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This mock test of VITEEE Maths Test - 5 for JEE helps you for every JEE entrance exam.
This contains 40 Multiple Choice Questions for JEE VITEEE Maths Test - 5 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

the area of the ellipse x^{2}/a^{2} + y^{2}/b^{2} = 1 is

Solution:

QUESTION: 2

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

Solution:

QUESTION: 3

Find the value of

Solution:

QUESTION: 4

If z₁,z₂ and z₃ are complex number such that

|z₁|=|z₂|=|z₃|=|1/z₁ + 1/z₂ + 1/z₃|=1,then |z₁ + z₂ + z₃ | is

|z₁|=|z₂|=|z₃|=|1/z₁ + 1/z₂ + 1/z₃|=1,then |z₁ + z₂ + z₃ | is

Solution:

QUESTION: 5

Solution:

QUESTION: 6

If is continuous at *x* = 0, then *k* =

Solution:

QUESTION: 7

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

Solution:

QUESTION: 8

The real part of is

Solution:

QUESTION: 9

Let

at x = 2

is

Solution:

QUESTION: 10

The order of the differential equation x2+y2+2gx+2fy+c=0, is

Solution:

QUESTION: 11

The solution of the differential equation is

Solution:

QUESTION: 12

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

Solution:

QUESTION: 13

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

Solution:

QUESTION: 14

If , then find f′ 2

Solution:

QUESTION: 15

Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A into B is

Solution:

QUESTION: 16

If where n > 1 , then I_{n} − I_{n−2}

Solution:

QUESTION: 17

∫[(x+sinx)/(1+cosx)] dx =

Solution:

QUESTION: 18

If cos^{-1}(x/a)+cos^{-1}(y/b)=α, then (x^{2}/a^{2})-(2xy/ab)cosα+(y^{2}/b^{2})=

Solution:

QUESTION: 19

Obtain

Solution:

QUESTION: 20

Solution:

QUESTION: 21

The statement "If x is divisible by 8, then it is divisible by 6" is false if x equals

Solution:

A sentence in "If....then..." form is called an implication.

The only time when an implication is false is when the "If" part of the sentence is true and the "then" part of the sentence is false.

The number 32 makes the first part of the statement true and the second part of the statement false.

QUESTION: 22

If the value of a determinants is 11, then the square of the determinant formed by its cofactor will be

Solution:

QUESTION: 23

If A is an 3x4 matrix and B is a matrix such that A'B and BA' both are defined, then size of B is

Solution:

QUESTION: 24

In a 12 storey building 3 persons enter a lift cabin. It is known that they will leave the lift at different storeys. In how many ways can they do so if the lift does not stop at the second storey.

Solution:

There are 10 storeys for three persons for leaving the lift

(these are other than second storey and one at which they enter the lift).

So required number is 10 P 3 = 720

QUESTION: 25

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

Solution:

QUESTION: 26

From a well-shuffled pack of 52 cards, 2 cards are drawn, the first being replaced before the second is drawn. The probability that the first in a diamond and the second is queen is

Solution:

QUESTION: 27

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

Solution:

QUESTION: 28

In ΔABC , r + r_{3} + r_{1} − r_{2} =

Solution:

QUESTION: 29

If the nth term of the geometric progression, 5, -5/2, 5/4, -5/8 is 5/1024, then the value of n is

Solution:

QUESTION: 30

If x and y are independent variables, then

Solution:

QUESTION: 31

The S.D. of 15 items is 6 and if each item is decreased by 1, then standard deviation will be

Solution:

QUESTION: 32

The one roots of the equation 2x^{5}-14x^{4}+31x^{3}-64x^{2}+19x+130=0 is

Solution:
So in this type of questions either match the options or apply hit and trial method.once you will get one root suppose a so divide the polynomial by (x-a) and get the quotient and then try to factorise the quotient as it will be of lesser degree.

QUESTION: 33

If one root of the equation a(b-c)x^{2}+b(c-a)x+c(a-b)=0, is 1 then the other root is

Solution:

QUESTION: 34

The equation of the sphere concentric with the sphere x^{2} + y^{2} + z^{2} - 4x - 6y - 8z - 5 = 0 and which passes through the origin is

Solution:

QUESTION: 35

The number of st. lines that are equally inclined to three dimensional co-ordinate axes is

Solution:

QUESTION: 36

If tanθ+cotθ=2, then θ=

Solution:

QUESTION: 37

Two common tangents to the circle x^{2} + y^{2} = 2a^{2} and parabola y^{2}= 8ax are

Solution:

QUESTION: 38

If the pairs of straigth lines x^{2} - 2pxy - y^{2} = 0 and x^{2} - 2qxy - y^{2} = 0 be such that each pair bisects the angle between the other pair, then

Solution:

QUESTION: 39

If makes an acute angle with , then is equal to

Solution:

QUESTION: 40

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:

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