Mathematics MCQ Class XI Chapter-11

Conic Section

MCQ BASED ON CIRCLE CLASS XI

Question 1

Find the equation of circle with centre at origin and radius
5 units.
a) x² + y² = 25
b) x² + y² = 5
c) x² = 25
d) y² = 25

Answer a

Question 2

The point (6, 2) lie ___________ the circle x² + y² – 2x -4y – 36 = 0.
a) inside circle
b) outside circle
c) on the circle
d) either inside or outside

Answer c

Question 3

Find the equation of circle with centre at (2, 5) and radius
5 units.
a) x² + y²   + 4x – 10y + 4 = 0
b) x² + y²  – 4x – 10y +
4 = 0
c) x² + y²  + 4x + 10y +
4 = 0
d) x² + y²  + 4x – 10y –
4 = 0

Answer b

Question 4

Find the centre of the circle with equation x² + y² – 4x – 10y + 4 =
0.
a) (-2, 5)
b) (-2, -5)
c) (2, -5)
d) (2, 5)

Answer: d
Explanation: Comparing the equation with general
form x² + y² + 2gx + 2fy + c =
0, we get
2g = – 4 ⇒ g = – 2
2f = -10 ⇒ f = – 5
c = 4
Centre is at (-g, -f) i.e. (2, 5).

Question 5

Find the radius of the circle with equation x² + y² – 4x – 10y + 4 =
0.
a) 25 units
b) 20 units
c) 5 units
d) 10 units

Answer: c

Question 6

The centre of
the circle 4x² + 4y² – 8x + 12y – 25 = 0 is

a) (-2, 3)

b) (1, -3/2)

c) (-4, 6)

d) (4, -6)

Answer: (b)
(1, -3/2)

Explanation:

Given circle
equation: 4x² + 4y² – 8x + 12y – 25 = 0

⇒ x² + y² –
(8x/4) + (12y/4) – (25/4) = 0

⇒ x² +y² -2x
+3y -(25/4) = 0 …(1)

As we know that the
general equation of a circle is x² + y² + 2gx + 2fy + c = 0,
and the centre of the circle = (-g, -f)

Hence, by comparing
equation (1) and the general equation,

2g = -2,  ⇒ g = -1

2f = 3,    ⇒ f = 3/2

Now, substitute the
values in the centre of the circle (-g, -f), we get,

Centre = (1, -3/2).

Question 7

If a circle pass through (2, 0) and (0, 4) and centre at
x-axis then find the radius of the circle.
a) 25 units
b) 20 units
c) 5 units
d) 10 units

Answer: c
Explanation: Equation of circle with centre at
x-axis (a, 0) and radius r units is
(x – a)² + (y)² = r²
⇒ (2 – a)² + (0)² = r²
And (0 – a)² + (4)² = r²
⇒ (a – 2)² = a² + 4² ⇒ (- 2)(2a
– 2) =16 ⇒ a – 1 = – 4 ⇒ a = – 3

So, r² = (2 + 3)² = 5 ²  ⇒ r = 5 units.

Question 8
The center of the circle 4x² + 4y² – 8x + 12y –
25 = 0 is?
(a) (2,-3)
(b) (-2,3)
(c) (-4,6)
(d) (4,-6)

Answer a

Question 9

If a circle pass through (4, 0) and (0, 2) and centre at
y-axis then find the radius of the circle.
a) 25 units
b) 20 units
c) 5 units
d) 10 units

Answer: c

Question 10

The point (1, 4) lie ___________ the circle x² + y² – 2x – 4y + 2 = 0.
a) inside circle
b) outside circle
c) on the circle
d) either inside or outside

Answer b

Question 11
The radius of the circle 4x² + 4y² – 8x + 12y –
25 = 0 is?
(a) √57/4
(b) √77/4
(c) √77/2
(d) √87/4

Answer c

MCQ BASED ON PARABOLA CLASS XI

Question 1

Find the focus of parabola with equation y² = 100x.
a) (0, 25)
b) (0, -25)
c) (25, 0)
d) (-25, 0)

Answer c

Question 2

Find the focus of parabola with equation y² = – 100x.
a) (0, 25)
b) (0, -25)
c) (25, 0)
d) (-25, 0)

Answer d

Question 3

Find the focus of parabola with equation x² = 100y.
a) (0, 25)
b) (0, -25)
c) (25, 0)
d) (-25, 0)

Answer a

Question 4

The focus of the
parabola y² = 8x is

a) (0,
2)

b) (2,
0)

c) (0,
-2)

d) (-2,
0)

Answer: (b)
(2, 0)

Explanation:

Given parabola
equation y² = 8x …(1)

Here, the
coefficient of x is positive and the standard form of parabola is y² =
4ax …(2)

Comparing (1) and
(2), we get

4a = 8

a = 8/4 = 2

We know that the
focus of parabolic equation y² = 4ax is (a, 0).

Therefore, the
focus of the parabola y² =8x is (2, 0).

Question 5

The length of
the latus rectum of x² = -9y is equal to

a)  3 units

b) – 3 units

c)  9/4 units

d)  9 units

Answer: (d) 9
units

Explanation:

Given parabola
equation: x² = – 9y …(1)

Since the
coefficient of y is negative, the parabola opens downwards.

The general
equation of parabola is x² = – 4ay…(2)

Comparing (1) and
(2), we get

-4a = -9

a = 9/4

We know that the
length of latus rectum = 4a = 4(9/4) = 9.

Therefore, the
length of the latus rectum of x² = -9y is equal to 9 units.

Question 6

The parametric
equation of the parabola y² = 4ax is

a) x = at; y = 2at

b) x = at²;
y = 2at

c) x = at²;
y² = at³

d) x = at²;
y = 4at

Answer: (b) x
= at²; y = 2at

Question 7

Find the equation of latus rectum of parabola y² = 100x.

a) x = 25
b) x = – 25
c) y = 25
d) y = – 25

Answer a

Question 8

Find the equation of latus rectum of parabola x² = – 100y.
a) x = 25
b) x = – 25
c) y = – 25
d) y = 25

Answer c

Question 9

Find the equation of directrix of parabola y²=-100x.
a) x = 25
b) x = – 25
c) y = – 25
d) y = 25

Answer a

Question 10
If a parabolic reflector is 20 cm in diameter
and 5 cm deep then the focus of parabolic reflector is
(a) (0 0)
(b) (0, 5)
(c) (5, 0)
(d) (5, 5)

Answer c

Question 11

The equation of parabola with vertex at origin the axis is
along x-axis and passing through the point (2, 3) is
(a) y² = 9x
(b) y² = 9x/2
(c) y² = 2x
(d) y² = 2x/9

Answer b

Question 12

Find the vertex of the parabola y² =
4ax.
a) (0, 4)
b) (0, 0)
c) (4, 0)
d) (0, -4)

Answer b

Question 13

Find the equation of axis of the parabola y² = 24x.
a) x = 0
b) x = 6
c) y = 6
d) y = 0

Answer d

Question 14

Find the equation of axis of the parabola x² = 24y.
a) x = 0
b) x = 6
c) y = 6
d) y = 0

Answer a

Question 15

Find the length of latus rectum of the parabola y² = 40x.

a) 4 units
b) 10 units
c) 40 units
d) 80 units

Answer c

Question 16

At what point of the parabola x² = 9y is the abscissa three times that of ordinate
(a) (1, 1)
(b) (3, 1)
(c) (-3, 1)
(d) (-3, -3)

Answer b

MCQ BASED ON ELLIPSE CLASS – XI

Question 1

An ellipse has ___________ vertices and ____________ foci.
a) two, one
b) one, one
c) one, two
d) two, two

Answer d

Question 2

Find the coordinates of foci of ellipse (x/25)² + (y/16)² = 1.
a) (±3, 0)
b) (±4, 0)
c) (0, ±3)
d) (0, ±4)

Answer a

Question 3
In an ellipse, the distance between its foci is
6 and its minor axis is 8 then its eccentricity is
(a) 4/5
(b) 1/√52
(c) 3/5
(d) 1/ 2

Answer c

Question 4
A rod of length 12 CM moves with its and always
touching the co-ordinate Axes. Then the equation of the locus of a point P on
the road which is 3 cm from the end in contact with the x-axis is
(a) x²/81 + y²/9 = 1
(b) x²/9 + y²/81 = 1
(c) x²/169 + y²/9 = 1
(d) x²/9 + y²/169 = 1

Answer a

Question 5

Find the coordinates of foci of ellipse (x/16)² + (y/25)² = 1.
a) (±3, 0)
b) (±4, 0)
c) (0, ±3)
d) (0, ±4)

Answer c

Question 6

What is major axis length for ellipse (x/25)² + (y/16)² = 1?
a) 5 units
b) 4 units
c) 8 units
d) 10 units

Answer d

Question 7

For the ellipse
3x² + 4y² = 12, the length of the latus rectum is:

a)  2/5
b)  3/5
c)  3
d) 4

Answer: (c) 3

Explanation:

Given ellipse
equation: 3x² + 4y² = 12

The given equation
can be written as (x²/4) + (y²/3) = 1…(1)

Now, compare the
given equation with the standard ellipse equation: (x²/a²)
+ (y²/b²) = 1, we get

a = 2 and b = √3

Therefore, a >
b.

If a>b, then the
length of latus rectum is 2b²/a

Substituting the
values in the formula, we get

Length of latus
rectum = [2(√3)²] /2 = 3

Question 8

What is minor axis length for ellipse (x/25)² + (y/16)² = 1?
a) 5 units
b) 4 units
c) 8 units
d) 10 units

Answer c

Question 9

What is equation of latus rectums of ellipse (x/25)² + (y/16)² = 1?

a) x = ±3
b) y = ±3
c) x = ±2
d) y = ±2

Answer a

Question 10

In an ellipse,
the distance between its foci is 6 and the minor axis is 8, then its
eccentricity is

a) 1/2

b)  1/5

c)   3/5

d)   4/5

Answer: (c)
3/5

Explanation:

Given that the
minor axis of ellipse is 8.(i. e) 2b = 8. So, b=4.

Also, the distance
between its foci is 6. (i. e) 2ae = 6

Therefore, ae = 6/2
= 3

We know that b² =
a²(1-e²)

b² =
a² – a²e²

b² =
a² – (ae)²

Now, substitute the
values to find the value of a.

(4)² =
a² -(3)²

16 = a² –
9

a² =
16+9 = 25.

So, a = 5.

The formula to
calculate the eccentricity of ellipse is e = √[1-(b²/a²)]

e = √[1-(4²/5²)]

e = √[(25-16)/25]

e = √(9/25) = 3/5.

Question 11

A man running a race course notes that the sum of the
distances from the two flag posts from him is always 10 meter and the distance
between the flag posts is 8 meter. The equation of posts traced by the man is
(a) x²/9 + y²/5 = 1
(b) x²/9 + y2 /25 = 1
(c) x²/5 + y²/9 = 1
(d) x²/25 + y²/9 = 1

Answer d

MCQ BASED ON HYPERBOLA CLASS XI

Question 1

A hyperbola has ___________ vertices and ____________ foci.

a) two, one

b) one, one

c) one, two

d) two, two

Answer d

Question 2

Find the coordinates of foci of hyperbola (x/9)²−(y/16)²=1.

a) (±5,0)

b) (±4,0)

c) (0,±5)

d) (0,±4)

Answer a

Question 3
The equation of a hyperbola with foci on the
x-axis is
(a) x²/a² + y²/b² = 1
(b) x²/a² – y²/b² = 1
(c) x² + y² = (a² + b²)
(d) x² – y² = (a² + b²)

Answer b

The eccentricity of hyperbola is
a. e =1
b. e > 1
c. e < 1
d. 0 < e < 1
Answer: (b) e > 1

Question 5

Find the coordinates of foci of hyperbola (y/16)²−(/x9)²=1.

a) (±5,0)

b) (±4,0)

c) (0,±5)

d) (0,±4)

Answer c

Question 6

What is transverse axis length for hyperbola (x/9)²−(y/16)²=1?

a) 5 units

b) 4 units

c) 8 units

d) 6 units

Answer d

Question 7

What is conjugate axis length for hyperbola (x/9)²−(y/16)²=1?

a) 5 units

b) 4 units

c) 8 units

d) 10 units

Answer c

Question 8

What is equation of latus rectums of hyperbola (x/9)²−(y/16)²=1?

a) x = ±5

b) y = ±5

c) x = ±2

d) y = ±2

Answer a 

Question 9

The length of
the transverse axis is the distance between the ____.

a)   Two vertices

b)   Two Foci

c)   Vertex and the
origin

d)   Focus and the
vertex

Answer: (a)
Two vertices

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  Mathematics

MCQ | Class 11 | Chapter 07
Permutations & Combinations

Multiple Choice Questions (MCQ)

Features

Action Plan

MCQ | CHAPTER 7 | CLASS 11
PERMUTATIONS & COMBINATIONS

(a) ^n/2C_r                    

(b) ^n/2C_r/2
                     

(c) ⁿC_r/2
                       

(d) ⁿC_r

Answer d

a) m + n                       

b) m – n                      

c) m x n                         

d) m/n

Answer c

a) 4
b) 8
c) 12
d) 16

Answer
d

Question : 14 How many 4 digits even
numbers are possible from digits 1 to 9 if repetition is not allowed?

a) 6561
b) 2016
c) 1344
d) 2916

Answer
c

Question : 15 How many 5-digit
telephone numbers can be constructed using the digits 0 to 9 if each number starts with
67 and no digit appears more than once?

a) 336                

b) 448              

c) 588                     

d) 235

Answer
a

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   Mathematics

MCQ | Class 11 | Chapter 06
Linear Inequalities

Multiple Choice Questions (MCQ)

Features

Action Plan

MCQ | CHAPTER 6 | CLASS 11
LINEAR INEQUALITIES

Question 12):  If
 , then

 

 

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  Mathematics

MCQ | Class 11 | Chapter 15
STATISTICS

Multiple Choice Questions (MCQ)

Features

Action Plan

MCQ | CHAPTER 15 | CLASS 11
STATISTICS

Q 1)  Find the mean deviation
about the median of the scores of a batsman given below

a) 10
b)10.5
c) 11
d) 9.
Ans: b

Q 2) If mode of a series exceeds its mean by 12, then mode exceeds the median by:
a. 4
b. 8
c. 6
d. 10

 Ans: b

Q 3) If the variance of the data is 121 then the standard deviation of the data is
(a) 121
(b) 11
(c) 12
(d) 21 

Ans: b

Q 4)  What
is the mean deviation from the mean for the following data?

117

156

206

198

223

a) 0
b) 3
c) 1
d) 5 

Ans: a

Q 5) Range of the data 4, 7, 8, 9, 10, 12, 13 and 17 is
(a) 4
(b) 17
(c) 13
(d) 21 

Ans: c

Q 6) The mean of 1, 3, 4, 5, 7, 4 is m. The numbers 3, 2, 2, 4, 3, 3, p have mean m – 1 and median q. Then, p + q =
a. 5
b. 7
c. 4
d. 6 

Ans: b

Q 7) The mean deviation of an ungrouped data is 150. If each observation is increased by 3.5%, then what is the new mean deviation?
a) 153.5
b) 3.5
c) 155.25
d) 150 

Ans: c

Q 8)  Find
the mean deviation about mean from the following data:

xi	3	5	20	25	27
fi	5	12	20	8	15

a) 7.7
b) 15
c) 8.7
d) 6.2 

Ans: a
Q 9)  If the mean of the following
data is 20.6, then the value of p is

X	10	15	p	25	35
F	3	10	25	7	5

(a) 30
(b) 20
(c) 25
(d) 10 

Ans: b

Q 10) In a class there are 20 juniors, 15 seniors and 5 graduate students. If the junior averaged 65 in the midterm exam, the senior averaged 70 and the graduate students averaged 91, then what is the mean of the centre class approximately?
a) 71
b) 74
c) 70
d) 72 

Ans: c

Q 11) The most frequently occurring number in a set of values is called
a. Median
b. Range
c. Mean
d. Mode 

Ans: d

Q 12)  Find
the variance of the observation values taken in the lab.

4.2

4.3

4

4.1

a) 0.27
b) 0.28
c) 0.3
d) 0.31
Ans: b

Q 13) If the standard deviation of a data is 0.012. Find the variance.
a) 0.144
b) 0.00144
c) 0.000144
d) 0.0000144 

Ans: c

Q 14) When tested the lives (in hours) of 5 bulbs were noted as follows: 1357, 1090, 1666, 1494, 1623. The mean of the lives of 5 bulbs is

(a) 1445
(b) 1446
(c) 1447
(d) 1448
Ans: b

Q 15) Find the variance of the first 10 natural numbers.
a) 7.25
b) 7
c) 8.25
d) 8
Ans: c

Q 16) The standard deviation of some temperature data in °C is 5. If the data were converted into °F, the variance would be

a. 81
b. 36
c. 25
d. 57
Ans: a

Q 17) The algebraic sum of the deviation of 20 observations measured from 30 is 2. So, the mean of observations is

(a) 30.0
(b) 30.1
(c) 30.2
(d) 30.3
Ans: b
Solution Hint
Given, algebraic sum of of the deviation of 20 observations measured from 30 is 2
⇒ ∑(xi – 30) = 2 {1 ≤ i ≤ 20} ⇒ ∑xi – 30 × 20 = 2
⇒ (∑xi)/20 – (30 × 20)/20 = 2/20 ⇒ (∑xi)/20 – 30 = 0.1
⇒ Mean – 30 = 0.1 ⇒ Mean = 30 + 0.1 ⇒ Mean = 30.1

Q 18) Assuming the variance of four numbers w, x, y, and z as 9. Find the variance of 5w, 5x, 5y and 5z.
a) 225
b) 5/9
c) 9/5
d) 54
Ans: a

Solution Hint (σ_x)² = h²(σ_u)², if u = (x –
h)/a
Now, h = (1/5). ⇒ Variance, (σ_u)² = 9 × 25 = 225

Q 19) The median and SD of a distributed are 20 and 4 respectively. If each item is increased by 2, the new median and SD are
(a) 20, 4
(b) 22, 6
(c) 22, 4
(d) 20, 6
Ans: c
Solution Hint 

Since each value is increased by 2, therefore the median value is also increased by 2. So, new median = 22
Again, the variance is independent of the change of origin. So it remains the same. Hence standard deviation also remain same.

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  Mathematics

MCQ | Class 11 | Chapter 13
LIMITS AND DERIVATIVES

Multiple Choice Questions (MCQ)

Features

Action Plan

MCQ | CHAPTER 13 | CLASS 11
LIMITS AND DERIVATIVES

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  Mathematics
MCQ | Class 11 | Chapter 10
STRAIGHT LINES

Multiple Choice Questions (MCQ)

• MCQ Based on the Angle of inclination.
• MCQ Based on the Slopes of the straight lines
• MCQ Based on the Different Types of Straight Lines.

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 Continuity and Differentiability.
• Start solving the NCERT Problems with examples.
• Solve the important assignments on the Straight Lines Chapter 10 Class XI.
• Then start solving the following MCQ.

MCQ | CHAPTER 10 | CLASS 11
STRAIGHT LINES

Question 1
What is the distance between (1, 3) and (5, 6)?
a) 3 units
b) 4 units
c) 5 units
d) 25 units
Answer: c

What is the distance of (5, 12) from origin?
a) 6 units
b) 8 units
c) 10 units
d) 13 units 

Answer: c

Question 8

What is the inclination of a line which is parallel to
x-axis?
a) 0°

b) 180°

c) 45° 

d) 90°

Answer: a

Question 9

What is the inclination of a line which is parallel to
y-axis?
a) 0°

b) 180°

c) 45° 

d) 90°

Answer: d

Question 10

The equation of the line which cuts off equal and positive
intercepts from the axes and passes through the point (α, β) is
(a) x + y =
α + β

(b) x + y = α

(c) x + y =
β

(d) None of these

Answer: a

Solution Hint:
Let the equation of the line be x/a + y/b = 1
which cuts off intercepts a and b with
the coordinate axes.
It is given that a = b, therefore the equation
of the line is
x/a + y/a = 1          ⇒ x + y = a …..1
But it is passes through (α, β)
So, α + β = a
Put this value in equation 1, we get
x + y = α + β

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   Mathematics
SEQUENCE AND SERIES
MCQ | Class 11 | Chapter 9

Multiple Choice Questions (MCQ)

MCQ Based on the ARITHMATIC PROGRESSION (AP).

MCQ Based on the GEOMETRIC PROGRESSION (GP)

MCQ Based on the ARITHMATIC MEAN (AM) AND GEOMETRIC MEAN (GM).

Features

Action Plan

MCQ | CHAPTER 9 | CLASS 11
SEQUENCE AND SERIES.

Q 1) If a, b, c are in AP then
(a) b = a + c
(b) 2b = a + c
(c) b²  = a + c
(d) 2b²  = a + c
Ans: b

Q 2) What is  the n^th term  of an A.P.?
a) a_n  = a + (n – 1) d
b) a_n  = a + (n) d
c) a_n = ar^n-1   
d) a_n = arⁿ  

Ans: a 

Ans: d

Q 4) If general term of an A.P. is 3n then find common difference.
a) 2
b) 3
c) 5
d) 6 

Ans: b

Q 5) In A.P. 171, 162, 153, ………. Find first negative term.
a) 0
b) – 2
c) – 6
d) – 9 

Ans: d

Q 6) Insert 4 numbers between 2 and 22 such that the resulting sequence is an A.P.
a) 4, 8, 12, 16
b) 5, 9, 13, 17
c) 4, 10, 15, 19
d) 6, 10, 14, 18 

Ans: d

Q 7) If two numbers are 2 and 6 then find their arithmetic mean.
a) 3
b) 4
c) 5
d) 8 

Ans: b

Q 8) The sum of n terms of two arithmetic progressions are in the ratio (2n – 7) : (7n + 5). Find the ratio of their 9^th terms.
a) 4 : 5
b) 5 : 4
c) 9 : 31
d) 31 : 9 

Ans: c

Q 9) If in an A.P., first term is 20, common difference is 2 and nth term is 42, then find n.
a) 10
b) 11
c) 12
d) 14 

Ans: c

Q 10) If 1/(b + c), 1/(c + a), 1/(a + b) are in AP then
(a) a, b, c are in AP
(b) a², b², c² are in AP
(c) 1/1, 1/b, 1/c are in AP
(d) None of these
Ans: b

Solution
Given, 1/(b + c), 1/(c + a), 1/(a + b)
⇒ 2/(c + a) = 1/(b + c) + 1/(a + b)

⇒ 2b² = a² + c²
⇒ a², b², c² are in AP

Q 11) The sum of AP 2, 5, 8, ….. up to 50 terms is
(a) 3557
(b) 3775
(c) 3757
(d) 3575
Ans: b

Solution
Given, AP is 2, 5, 8, …..up to 50
Now, first term a = 2
common difference d = 5 – 2 = 3
Number of terms = 50
Now, Sum = (n/2) × {2a + (n – 1)d}
= (50/2) × {2 × 2 + (50 – 1)3}
= 25 × {4 + 49 × 3}
= 25×(4 + 147)
= 25 × 151 = 3775

Q 12) If 2/3, k, 5/8 are in AP then the value of k is
(a) 31/24
(b) 31/48
(c) 24/31
(d) 48/31
Ans: b 

Solution

Given, 2/3, k, 5/8 are in AP
⇒ 2k = 2/3 + 5/8
⇒ 2k = 31/24
⇒ k = 31/48
So, the value of k is 31/48

Q 13)  If the third term of an A.P. is 7 and its 7^th  term is 2 more than three times of its third term, then the sum of its first 20 terms is
(a) 228
(b) 74
(c) 740
(d) 1090
Ans: c

Solution

Let a is the first term and d is the common difference of AP
Given the third term of an A.P. is 7 and its 7th term is 2 more than three times of its third term
⇒ a + 2d = 7 ………….. (1)
and
3(a + 2d) + 2 = a + 6d
⇒ 3×7 + 2 = a + 6d
⇒ 21 + 2 = a + 6d
⇒ a + 6d = 23 ………….. (2)
From equation 1 – 2, we get
4d = 16 ⇒ d = 16/4 ⇒ d = 4
From equation 1, we get
a + 2×4 = 7 ⇒ a + 8 = 7 ⇒ a = -1
Now, the sum of its first 20 terms
= (20/2) × {2 × (- 1) + (20 – 1) × 4} = 10 × {- 2 + 19 × 4)}
= 10 × {- 2 + 76)} = 10 × 74 = 740

Q 14) If the sum of the first 2n terms of the A.P. 2, 5, 8, ….., is equal to the sum of the first n terms of the A.P. 57, 59, 61, ….., then n equals
(a) 10
(b) 12
(c) 11
(d) 13
Ans: c 

Explanation

Given, the sum of the first 2n terms of the A.P. 2, 5, 8, …..= the sum of the first n terms of the A.P. 57, 59, 61, ….
⇒ (2n/2) × {2 × 2 + (2n – 1) 3} = (n/2) × {2 × 57 + (n – 1)2}
⇒ n × {4 + 6n – 3} = (n/2) × {114 + 2n – 2}
⇒ 6n + 1 = {2n + 112}/2
⇒ 6n + 1 = n + 56
⇒ 6n – n = 56 – 1
⇒ 5n = 55
⇒ n = 55/5
⇒ n = 11

Q 15)  If 7^th and 13^th
terms of an AP  be 34 and 64
respectively, then its 18^th term is
a) 87
b) 88
c) 89
d) 90 

Ans: c

Q 16) If sum of p terms of an AP is q and sum of q terms is p then what is the sum of p + q terms
a) 0
b) p – q
c) p + q
d –(p + q) 

Ans: d

Solution Hint: Find S_p = q and S_q = p and then
subtract these two

Q 17) If the sum of n terms of an AP be 3n² – n and its common difference is 6, then its first term is
a) 2
b) 3
c) 1
d) 4 

Ans: a

Q 18) The first and last term of an AP is 1 and 11. If the sum of its term is 36, then the number of terms will be
a) 5
b) 6
c) 7
d) 8 

Ans: b

Q 19) If sum of its first n terms of an AP is 3n²
+ 5n then which of its term is 164 ?
a) 26^th
b) 27^th
c) 28^th
d) None of these 

Ans: b

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COMPLEX NUMBERS

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COMPLEX NUMBERS

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