(a) r²

(b) 1/2r²

(c) 2r²

(d) √2r²
Ans: a

(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

(b) 462 cm²

(c) 386 cm²

(d) 512 cm²
Ans: b

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 

Solution Hint 

Ans: b

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

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

(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

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

(a)
50√2 cm                                     
 

(b)
100/π cm

(c)
50√2/π cm                                   

(d)
100√2/π cm

Ans: c

Read more

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 

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 

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

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

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

a) 2                              

b) -1                          

c) 1                               

d) 0

Ans:  c

a) -30°                         

b) 30°                       

c) 90°                             

d) 60°

Ans:  a

a) 2                        

b) 0                                 

c) 1                                

d) ∞

Ans:  c

a) 0                          

b) 2                               

c) 1                                 

d) 3

Ans:  c

a) sin
2A = 2sinA                                  

b) tan
A = 

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

d) (sin
A)² = sin² A

Ans:  d

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 60^o                      

b)  cos 30^o                      

c)  tan 30^o                    

d)  sin 30^o

Ans: c

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

a)  24^o, 18^o              

b)  18^o, 24^o

c)  24^o, 28^o         

d)  20^o, 24^o    

Ans: b

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

a)  24^o, 18^o                                           

b)  18^o, 26^o

c)  28^o, 24^o                                           

d)  24^o, 30^o    

Ans: a

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

a) 0^o                   

b)  30^o                            

c)  60^o                         

d)  90^o 

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 = 45^o

Using this value
of  θ and find the required value

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 (tanθ cosecθ)² – (sinθ secθ)²

(a)
-1                                              

(b)
0

(c)
1                                                

(d)
2

Ans: c

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

 

  

 

Ans: d

Q 65) If
x = 2sin²θand y = 2cos²θ+ 1 then x + y is

(a)
3                                                

(b)
2

(c)
1                                                

(d)
1/2

Ans: a

Q 66) If
cosθ + 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 cotθ  equals

(a)
3/4                                            

(b)
5/12

(c)
4/3                                            

(d)
12/5

Ans: d

Standard
Mathematics SP(041)

(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

(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

(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

(a)
0^o  

(b)
90^o

(c)
45^o

(d)
30^o

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

Read more

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.

• 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

• 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.

• 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.

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

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

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

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 

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 

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 

Q 12) If and are zeroes of  10x² + 20x – 80, then the value of     is

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 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 

Q1) HCF of 8, 9, 25 is
a) 8
b) 9