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This contains 40 Multiple Choice Questions for JEE VITEEE Maths Test - 8 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

When the function f(x) = sin 2x(1 + cos 2x) has a maximum, one value of x is equal to

Solution:

QUESTION: 2

The area bounded by the curve y = x^{3}, the x-axis and the ordiantes at x = -2 and x = 1 is

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QUESTION: 3

If z = [(1-i√3)/(1+i√3)], then arg (z) =

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QUESTION: 4

If ω is a complex cube root of unity, then 225 + (3ω+8ω^{2})^{2}+3ω^{2}+8ω)^{2}=

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QUESTION: 5

If is continuous at π/4 , then *a* =

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QUESTION: 6

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QUESTION: 7

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QUESTION: 8

In determinant radio of the cofactor of -3 and subdeterminant is

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QUESTION: 9

Let

Then is

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QUESTION: 10

The degree and order of the differential equation of the family of all parabolas whose axis is x-axis are respectively

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QUESTION: 11

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QUESTION: 12

The order and degree of the differential equation d^{2}y/dx^{2} + (dy/dx)^{1/3} + x^{1}=0 are respectively

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QUESTION: 13

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

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QUESTION: 14

The differential of sin^{-1}[(1-x)/(1+x)] w.r.t. √x is equal to

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QUESTION: 15

If

for x > 2, then f 11

=

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QUESTION: 16

If constant , then f (x) =

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QUESTION: 17

If then x =

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QUESTION: 18

∫[(x^{2}+1)/(x^{4}-x^{2}+1)] dx =

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QUESTION: 19

The value of is

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QUESTION: 20

A function *f(x)* is defined as , where [*x*] denotes the greatest integer not exceeding *x*. The function *f(x)* is discontinuous at *x* = 0 because

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QUESTION: 21

Negation of "Sohan is in class X or Rani is in class XII" is

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QUESTION: 22

If A is a non-singular, then adj A is

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QUESTION: 23

If A is a square matrix of order 3, then which of the following is correct.(where I is a unit matrix)

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QUESTION: 24

The number of 4-digit even numbers that can be formed using 0, 1, 2, 3, 4, 5, 6 without repetition is

Solution:

Each even number must have 0, 2, 4 or 6 in is units place

Here total number of digits = 7

When 0 occurs at units place there is no restriction on other places and when 2 or 4 occurs at units place there is restriction on thousands' place as 0 can not be put at thousands' place

Case I When 0 occurs at units place:

The units' place can be filled up by any one of the three digits 2, 4 and 6 in 3 ways

∴ The number of numbers formed in this case

QUESTION: 25

A,B,C in order toss a coin. The first one to throw a head wins. Assuming the game continues indefinitely, their respective chances of winning the game are

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QUESTION: 26

Three letters are written to different persons and addresses on three envelopes are also written. Without looking at the addresses, the probability that the letters go into the right envelope, is

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QUESTION: 27

Give two independent events A and B such that P(A) = 0.30 and P(B) = 0.60. Prob of getting neither A nor B is

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QUESTION: 28

In a triangle ABC, A = 30^{0}, b = 8, a = 6, then B = sin^{-1} x where x =

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QUESTION: 29

The number of terms common to two A.P.'s 3, 7, 11, ..., 407 and 2, 9, 16,...., 709 is

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QUESTION: 30

The first of the two samples has 63 items with mean 27.6 and standard deviation 7.1. If the whole group has 89 items with mean 25.1 and standard deviation 7.8, the standard deviation of the second group is

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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

In ∆ABC angle A is defined by 5 cos A + 3 = 0, the equation whose roots are sinA and tanA, is

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QUESTION: 33

The roots of the equation x^{3} + x^{2} + x + 1 = 0 are___

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QUESTION: 34

The shortest distance from the point (1, 2, -1) to the surface of the sphere x^{2} + y^{2} + z^{2} = 24 is

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QUESTION: 35

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

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QUESTION: 36

If sin^{2}θ-2cosθ+(1/4)=0, the general value of θ is

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QUESTION: 37

The length of the tangent from the point (5, 4) to the circle

x^{2} + y^{2} + 2x - 6y = 6 is

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QUESTION: 38

The locus of a point P(α, β) moving under the condition that the line y = αx + β is a tangent to the hyperbola (x^{2}/a) - (y^{2}/b^{2}) = 1 is

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QUESTION: 39

If are three unit vectors such that are non collinear, then the angles that â makes with b̂ and ĉ respectively are

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QUESTION: 40

In a If the area of triangle is of unit magnitude, then

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