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This mock test of JEE Main Mathematics Mock - 5 for JEE helps you for every JEE entrance exam.
This contains 25 Multiple Choice Questions for JEE JEE Main Mathematics Mock - 5 (mcq) to study with solutions a complete question bank.
The solved questions answers in this JEE Main Mathematics Mock - 5 quiz give you a good mix of easy questions and tough questions. JEE
students definitely take this JEE Main Mathematics Mock - 5 exercise for a better result in the exam. You can find other JEE Main Mathematics Mock - 5 extra questions,
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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

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

Solution:

QUESTION: 6

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 :- α + β = - b/aProducts of the roots of equation :- αβ = c/a squaring on both side sum of roots of equation α^2 +β^2 +2αβ = 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 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: 18

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: 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:

*Answer can only contain numeric values

QUESTION: 21

If then value of L/128 is :-

Solution:

*Answer can only contain numeric values

QUESTION: 22

If the function is continuous in the interval (–∞, 6) then value of is

Solution:

*Answer can only contain numeric values

QUESTION: 23

Value of is equals to

(where [.] denotes greatest integer function)

Solution:

*Answer can only contain numeric values

QUESTION: 24

If the area bounded by curve x + |y| = 1 and the y-axis is k, then k/4 is equals to

Solution:

*Answer can only contain numeric values

QUESTION: 25

If value of is k then k/4 is

Solution:

k = 3

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