The pair of equations x = 0 and x = 5 has
(a) no solution
(b) unique/one solution
(c) two solutions
(d) infinitely many solutions 
Ans: a
Q 7) What will be the value of k, if the lines given by (5 + k)x – 3y + 15 = 0 and (k – 1)x – y + 19 = 0 are parallel?
a) 5
b) 4
c) 6
d) 7 
Ans: b
Q 8) What will be the value of k, if the lines given by 3x + ky – 4 = 0 and 5x + (9 + k)y + 41 = 0 represent two lines intersecting at a point?
 
  
 Ans: d
Q 9) What will be the value of k, if the lines given by x + ky + 3 = 0 and 2x + (k + 2)y + 6 = 0 are coincident?
a) 4
b) 2
c) 6
d) 8 
Ans: b
Q 10) The pair of equation x = – 4 and y = – 5 graphically represents lines which are
a) intersecting at (- 5, – 4)
b) intersecting at (- 4, – 5)
c) intersecting at (5, 4)
d) intersecting at (4, 5) 
Ans: b
Q 11) The sum of a two digit number and the number obtained by reversing the order of the digits is 187. If the digits differ by 1, then what will be the number?
a) 67
b) 54
c) 89
d) 67 
Ans: c
Q 12) It takes 10 men and 6 women to finish a piece of work in 4 days, while it takes 5 men and 7 women to finish the same job in 6 days. What will be the time taken by 1 man and 1 woman to finish the job?
a) Man = 34 days, Woman = 45 days
b) Man = 45 days, Woman = 34 days
c) Man = 53 days, Woman = 96 days
d) Man = 54 days, Woman = 96 days 
Ans: d
Q 13) 10 years ago, a woman was thrice the age of her daughter. Two years later daughter’s age will be 30 less than the age of the mother. What are the present ages of the woman and the daughter?
a) 70 years, 40 years
b) 60 years, 40 years
c) 55 years, 25 years
d) 45 years, 20 years 
Ans: c
Q 14) The sum of two numbers is 13 and the sum of their reciprocals is 13/ 40What are the two numbers?
a) 5, 8
b) 10, 3
c) 12, 1
d) 9, 4 
Ans: a
Q 15) In a piggy bank the total number of coins of Rs. 5 and Rs. 1 is 100. If the total coins amount is 300, then what is the number of coins of each denomination?
a) 30, 70
b) 50, 50
c) 45, 55
d) 60, 40 
Ans: b
Q 16) 5 years hence, the age of a man shall be 3 times the age of his son while 5 years earlier the age of the man was 7 times the age of his son. The present age of the man is
a) 50 years
b) 45 years
c) 47 years
d) 40 years 
Ans: d
Q 17) A father gives Rs. 500 to his children every month. If the boy gets Rs. 100 then, the girl gets Rs. 200 and if the boy gets Rs. 200 the girl gets Rs. 150. How many children does he have?
a) 0
b) 3
c) 2
d) 1 
Ans: b
Q 18) For what value of k, do the equations 2x – 3y + 10 = 0 and 3x + ky + 15 = 0 represent coincident lines
a) -9/2
b) -11
c) 9/2
d) -7 
Ans: a

Q 19) A pair of linear equations a1x + b1y + c1 = 0; a2x + b2y
+ c2 = 0
 is said to be inconsistent, if

Ans: b
Q 20) If x = a, y = b is the solution of the equations x + y = 5 and 2x – 3y = 4, then the values of a and b are respectively
(a) 6, -1
(b) 2, 3
(c) 1, 4
(d) 19/5, 6/5
Ans: d

Q 21) If the lines given by 2x + ky = 1 and 3x – 5y = 7 are parallel, then the value of k is
a) -10/3
b) 10/3
c) -13
d) -7
Ans a

Q 22) The graph of x = -2 is a line parallel to the
a) x-axis
b) y-axis
c) both x- and y-axis
d) none of these 
Ans: b

Maths MCQ Ch-2 Class 10 | Polynomial

Mathematics
Multiple Choice Questions (MCQ)
Class 10 | Chapter 2 | Polynomials

MCQ Based on the different types of Polynomials
MCQ  Based on the Relationships between zeroes and coefficients.
MCQ Based on the Polynomials from the zeroes.
MCQ Based on the Quotient and Remainder obtained after dividing P(x) by g(x).
MCQ Based on the Division Algorithm.
MCQ Based from the CBSE Sample Questions

In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations. Solution Hints are also given to some difficult problems. Each MCQ contains four options from which one option is correct. On the right hand side column of the pdf Answer option is given.

Action Plan
First of all students should Learn and write all basic points and Formulas related to the Polynomials.
Start solving  the NCERT Problems with examples.
Solve the important assignments on the Polynomials.
Then start solving the following MCQ.

MCQ | CHAPTER 2 | POLYNOMIALS

Q1) How many points will the graph of x2 + 2x + 1 will cut the x-axis?
a) 3
b) 2
c) 1
d) 0
Ans: b

Q2) If the graph of a polynomial cuts the x-axis at 3 points, then the polynomial is a) Linear
b) Quadratic
c) Cubic
d) Biquadratic
Ans: c

Q3) What will be the nature of the zeros of a quadratic polynomial if it cuts the x-axis at two different points?
a) Real
b) Distinct
c) Real, Distinct
d) Complex 

Ans: c
Q4) Which of the following is a polynomial

a) x2 + 2x + 5

Ans: a


Q5) Which of the following is not a polynomial ?
a) x2 + 5x + 10
b) x – 2 + 2x + 4
c) x12 + 10x
d) 5x + 4 

Ans b


Q6) If the zeros of a polynomial are 3 and -5, then they cut the x-axis at ____ and _____ points.
a) (8, 0) and (-4, 0)
b) (3, -3) and (-5, 5)
c) (-3, 0) and (5, 0)
d) (3, 0) and (-5, 0)
Ans: d

Q7) The sum and product of zeros of a quadratic polynomial are 10 and 5/2 respectively. What will be the quadratic polynomial?
a) 2x2 – 20x + 10
b) 2x2 – x + 5
c) 2x2 – 20x + 5
d) x2 – 20x + 5 

Ans c
Q8) If α and β are the zeros of x2 + 20x – 80, then the value of α + β is
a) -15
b) -5
c) -10
d) -20
Ans d

Q9) If α and β are the zeros of 3x2 – 5x – 15, then the value of αβ is
a) -5
b) – 10
c) – 15
d) – 20
Ans: a

Q 10) What will be the value of other zero, if one zero of the quadratic polynomial is 5 and the sum of the zeros is 10?
a) 10
b) 5
c) -5
d) -10
Ans: b

Q 11) The value of a and b, if the zeros of x2 + (a + 5)x – (b – 4) are -5 and 9 will be
a) 47, -5
b) -5, 47
c) -9, 49
d) -4, 45 

Ans: c

Q 12) If and are zeroes of  10x2 + 20x – 80, then the value of     is
a) 5/ 4
b) 1/5
c) 3/ 4
d) 1/ 4 
Ans d

Q13) If α, β and γ are the zeros of 5x3 + 10x2 – x + 20, then the value of αβγ is
a) -1
b) 5
c) -10
d) – 4
Ans: d

Q14) If α, β and γ are the zeros of 2x3 – 6x2 + 5x + 2, then the value of α + β + γ is
a) 0
b) 1
c) 3
d) 2
Ans c

Q15) If the two zeros of the polynomial x3 – 9x2 -x + 9, are 1 and 9, then the third zero is
a) 9
b) 1
c) 2
d) -1
Ans: d

Q 16) If the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and -3, then
(a) a = -7, b = -1
(b) a = 5, b = -1
(c) a = 2, b = -6
(d) a =0, b = -6
Ans: d

Q 17) Find k, if one zero of polynomial kx2 + 2x + (3k – 1) is 1
a) -1/ 2
b) 3/ 2
c) -1/ 4
d) – 3/ 2 
Ans: c

Q 18) A quadratic polynomial, whose zeroes are -4 and -5, is
(a) x² – 9x + 20
(b) x² + 9x + 20
(c) x² – 9x – 20
(d) x² + 9x – 20 

Ans b
Q19) If x3 + 1 is divided by x² + 5, then the possible degree of
quotient is

(a) 0
(b) 1
(c) 2
(d) 3
Ans b

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