VITEEE Maths Test - 6

If x² + x + 1 is a factor of ax³ + bx² + cx +d,then the real root of ax³ + bx² + cx + d = 0

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

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

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

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

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

The solution of the equation ydx+(1+x²)tan^-1xdy=0 is

If S is the set of all real x such that 2x - 1/2x³ + 3x² + x is positive, then S contains

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

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

∫ x²e^xx=

If cos^-1p + cos^-1q+cos^-1r = π, then p² + q² + r² + 2pqr is equal to

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

The value of

Which of the following is not a statement in logic ?
1. Earth is planet .
2. Plants are living object .
3. is rational number .
4. x² - 5x + 6 < 0, where x ∈ − R

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

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

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

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

If in ∆ABC ∠A=45⁰, ∠C=60⁰, then a+c√2=

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

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

The quartile deviation of daily wages (in Rs.) of 7 persons given below:
12, 7, 15, 10, 17, 17, 25 is

The roots of the equation (q-r)x²+(r-p)x+(p-q)=0 are

Roots of the equation 5x²-7x+k=0 are reciprocal of each other, then the value of k is

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 sin²β = 3sin²θ, then cos²θ equals:

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

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

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

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

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

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