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This mock test of VITEEE Maths Test - 10 for JEE helps you for every JEE entrance exam.
This contains 40 Multiple Choice Questions for JEE VITEEE Maths Test - 10 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If x +y = 60; x, y > 0, then maximum value of xy^{3} is

Solution:

QUESTION: 2

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

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QUESTION: 3

If R → R is continuous such that then *f*(100) =

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QUESTION: 4

The value of arg [(1-i√3)/(1+i√3)] is

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QUESTION: 5

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QUESTION: 6

(x + y + z) (x + y ω + z ω^{2}) (x + yω^{2} + z ω) =

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QUESTION: 7

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QUESTION: 8

Solution:

Multiply R_{1}, R_{2}, R_{3} by a, b, c respectively and divide by abc

Take abc common from C_{3} so that C_{1}, C_{3} are identical

QUESTION: 9

The differential equation with respect to the curve y=e^{mx} is

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QUESTION: 10

Which equation has the solution y=A sinx+B cosx?

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QUESTION: 11

The solution of the differential equation x^{2} dy/dx-xy=1+cos y/x is

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QUESTION: 12

Let f(x) = log |x - 1|, x ≠ 1. The value of is

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QUESTION: 13

The solution of the equation (1+x^{2})(1+y)dy+(1+x)(1+y^{2})dx=0 is

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QUESTION: 14

(d/dx)[cos(1-x^{2})^{2}]=

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QUESTION: 15

If f x = log x , g x = x^{3} then f[ga]+f[gb]

=

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QUESTION: 16

If ∫(sin 2x - cos 2x)dx = (1/√2) sin (2x-a) + b

Solution:

QUESTION: 17

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QUESTION: 18

If then *I* is equal to

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QUESTION: 19

The valuie of sin^{-1} cos(sin^{-1} x) + cos^{-1} sin (cos^{-1} x) is

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QUESTION: 20

True statement for

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QUESTION: 21

Consider the sentence: x < 5

Which of the following integers makes this open sentence true?

Solution:

The only number less than 5 in the list of answers is 4.

QUESTION: 22

If |A| represents the determinant of a square matrix of order 3 then (-2A)=

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QUESTION: 23

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

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QUESTION: 24

Five seats are vacant in a railway compartment, then in how many ways can three passengers be seated on these seats?

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QUESTION: 25

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: 26

If *S* is a sample space, , where *A, B* are two mutually exclusive events, then *P(A)* =

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QUESTION: 27

In a Poisson distribution mean is 16, then S.D is

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QUESTION: 28

In Δ A B C , i f A = 60^{0}then

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QUESTION: 29

11^{3} + 12^{3} + 13^{3} + ... + 20^{3} is

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QUESTION: 30

For a frequency distribution mean deviation from mean is computed by

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QUESTION: 31

The average weight of students in a class of 35 students is 40 kg. If the weight of the teacher be included, the average rises by (1/2) kg ; the weight of the teacher is

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QUESTION: 32

If x = 2 + i √3, then the value of, 4x^{2} + 8x + 13 is____

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QUESTION: 33

A quadratic equation whose one root is the square root of -47+8√-3 is

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QUESTION: 34

The intersection of the spheres x^{2} + y^{2} + z^{2} + 7x - 2y - z = 13 and x^{2} + y^{2} + z^{2} - 3x + 3y + 4z = 8 is the same as the intersection of one of the sphere and the plane

Solution:

QUESTION: 35

The smallest values of θ satisfying the equation √ 3 cot θ + tan θ = 4 is

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QUESTION: 36

A tetrahedron has vertices at O (0, 0, 0), A(1, 2, 1), B(2, 1, 3) and C (-1, 1, 2). Then the angle between the faces OAB and ABC will be

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QUESTION: 37

The angle between the two straight lines represented by 6y^{2} - xy - x^{2} + 30y + 36 = 0 is

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QUESTION: 38

The orthocentre of the triangle whose vertices are (5, -2), (-1, 2) and (1, 4) is

Solution:

QUESTION: 39

Let a, b and c be distributed non-vegetative numbers. If the vectors aî + aĵ + ck̂, î + k̂ and cî̂ + cĵ̂ + bk̂ lie in a plane, then c is

Solution:

QUESTION: 40

If vectors i+2j+3k and 3i-2j+k represents the adjacent sides of a parallelogram, the area of parallelogram is

Solution:

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