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This mock test of JEE(MAIN) Mathematics Mock Test - 5 for JEE helps you for every JEE entrance exam.
This contains 30 Multiple Choice Questions for JEE JEE(MAIN) Mathematics Mock Test - 5 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Solution:

QUESTION: 2

The area of the circle with centre (h,k) and radius a is

Solution:

QUESTION: 3

[(1+cosθ+i sinθ)/(i+sinθ+i cosθ)]^{4} = cos nθ + isin nθ, then n=

Solution:

QUESTION: 4

Solution:

QUESTION: 5

Solution:

QUESTION: 6

The differential equation which represents the family of plane curves y=exp. (cx) is

Solution:

QUESTION: 7

If the domain of function f(x) = x^{2} - 6x + 7 is (-∞, ∞), then the range of function is :

Solution:

QUESTION: 8

In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-

Let a, b, c, p, q be real numbers. Suppose α,β are the roots of the equation x^{2} + 2px + q = 0 and a, 1/β are the roots of the equation ax^{2} + 2bx + c = 0, where β^{2} ∉ {-1, 0, 1}

Statement-1:

(p^{2}-q)(b^{2}-ac)≥0

Statement-2:

b≠pa or c≠qa

Solution:

QUESTION: 9

The angle between the pair of tangents drawn from the point (1,2) to the ellipse 3x^{2} + 2y^{2}= 5 is

Solution:

QUESTION: 10

(d/dx)[cos(1-x^{2})^{2}]=

Solution:

QUESTION: 11

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

Assertion(A): e^{x} , log_{e} x are two functions such that each is the image of the other with respect to the line *x = y*

Reason (R): The inverse of every bijective function is symmetric about the line *x = y*

Solution:

QUESTION: 12

A square tank of capacity 250 cubic m has to be dug out. The cost of land is Rs 50 per sq.m. The cost of digging increases with the depth and for the whole tank is 400 (depth)^{2} rupees. The dimensions of the tank for the least total cost are

Solution:

QUESTION: 13

The same roots of 3-4 i are

Solution:

QUESTION: 14

Everybody in a room shakes hands with every body else. The total number of hand shakes is 66. Then the number of persons in the room is

Solution:

There are n people in the room

n(n - 1)/2 = 66

n^{2} - n = 132

n^{2} - n - 132 = 0

n^{2} - 12n + 11n - 132 = 0

n(n - 12) + 11(n - 12) = 0

(n + 11) (n - 12) = 0

n = 12, - 11

Hence total no of persons = 12

QUESTION: 15

If the sum of the squares of the roots of *x ^{2} + px* - 3 = 0 is 10, then the values of

Solution:
Sum of the roots of equation :- Î± + Î² = - b/aProducts of the roots of equation :- Î±Î² = c/a squaring on both side sum of roots of equation Î±^2 +Î²^2 +2Î±Î² = b^2/a^2 put values in above equation 10 + 2(-3) =b^2 b = +2 or b = -2

QUESTION: 16

Three identical dice are rolled. The probability that the same number will appear on each of them, is

Solution:

QUESTION: 17

If the two lines of regression are 5x + 3y = 55 and 7x + y = 45, then the correlation coefficient between x and y is

Solution:

QUESTION: 18

If A is the single A.M. between two numbers a and b and S is the sum of n A.M.'s between them, then S/A depends upon

Solution:

QUESTION: 19

*M* telegrams are distributed at random over *N* communication channels (N > M). The probability of the event

*A* = {not more than one telegram will be sent over any channel} is

Solution:

The total no. of ways of distributing M telegrams over N channels = N^{M}

The number of ways of choosing M channels out of N to send one telegram over each channel = ^{N}C_{M}

∴ Total no. of ways to send M telegrams over each channel = ^{N}C_{M} . M!

∴ Required probubility

QUESTION: 20

The equation of a line passing through (-a,0) and form a triangle of area 'T' with coordinates axes, is

Solution:

QUESTION: 21

The distance between the parallel planes x + 2y - 3z = 2 and 2x + 4y - 6z + 7 = 0 is

Solution:

QUESTION: 22

The co-ordinates of a point P are (3,12,4) w.r.t. the origin O, then the direction consines of OP are

Solution:

QUESTION: 23

sin 163° cos347° + sin 73° sin 167°

Solution:

sin 163° cos 347 + sin 73° sin 167

= sin (180° - 17°) cos (360° - 13°) + sin (90° - 17°) sin (180° - 13°)

= sin 17° cos 13° + cos 17° sin 13°

= sin (17° + 13°) = sin 30° = 1/2

QUESTION: 24

If represent the sides AB and BC of a regular hexagon ABCDEF, then the vector equals

Solution:

QUESTION: 25

The integral is equal

Solution:

QUESTION: 26

A line has intercepts a, b on the coordinate axes. If the axes are rotated about the origin through an angle α then the line has intercepts p, q on the new position of the axes respectively. Then:

Solution:

QUESTION: 27

Let the equation of a curve be x = a (θ + sin θ), y = a(1 − cos θ). Let θ change at a constant rate *k* then the rate of change of the slope of the tangent to the curve at θ = π/3 is

Solution:
Basically it is asking d2y/dx2 at (theta = Ï€/3)

dy/dx = (dy/dz)/(dx/dz) where z is theta

dy/dz = asinz

dx/dz = a(1+cosz)

where z is theta

so dy/dx = sinz/(1+cosz)

=tan(z/2)

second differential = kÃ— 1/2 {sec(z/2)}^2

at z=Ï€/3

answer is 2k/3

dy/dx = (dy/dz)/(dx/dz) where z is theta

dy/dz = asinz

dx/dz = a(1+cosz)

where z is theta

so dy/dx = sinz/(1+cosz)

=tan(z/2)

second differential = kÃ— 1/2 {sec(z/2)}^2

at z=Ï€/3

answer is 2k/3

QUESTION: 28

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

Assertion(A): If y = 4x - 5 is a tangent to the curve y^{2} = px^{3} + q at (2,3) , then p = 2 and q = -7.

Reason: If tangent is parallel to x-axis, θ = 0°,

Solution:

QUESTION: 29

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

Assertion(A): The chord of the hyperbola 25x^{2} - 16y^{2} = 400 whose middle point is (6,2) if 16x - 75y = 418.

Reason(R): Chord whose mid-point is (h,k) is given by T = S_{1}.

Solution:

QUESTION: 30

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

Assertion(A): The values of p for which the equation 2x^{2} - √2px + p = 0 has equal roots are 0 and 4.

Reason(R): Equation ax^{2} + bx + c = 0 has real and equal roots, if its discriminant is zero.

Solution:

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