# Sample BITSAT Maths Test

## 45 Questions MCQ Test BITSAT Subject Wise & Full Length Mock Tests | Sample BITSAT Maths Test

Description
This mock test of Sample BITSAT Maths Test for JEE helps you for every JEE entrance exam. This contains 45 Multiple Choice Questions for JEE Sample BITSAT Maths Test (mcq) to study with solutions a complete question bank. The solved questions answers in this Sample BITSAT Maths Test quiz give you a good mix of easy questions and tough questions. JEE students definitely take this Sample BITSAT Maths Test exercise for a better result in the exam. You can find other Sample BITSAT Maths Test extra questions, long questions & short questions for JEE on EduRev as well by searching above.
QUESTION: 1

Solution:
QUESTION: 2

### The greatest term in the expansion of (3 + 2x)9, when x = 1, is

Solution: The greatest term of any expansion is its middle termIn (a+x) ^n the middle term will be (n+2)/2 if n is even and if n is odd then there will be two middle terms that is (n+1)/2 and (n+3)/2 Here n is odd therefore the greatest term will be 4 and 5
QUESTION: 3

### The coordinates of the pole of the line lx+my+n=0 with respect to the circle x2+y2=1 are

Solution:

Solution :- Let (x1,y1) be the pole of the line lx+my+n=0 with respect to the hyperbola x2a2−y2b2=1. Then, the equation of the polar is

xx1/ + yy1/ = 1………(i)

Since, (x1,y1) is the pole of the line lx+my+n=0. So, the polar of (x1,y1) is also the line

lx+my+n=0...(ii)

clearly, (i) and (ii) represent the same line. Therefore,

x1(l) = y1(m) = 1/(−n)

⇒x1 = −l/n,  y1 = -m/n.

Hence, the pole of the given line with respect to the given hyperbola is

(−l/n, -m/n)

QUESTION: 4

If the line 2x - y + k = 0 is a diameter of the circle x2 + y2 + 6x -6y + 5 =0, then k is equal to

Solution: If the given line 2x-y+k=0 is the diameter of the circle then it passes through the centre of the given circle. Which on comparing we get as (-3,3).On substituting this in the line equation we get 2(-3)- 3+k=0=> -9+k=0 K=9.
QUESTION: 5

If z = i log(2 - √3), then cos z =

Solution:
QUESTION: 6

The differential equation of the family of lines passing through the origin is

Solution:

The equation of line passing through the origin is y = mx , when m is constant
Diffrence w.r.t x QUESTION: 7

Which of the following is a solution of the differential equation Solution: QUESTION: 8

If y' = x-y/x+y, then its solution is

Solution:

dy/dx= x−y/x+y

Put,y=vx

⟹dy/dx=v+x(dv/dx)

⟹v+xdv/dx=1−v/1+v

⟹xdv/dx = 1−2v−v^2/(1+v)

⟹∫v+1/(v+1)^2−2dv=−∫1/xdx

⟹1/2ln⁡|[(v+1)^2−2]| = 2ln⁡|c1/x|

⟹x^2(v^2+2v−1)=C

Where C = 2ln⁡|c1/x|

Since,v=y/x, we get

⟹ y2+2xy−x2=C

QUESTION: 9 Solution:  QUESTION: 10

(d/dx)[tan⁻1((sinx+cosx)/(cosx-sinx))]

Solution: QUESTION: 11

Value of 1 + log x + (log x)2/2! + (log x)3/3! + ..... ∞ is

Solution:
QUESTION: 12

The angle of elevation of a cloud from a point h mt above the surface of a lake is θ and the angle of depression of its reflection in the lake is φ . The height of the cloud is

Solution:
QUESTION: 13

The eccentricity of the conjugate hyperbola of the hyperbola x2 - 3y2 = 1 is

Solution:
QUESTION: 14

Which of the following functions is a solution of the differential equation (dy/dx)2 - x (dy/dx) + y = 0?

Solution:
QUESTION: 15

The solution of the differential equation (dy/dx) = (y/x) + (φ (y/x)/φ' (y/x)) is

Solution:
QUESTION: 16

tan⁻1(1/4)+ tan⁻1(2/9) is equal to

Solution:
QUESTION: 17

f(x) = ||x| - 1| is not differentiable at

Solution:
QUESTION: 18

For every n ∈ N, 23n-7n-1 is divisible by

Solution:

Solution :- 23n−7n−1=8n−7n−1

=(7+1)n−7n−1

=C(n,0)7n+C(n,1)7n−1+...+C(n,n−2)72+C(n,n−1)71+C(n,n)70−7n−1

Now, C(n,0)7n+C(n,1)7n−1+...+C(n,n−2)72 is clearly divisible by 49.

So, we can write it as 49k.

So, our expression becomes,

=49k+C(n,n−1)71+C(n,n)70−7n−1

=49k+7n+1−7n−1

=49k

∴23n−7n−1=49k

So, clearly 23n−7n−1 is divisible by 49.

QUESTION: 19

If A, B are two square matrices such that AB = A and BA = B, then

Solution:
QUESTION: 20

For a square matrix A, it is given that AA' = I, then A is a

Solution:
QUESTION: 21

The maximum value of xy subject to x+y=8 is

Solution: Because x and y should have value 4 so that 4+4=8 and 4*4=16
QUESTION: 22

The real value of α for which the expression 1-i sin α/1+2 i sin α is purely real is

Solution:
The real value of α for which the expression (1-i sin α) / (1+2 i sin α) is purely QUESTION: 23

The angle between lines xy=0 is

Solution:

For xy = 0
The lines are: x = 0 & y = 0 which are the Y and X axis respectively which are perpendicular.

QUESTION: 24

The focus of the parabola (y-2)2=20(x+3) is

Solution:
QUESTION: 25

The equation of the normal to the curve x2 = 4y at (1, 2) is

Solution:
QUESTION: 26

Two finite sets have m and n elements, the total number of subsets of the first set is 56 more than the total number of subsets of the second. The value of m and n are respectively

Solution:

Let A denote the first set and B denote the second set
We have, n(A) = 2m and n(B) = 2n
As per the question, we have
n(A) = 56 + n(B)
⇒ n(A) - n(B) = 56
⇒ 2m - 2n = 56
⇒ 2n (2m - n - 1)
⇒ 2n (2m - n - 1) = 8 x 7
⇒ 2n = 8 = 23 or (2m - n - 1) = 7
⇒ n = 3 or 2m - n = 8 = 23 = 26 - 3
⇒ n = 3 or m - n = 3
⇒ n = 3 or m = 6
Hence, the required values of m and n are 6 and 3 respectively

QUESTION: 27

In how many ways can the letters of the word ARRANGE be arranged so that R's are never together?

Solution:

Reqd. ways = = 1260 - 360 = 900

QUESTION: 28

A and B are events such that P(A ∪ B) = 3/4, P(A ∩ B) = 1/4, P(A̅)= 2/3, then P(A̅ ∩ B) is

Solution:
QUESTION: 29

The probability that a number selected at random from the set of numbers {1,2,3,....,100} is a cube is

Solution:
QUESTION: 30

In a equilateral triangle r : R : r1 is

Solution:

A = B = C = 60o
r : R : r1 = 4R sin (A/2) sin (B/2) sin (C/2) : R : 4R sin (A/2) cos (B/2) cos (C/2)
= 4 (1/2) (1/2) (1/2) : 1 : 4 (1/2) (√3 /2) (√3 /2) = (1/2) : 1 : (3/2) = 1 : 2 : 3

QUESTION: 31

The perimeter of a triangle is 16cm. One of the sides is of length 6cm. If the area of the triangle is 12sq.cm, then the triangle is

Solution:
QUESTION: 32

The product of cube roots of -1 is equal to

Solution:
QUESTION: 33

The sum of all 2-digit odd numbers is

Solution: The two digit odd numbers
11,13,15,...., 99

a = 11, n = 45, d = 2

Sn = n/2[2a + (n-1)d}]

= 45/2 [22 + 44 × 2]

= 45/2 × 110

= 45 × 55

= 2475
QUESTION: 34

If the sum of first n terms of an A.P. be 3n2 - n and its common difference is 6, then its first term is

Solution:
QUESTION: 35

In a town of 10,000 families it was found that 40% family buy newspaper A, 20% buy newspaper B, and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then number of families which buy A only is

Solution:
QUESTION: 36

If f : N x N → N is such that f (m,n) = m + n where N is the set of natural numbers, then which of the following is true?

Solution:
QUESTION: 37

The ortho centre of triangle whose vertices are (0,0), (3,0) and (0,4) is

Solution:
QUESTION: 38

The angle between the curves y2=x at x2=y at (1,1) is

Solution:
QUESTION: 39

The angle between the planes 2x-y+z=6 and x+y+2z=7 is

Solution:
QUESTION: 40

The acute angle between the planes 2x-y+z=6 and x+y+2z=3 is

Solution:
QUESTION: 41

If 2cos2x+3sinx-3=0, 0≤x≤180o, then x=

Solution:
QUESTION: 42

The equation sinx+cosx=2 has

Solution:
QUESTION: 43

Maximum value of cos2x+cos2y-cos2z is

Solution:

Max. value will occur when cosx=cosy=1 and cosz=0

QUESTION: 44

If 3i+4j and -5i+7j represent the sides of a triangle, then its area is

Solution:
QUESTION: 45

If and are mutually perpendicular, then (a+b)2=

Solution: