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This mock test of BITSAT Maths Test - 2 for JEE helps you for every JEE entrance exam.
This contains 45 Multiple Choice Questions for JEE BITSAT Maths Test - 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The area (in square units) of the region enclosed by the curves *y = x ^{2}* and

Solution:
By solving equations 1and 2 we can get 0,1as values for x which can be the limits and by subtracting y=x^2 from x^3 and integrating the result within the limits 0 to 1 we can get area = 1\12

QUESTION: 2

In the expansion of (y^{1/6 }- y^{-1/3})^{9} the term independent of y is :

Solution:

QUESTION: 3

Equation of the diameter of the circle x^{2} + y^{2} - 6x + 2y = 0 which passes thro' the origin is

Solution:

QUESTION: 4

If the two circles 2x^{2} + 2y^{2} -3x + 6y + k = 0 and x^{2} + y^{2} - 4x + 10y + 16 = 0 cut orthogonally, then the value of k is

Solution:

QUESTION: 5

If then *a* and *b* are

Solution:

QUESTION: 6

The order and degree of differential equation √(dy/dx) - 4 (dy/ dx) - 7x = 0 are

Solution:

√(dy/ dx)- 4 (dy/dx) -7x = 0

or √(dy/ dx) = 4 (dy/dx) + 7x

Squaring both side

dy/ dx = [4 (dy/dx ) + 7x]^{2}

or dy dx = 16 ( dy/dx )^{2} + 49x^{2} + 56 dy/ dx x

∴ order = 1

degree = 2

QUESTION: 7

If x dy = y(dx + y dy), y > 0 and y (1) = 1, then y (-3) is equal to

Solution:

QUESTION: 8

Solution of the differential equation

Solution:

QUESTION: 9

If x=a[(cost)+(log tan(t/2))], y=a sint, (dy/dx)=

Solution:

QUESTION: 10

then = f '(1)

Solution:

QUESTION: 11

1/2! - 1/3! + 1/4! - 1/5! + ....... equals

Solution:

QUESTION: 12

The length of the shadow of a rod inclined at 10^{o} to the vertical towards the sun is 2.05 metres when the elevation of the sun is 38^{o}.The length of the rod is

Solution:

QUESTION: 13

The area of the region bounded by the curve y = x - x^{2} between x = 0 and x = 1 is

Solution:

QUESTION: 14

The product of the perpendicular, drawn from any point on a hyperbola to its asymptotes is

Solution:

QUESTION: 15

The area bounded by the curve x = at^{2}, y = 2at and the X-axis is 1 ≤ t ≤ 3 is

Solution:

QUESTION: 16

The sum of first 50 terms of the series cot^{⁻1}3 + cot^{⁻1} 7 + cot^{⁻1} 13 + cot^{⁻1} 21 + ... is

Solution:

QUESTION: 17

The domain of the function f(x) = √(2 - 2x - x^{2}) is

Solution:

QUESTION: 18

The difference of an integer and its cube is divisible by

Solution:

QUESTION: 19

If A and B are two matrices such that AB = B and BA = A, then A^{2} + B^{2} is equal to

Solution:

QUESTION: 20

if A is a 3 x 3 matrix and B is its adjoint matrix. If ∣B∣ = 64, then ∣A∣ =

Solution:

QUESTION: 21

The strength of a beam varies as the product of its breadth *b* and square of its depth *d*. A beam cut out of a circular log of radius *r* would be strong when

Solution:

QUESTION: 22

Which of the following is correct

Solution:

QUESTION: 23

Equation x^{2}+7xy+3y^{2}+8x+14y+λ=0 represents a pair of straight lines, value of λ is

Solution:

QUESTION: 24

The pole of the line lx+my+n=0 w.r.t. the parabloa y^{2} =4ax

Solution:

QUESTION: 25

The latus rectum of the parabola y^{2} = 5x + 4y + 1 is

Solution:

y^{2} = 5x + 4y + 1

or y^{2} - 4y = 5x + 1

or y^{2} - 2.2.y + (2)^{2} - (2)^{2} = 5x + 1

or (y - 2)^{2} = 5x + 5

or (y - 2)^{2} = 5(x + 1)

Length of the latus rectum = 5

QUESTION: 26

How many total words can be formed from the letters of the word INSURANCE in which vowels are always together?

Solution:

QUESTION: 27

A polygon has 44 diagonals. The number of its sides is

Solution:
The number of diagonals for n sided polygon = [n(n-3)]/2Â .
therefore,
=> 44 = [n(n-3)]/2Â .
=> n^2 - 3n - 88 = 0Â .
=> (n+8)(n-11) =0.
=> n = -8 or 11.
Neglect n = -8.
Therefore,
=> n = 11Â .
therefore, the no. of sides = 11
Hence, correct answer is (B).

QUESTION: 28

A committee consists of 9 experts from three institutions A, B and C, of which 2 are from A, 3 from B and 4 from C. If three experts resign, then the probability that they belong to different institutions is

Solution:

QUESTION: 29

A single letter is selected at random from the word "PROBABILITY". The probability that it is a vowel is

Solution:

QUESTION: 30

If the area of a Δ A B C be λ then a^{2} sin 2B + b^{2} sin 2A is equal to

Solution:

QUESTION: 31

In a Δ A B C , a = 1 and the perimeter is six times the AM of the sines of the angles. The measure of ∠ A is

Solution:

QUESTION: 32

If α, β are the roots of the equation x^{2}- 2x + 2 = 0, then the value of α^{2} + β^{2} is

Solution:

QUESTION: 33

The sum of an infinite G.P. is 3. The sum of the series formed by squaring its terms is also 3. The series is

Solution:

QUESTION: 34

The 5th term of a G.P. is 2, then the product of its first 9 term is

Solution:

QUESTION: 35

If f : R → R is given as f (x) = |x| and A = {x ∈ R : x > o}, then f^{⁻1}(A) =

Solution:

QUESTION: 36

If f (x) = {2x - 3, x ≤ 2} {x, x < 2} then f (1) is equal to

Solution:

QUESTION: 37

The equation line passing through the point P(1,2) whose portion cut by axes is bisected at P, is

Solution:

QUESTION: 38

The equation of the common tangent to the curves y^{2}=8x and xy=-1 is :

Solution:

QUESTION: 39

The radius of the circle in which the sphere x^{2} + y^{2} + z^{2} + 2x - 2y - 4z - 19 = 0 is cut by the plane x + 2y + 2z + 7 = 0, is

Solution:
Radius of sphere is=5 then perpen dicular dice Frome plane=4 now radius of circle r,sqr=25_16=9so r=3

QUESTION: 40

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

Solution:

QUESTION: 41

If 0≤x≤π and 81^{sin2x} + 81 ^{cos2x} = 30, then x is equal to

Solution:

QUESTION: 42

If 1 + sin x + sin ^{2} x + … ∞ = 4 + 2 √ 3 , 0 < x < π , x ≠ π/2 then x =

Solution:

QUESTION: 43

(secA+tanA-1)(secA-tanA+1)-2 tanA=

Solution:

QUESTION: 44

The value of b such that the scalar product of the vector î+ĵ+k̂ with the unit vector parallel to the sum of the vectors 2î + 4ĵ - 5k̂ and bî+ 2ĵ + 3k̂ is one is

Solution:

** Parallel vector =(2+b)i+6j−2k**

**Unit vector = (2+b)i+6j−2k / (b ^{2}+4b+44)^{1/2}**

**According to the question, **

**1 = (2+b)+6−2/b ^{2}+4b+44**

**⇒b ^{2}+4b+44=b^{2}+12b+36**

**⇒8b=8⇒b=1**

QUESTION: 45

The angle between the vectors 3i+j+2k and 2i-2j+4k is

Solution:

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