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This mock test of VITEEE Maths Test - 2 for JEE helps you for every JEE entrance exam.
This contains 40 Multiple Choice Questions for JEE VITEEE Maths Test - 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The area of the region bounded by a^{2} y^{2} = x^{2} (a^{2} − x^{2}) is

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QUESTION: 2

The area bounded by the parabola y^{2}=4ax and the straight line y=2ax is

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QUESTION: 3

If then *a* and *b* are

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QUESTION: 4

If and if *f* is continuous at *x* = 1 then *f*(1) =

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QUESTION: 5

Let z₁ and z₂ be nth roots of unity which subtend a right angle at the origin. Then n must be of the form

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QUESTION: 6

The surface area of a cone including the base is 4π sq.ft., then the dimensions of the cone when the volume is maximum are

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QUESTION: 7

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QUESTION: 8

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

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QUESTION: 9

Which one of the following differential equations represents the system of circles touching *y*-axis at the origin ?

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QUESTION: 10

The solution of is

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QUESTION: 11

The order of differential equation (d^{2}y/dx^{2})^{3}=(1+dy/dx)^{1/2} is

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QUESTION: 12

Solution of cos x dy/dx+y sin x =1 is

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QUESTION: 13

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QUESTION: 14

If x^{y}=e^{(x-y)}, (dy/dx)=

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QUESTION: 15

If f, g : R → R, f(x) = (x + 1)^{2} g(x) = x^{2} + 1 then (fog) (-3) =

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QUESTION: 16

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QUESTION: 17

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QUESTION: 18

tan^{⁻1}(1/5)+tan^{⁻1}(1/7)+tan^{⁻1}(1/3)+tan^{⁻1}(1/8)=

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QUESTION: 19

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QUESTION: 20

The value of is

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QUESTION: 21

Negation of the conditional , ' if it rains , I shall go to school ' is

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QUESTION: 22

If *A* is a square matrix and *I* is the unit matrix of the same order 3 x 3 , then A .(adj A) is

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QUESTION: 23

Each coefficients in the equation ax^{2}+bx+c=0 is determined by throwing an ordinary die. The probability that the equation will have equal roots is

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QUESTION: 24

A coin tossed until a head appears or until the coin has been tossed 5 times. If a head does not occur on the first two tosses, then the probability that the coin will be tossed 5 times is

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QUESTION: 25

Sum of all terms of a G.P. is 5 times the sum of odd terms. The common ratio is

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QUESTION: 26

If the side of a triangle are 13, 14, 15, then the radius of the incircle is

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QUESTION: 27

If B is a non-singular matrix and A is a square matrix, then det (B^{-1}AB) =

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QUESTION: 28

If A and B are such events that P(A)>0 and P(B)≠1, then P(A̅/B̅) is equal to

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QUESTION: 29

There are five roads from a village to a town. In how many ways can a villager return after reaching the town?

Solution:

Permutation : - A Permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement.

For example, Suppose we have a set of three letters :A, B and C..... each possible arrangement would be an example of permutation.

Here in this question, there are 5roads leading to a town from a village.

He can go by 5 ways and can return by 4 ways

So the number of different ways in which a villager can go to the town and return back is 5×4=20

QUESTION: 30

If cov. (x, y) = 0, then ρ(x, y) equals

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QUESTION: 31

If cotθ=sin2θ(θ≠nπ), n ∈ Z then θ=

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QUESTION: 32

If a,b are odd integers, the roots of the equation 2ax^{2}+(2a+b)x+b=0, a≠0 are

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QUESTION: 33

A student obtain 75%, 80% and 85% in three subjects. If the marks of another subject are added, then his average cannot be less than

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QUESTION: 34

The number of real roots of equation x^{2}-3|x|+2=0 is

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QUESTION: 35

The equation of the plane which bisects the line joining (2,3,4) and (6,7,8) is

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QUESTION: 36

The equation of a circle with origin as a centre and passing through equilateral triangle whose median is of length 3a is

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QUESTION: 37

The equation of the sphere with centre (3, 6, -4) and touching the plane

2x - 2y - z - 10 = 0 is

Solution:

As the required sphere touches the plane

2x - 2y - z - 10 = 0 .....(1)

∴ Radius of the required sphere = ⊥ from the center (3, 6, -4) of the required sphere to the plane (1)

∴ The required equation of the sphere is given by

(x - 3)^{2} + (y - 6)^{2} + (z + 4)^{2} = 16 (Central form)

⇒ x^{2} + 9 - 6x + y^{2} + 36 - 12y + z^{2} + 16 + 8z = 16

⇒ x^{2} + y^{2} + z^{2} - 6x - 12y + 8z + 45 = 0

QUESTION: 38

The vertex of the parabola x^{2} + 8x + 12y - 8 = 0 is

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QUESTION: 39

Vectors 2i+3j-4k and ai+bj+ck are perpendicular, when

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QUESTION: 40

The moment of force F=i+2j+3k about the point 2i-j+k is

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