VITEEE Maths Test - 2

Let z₁ and z₂ be nth roots of unity which subtend a right angle at the origin. Then n must be of the form

If  and if f is continuous at x = 1 then f(1) =

The surface area of a cone including the base is 4π sq.ft., then the dimensions of the cone when the volume is maximum are

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

Which one of the following differential equations represents the system of circles touching y-axis at the origin ?

The solution of is

The order of differential equation (d²y/dx²)³=(1+dy/dx)^1/2 is

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

If x^y=e^(x-y), (dy/dx)=

If f, g : R → R, f(x) = (x + 1)² g(x) = x² + 1 then (fog) (-3) =

tan^⁻1(1/5)+tan^⁻1(1/7)+tan^⁻1(1/3)+tan^⁻1(1/8)=

The value of  is

Negation of the conditional , ' if it rains , I shall go to school ' is

If A is a square matrix and I is the unit matrix of the same order 3 x 3 , then A .(adj A)    is

Each coefficients in the equation ax²+bx+c=0 is determined by throwing an ordinary die. The probability that the equation will have equal roots is

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

Sum of all terms of a G.P. is 5 times the sum of odd terms. The common ratio is

If the side of a triangle are 13, 14, 15, then the radius of the incircle is

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

There are five roads from a village to a town. In how many ways can a villager return after reaching the town?

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

If a,b are odd integers, the roots of the equation 2ax²+(2a+b)x+b=0, a≠0 are

If cov. (x, y) = 0, then ρ(x, y) equals

If cotθ=sin2θ(θ≠nπ), n ∈ Z then θ=

The number of real roots of equation x²-3|x|+2=0 is

A student obtain 75%, 80% and 85% in three subjects. If the marks of another subject are added, then his average cannot be less than

The equation of the plane which bisects the line joining (2,3,4) and (6,7,8) is

The equation of a circle with origin as a centre and passing through equilateral triangle whose median is of length 3a is

The equation of the sphere with centre (3, 6, -4) and touching the plane
2x - 2y - z - 10 = 0 is

The vertex of the parabola x² + 8x + 12y - 8 = 0 is

Vectors 2i+3j-4k and ai+bj+ck are perpendicular, when

The moment of force F=i+2j+3k about the point 2i-j+k is