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This mock test of VITEEE Maths Test - 6 for JEE helps you for every JEE entrance exam.
This contains 40 Multiple Choice Questions for JEE VITEEE Maths Test - 6 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The equation of the tangent to the curve (1 + x^{2})y = 2 - x where it crosses x-axis is

Solution:

QUESTION: 2

The area bounded by the parabola x = 4 - y^{2} and the y-axis in square units, is

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QUESTION: 3

If z (2 - i)= 3 + i,z^{20} =

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QUESTION: 4

If x^{2} + x + 1 is a factor of ax^{3} + bx^{2} + cx +d,then the real root of ax^{3} + bx^{2} + cx + d = 0

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QUESTION: 5

If *f*: R → R is defined by f x = x − [ x ] , where [*x*] is the greatest integer not exceeding *x*, then the set of discontinuities of *f* is

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QUESTION: 6

The area bounded by the curve y=xsinx and x-axis between x=0 and x=2π is

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QUESTION: 7

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QUESTION: 8

The value of determinant ∆ of 3rd order is 9 then the value of ∆′^{2} where ∆′ is a determinant formed by cofactors of the element of ∆ is

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QUESTION: 9

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

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QUESTION: 10

Integrating factor of differential equation cos x dy/dx+y sin x = 1 is

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QUESTION: 11

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QUESTION: 12

The number of solutions of y'=y+1/x-1, y(1)=2 is

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QUESTION: 13

The solution of the equation ydx+(1+x^{2})tan^{-1}xdy=0 is

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QUESTION: 14

If S is the set of all real x such that 2x - 1/2x^{3} + 3x^{2} + x is positive, then S contains

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QUESTION: 15

The value of ∫ sin^{−1} (cos x) dx is equal to

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QUESTION: 16

(d/dx)[tan^{-1}((cosx-sinx)/(cosx+sinx))]=

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QUESTION: 17

∫ x^{2}e^{x}x=

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QUESTION: 18

If cos^{-1}p + cos^{-1}q+cos^{-1}r = π, then p^{2} + q^{2} + r^{2} + 2pqr is equal to

Solution:

Let cos^{-1} p = α, cos^{-1} q = β and cos^{-1} r = γ

⇒ cosα = p, cosβ = q and cosγ = r

From question, α + β + γ = π

∴ cos (α + β) = cos (π - γ)

Squaring, we get p^{2}q^{2} + r^{2} + 2pqr = 1 - p^{2} - q^{2} + p^{2}q^{2}

or, p^{2} + q^{2} + r^{2} + 2pqr = 1

QUESTION: 19

If for [ x ] = 0 where [x] denotes the greatest integer not exceeding x, then

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QUESTION: 20

The value of

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QUESTION: 21

Which of the following is not a statement in logic ?

1. Earth is planet .

2. Plants are living object .

3. is rational number .

4. x^{2} - 5x + 6 < 0, where x ∈ − R

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QUESTION: 22

If *A * is a square matrix of order 3 x 3 , then *adj (adj A)* is equal to

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QUESTION: 23

If A is singular matrix of order n, then a (adj A) equals,

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QUESTION: 24

P,Q,R and S have to deliver lecture, then in how many ways can the lectures be arranged?

Solution:

Total no. of ways delivering lectures = ^{4}P_{4} = 4! = 24

QUESTION: 25

The chance of getting a doublet with 2 dice is

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QUESTION: 26

When two balls are drawn from a bag containing 2 white, 4 red and 6 black balls, the chance for both of them to be red is

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QUESTION: 27

Let E₁,E₂, E₃ be three arbitrary events of a sample space S consider the following statements which of the following statement is correct?

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QUESTION: 28

If in ∆ABC ∠A=45^{0}, ∠C=60^{0}, then a+c√2=

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QUESTION: 29

The nth term of the series 3, √3, 1,... is 1/243, then n is

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QUESTION: 30

The co-efficient of correlation between two variables x and y is 0.5, their covariance is 16. If the S.D. of x is 4, then the S.D. of y is equal to

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QUESTION: 31

The quartile deviation of daily wages (in Rs.) of 7 persons given below:

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

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QUESTION: 32

The roots of the equation (q-r)x^{2}+(r-p)x+(p-q)=0 are

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QUESTION: 33

Roots of the equation 5x^{2}-7x+k=0 are reciprocal of each other, then the value of k is

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QUESTION: 34

A line makes the same angle θ, with each of the x and z axis. If the angle β, which it makes with y-axis, is such that sin^{2}β = 3sin^{2}θ, then cos^{2}θ equals:

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QUESTION: 35

The shortest distance between the lines (x - 3)/3 = (y - 8)/-1 = (z - 3)/1 and (x + 3)/-3 = (y + 7)/2 = (z -6)/4 is

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QUESTION: 36

The general solution of the equation tan2θ.tanθ=1 for n∈I is, θ is equal to

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QUESTION: 37

A circle touches the x-axis and also touches the cirlce with centre at (0, 3) and radius 2. The locus of the centre of the cirlce is

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QUESTION: 38

The locus of a point whose abscissa and ordinate are always equal is

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QUESTION: 39

If |a|=3, |b|=4, |c|=5 and a+b+c=0, the angle between a and b is

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QUESTION: 40

If vectors 3i+2j-k and 6i-4xj+yk are parallel, then the value of x and y are

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