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This mock test of VITEEE Maths Test - 3 for JEE helps you for every JEE entrance exam.
This contains 40 Multiple Choice Questions for JEE VITEEE Maths Test - 3 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The abcissa of the points of the curve y = x(x - 2)(x - 4) where tangents are parallel to x-axis is obtained as

Solution:

QUESTION: 2

*AOB* is the positive quadrant of the ellipse x^{2} ∕ a^{2} + y^{2} ∕ b^{2} = 1, where *OA = a, OB = b*. The area between the arc *AB* and the chord *AB* of the ellipse is

Solution:

QUESTION: 3

Let z₁ and z₂ be two roots of the equation z^{2} + az + b = 0, z being complex further, assume that the origin, z₁ and z₂ form an equilateral triangle, then

Solution:

As z1, z2 are roots of z^2 + az + b

z1 + z2 = â€“a and z1 z2 = b

Again 0, z1, z2 are vertices of an equilateral triangle.

Therefore, 0^2 + z1^2 + z2^2 = 0z1 + z1z2 + 0z2 = 0

z1^2 + z2^2 = z1z2

(z1 + z2)^2 = 3z1z2

The correct option is B.

QUESTION: 4

Solution:

QUESTION: 5

where *z* is non real, can be the angle of a triangle if

Solution:

QUESTION: 6

If for x ∈ ℝ then f ′ 0 =

Solution:

QUESTION: 7

The value of *f*(0) so that f x = sin x/x is continuous at *x* = 0 is

Solution:

QUESTION: 8

Solution:

QUESTION: 9

If and then

Solution:

QUESTION: 10

The solution of differential equation (xdy/dx)=y+x^{2} is

Solution:

QUESTION: 11

Solution of (x+y-1) dx+(2x+2y-3) dy = 0 is

Solution:

QUESTION: 12

The general solution of the equation x^{2}(dy/dx)=2 is

Solution:

QUESTION: 13

The general solution of the differential equation is given by

Solution:

QUESTION: 14

If y=x^{2}(x-2)^{2}, then the values of x for which y is increasing, are

Solution:

QUESTION: 15

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

Solution:

QUESTION: 16

∫tan^{-1}x dx =

Solution:

QUESTION: 17

∫[(1)/(x+xlogx)]dx=

Solution:

QUESTION: 18

sec^{-1}[sec(-30^{0})]=

Solution:

QUESTION: 19

Solution:

QUESTION: 20

Solution:

QUESTION: 21

The dual of the statement [ p ∨ ∼ q ] ∧ ∼ p is

Solution:

QUESTION: 22

If A,B,C are matrices of order nxn then (ABC)'=

Solution:

QUESTION: 23

If A^{2} = 2A − I then for n ≠ 2, A^{n} =

Solution:

QUESTION: 24

Out of 15 points in a plane, no three are in a straight line except 8 points which are collinear. How many triangles can be formed by joining them?

Solution:

**Solution :- No. of Δs = 15C3 - 8C3**

****

**= 15!/(3!*12!) - (8!/(3!*5!)**

**= 455 - 56 = 399**

QUESTION: 25

Let A and B be two events such that P(A) = 0.3, P(A∪B) = 0.8, if A and B are independent events, then P(B) is equal to

Solution:

QUESTION: 26

The probability that a man can hit a target is 3/4. He tries 5 times. The probability that he will hit the target at least three times is

Solution:

QUESTION: 27

In two events P(A∪B) = 5/6, P(A) = 5/6, P(B) = 2/3 then A and B are

Solution:

QUESTION: 28

In a ΔABC , a = 8 , b = 10 and c = 12. Then C is equal to

Solution:

QUESTION: 29

If a, b, c of a triangle are in A.P., then cot C/2 =

Solution:

QUESTION: 30

The most stable measure of central tendency is

Solution:

QUESTION: 31

A group of 10 items has mean 6. If the mean of 4 of these items is 7.5, then the mean of the remaining items is

Solution:

QUESTION: 32

If

Solution:

From (1), x must be greater than 1 (taking + ve sign.)

∴ 1 < x < 2

QUESTION: 33

If the roots of the equation x^{2}+2mx+m^{2}-2m+6=0 are equal, then the value of m is

Solution:

QUESTION: 34

If a line makes angles α,β,γ with the +ve direction of x,y and z axis respectively, then cos^{2}α+cos^{2}β+cos^{2}γ

Solution:

QUESTION: 35

If the direction cosines of a line are < (1/c), (1/c), (1/c) >, then

Solution:

QUESTION: 36

The general value of θ which satisfies the equations sinθ=-(1/2) and tanθ=(1/√3) is

Solution:

QUESTION: 37

If a, b, c are in A.P. then the straight line ax + by + c = 0 will always pass through a fixed point whose coordinates are

Solution:

QUESTION: 38

The equation of the circle having its centre on the line x + 2y - 3 = 0 and passing through the points of intersection of the circles x^{2}+ y^{2} - 2x - 4y + 1 = 0 and x^{2} + y^{2} - 4x - 2y + 4 = 0 is

Solution:

QUESTION: 39

If a=i+j-k, b=-i+2j+k and c=-i+2j-k, the unit vector perpendicular to a+b and b+c is

Solution:

QUESTION: 40

Let p=(x+4y)a+(2x+y+1)b and q=(y-2x+2)a+(2x-3y-1)b, where a and b are non-coplanar vectors. If 3p=2q, then the value of x and y are

Solution:

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