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This mock test of VITEEE Maths Test - 4 for JEE helps you for every JEE entrance exam.
This contains 40 Multiple Choice Questions for JEE VITEEE Maths Test - 4 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

A condition for a function y = f(x) to have inverse is that it should be

Solution:

QUESTION: 2

The area bounded by the *x*-axis and the curve y = 4 x − x^{2} − 3 is

Solution:

y = 0, y = 4x - x^{2} - 3

⇒ 4x - x^{2} - 3 = 0

⇒ x^{2} - 4x + 3 = 0

⇒ (x - 1) (x - 3) = 0

⇒ x = 1, 3

QUESTION: 3

If

Solution:

QUESTION: 4

If then

Solution:

QUESTION: 5

If the function *f* is defined by then at what points is *f* differentiable

Solution:

QUESTION: 6

If *z ^{2} + z + 1 = 0*, where

Solution:

QUESTION: 7

If is continuous at π/4 , then *a* =

Solution:

QUESTION: 8

Solution:

QUESTION: 9

The solution of the differential equation *cos(x + y)dy = dx* is

Solution:

QUESTION: 10

The solution of differential equation (dy/dx)=[(x(2logx+1))/(siny+ycosy)] is

Solution:

QUESTION: 11

The roots of the equation are

Solution:

QUESTION: 12

The degree of the differential equation

Solution:

QUESTION: 13

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

Solution:

y = e^{cx}

dy dx = c. e^{cx}

y' = cy

QUESTION: 14

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

Solution:

QUESTION: 15

The range of the function f(x) = x^{2} - x/x^{2} + 2x is

Solution:

QUESTION: 16

Solution:

QUESTION: 17

If where n > 1 , then I_{n} − I_{n − 2}

Solution:

QUESTION: 18

sec^{2}(tan^{-1} 2) + cosec^{2}(cot^{-1} 3) =

Solution:

QUESTION: 19

Let

What is the value of

Solution:

QUESTION: 20

The value of

Solution:

QUESTION: 21

Which is logically equivalent to "If today is Sunday, Matt cannot play hockey."?

Solution:

Statements are logically equivalent to their contrapositives.

QUESTION: 22

If A is a singular matrix, then A adj (A)

Solution:

QUESTION: 23

If *A* and *B* both are of order 2 x 3 , which one of these is not defined ?

Solution:

QUESTION: 24

Twelve students compete for a race. The number of ways in which first three prizes can be taken is

Solution:

QUESTION: 25

An unbaised die with faces marked 1,2,3,4,5 and 6 is rolled four times. Out of four face value obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is

Solution:

QUESTION: 26

A committee of 5 is to be chosen from a group of 9 people. What is the probability that a certain married couple serve together or not at all ?

Solution:

QUESTION: 27

Two dice are thrown simultaneously. The probability of obtaining a total score of seven is

Solution:

There are six possible ways as to the number of points on the first die; and to each of these ways, there corresponding 6 possible numbers of points on second die.

Hence total number of ways S = 6 x 6 = 36

We now find out how many ways are favorable to the total of 7 points.

This may happen only in following ways:

(1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3).

Hence, required Probability = 6/36 =1/6.

QUESTION: 28

In a triangle , then b =

Solution:

QUESTION: 29

If the sum of n terms of the series 2^{3} + 4^{3} + 6^{3} + ... ∞ is 3528, then n equals

Solution:

QUESTION: 30

The Quartile Deviation of the daily wages (in Rs) of 7 persons given below :

12, 7, 15, 10, 17, 19, 25 is

Solution:

QUESTION: 31

The S.D. of 5 scores

1 2 3 4 5 is

Solution:

QUESTION: 32

If x is positive, the greatest value of 5+4x-4x^{2} is

Solution:

QUESTION: 33

The degree of the equation is ____

Solution:

QUESTION: 34

A st. line which makes an angle of 60^{0} with each of y and z axes, inclines with x-axis at an angle

Solution:

QUESTION: 35

The direction ratios of a normal to the plane through (1, 0, 0), (0, 1, 0), which makes an angle of π/4 with the plane x + y = 3 are

Solution:

QUESTION: 36

If sin2x+sin4x=2sin3x, then x=

Solution:

QUESTION: 37

Locus of centroid of the triangle whose vertices are (a cost, a sint), (b sint, -b cost) and (1, 0), where t is a parameter, is

Solution:

QUESTION: 38

In a ∆ABC, if A is the point (1, 2) and equations of the median through B and C are respectively x + y = 5 and x = 4, then B is

Solution:

QUESTION: 39

If θ is the angle between vectors a and b and |axb|=a.b, then θ=

Solution:

QUESTION: 40

The sine of the angle between the vectors 3i+2j-k and 12i+5j-5k is

Solution:

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