VITEEE Maths Test - 1

The real part of 1/(1-cosθ + i sin θ) is

If the matrix is singular, then θ =

If f x = x 2 | x | for x ≠ 0, f 0 = 0, then f x at x = 0 is

If f( x)   = sin π [ x ] then f ′ (1 − 0)    is equal to

The family of curves, in which the subtangent at any point to any curve is double the abscissa, is given by

Observe the following statements

Which of the following is a correct statement?

The solution of

 is

The solution of the equation (dy/dx)=cotx coty is

The differential of sin^-1[(1-x)/(1+x)] w.r.t. √x is equal to

Suppose that g(x) = 1 + √x and f(g(x)) = 3 + 2√x + x, then f(x) is

∫[(1)/(1-x²)]dx=

If sin^-1x + sin^-1y = 2π/3, then cos^-1 x + cos^-1 y is equal to

 if  is

If f : ℝ → ℝ is defined by f x = 

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

m [ − 3 4 ] + n [ 4 − 3 ] = [ 10 − 11 ]

so, 3 m + 7 n =

If the probability that A and B will die within a year are p and q respectively, then the probability that only one of them will be alive at the end of the year, is

We have (n+1) white balls and (n+1) black balls. In each set the balls are numbered from 1 to (n+1). If these balls are to be arranged in a row so that two consecutive balls are of different colours, then the number of these arrangements is

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour is

A fair dice is tossed repeatedly until six shows up 3 times. The probability that exactly 5 tosses are needed is

If in ∆ABC ∠A=45^o, ∠C=60^o, then a+c√2=

Let the harmonic means and the geometric mean of two positive numbers be in the ratio 4 : 5. The two numbers are in the ratio

Which one of the following is a source of data for primary investigations?

If each observation of a raw data, whose variance is σ², is multiplied by λ, then the variance of new set is

The degree of the equation  is ____

If the roots of the equation (a² + b²)x² - 2(ac + bd)x + (c² + d²) = 0 are equal is

If A (1,2,3),B(-1,-1,-1) be the pts., then the distance AB is

The plane of intersection of x²+y²+z²+2x+2y+2z+2=0 and 4x²+4y²+4z²+4x+4y+4z-1=0 is

The equation 3sin²x + 10cosx - 6 = 0 is satisfied if

The angle between the two straight lines represented by 6y² - xy - x² + 30y + 36 = 0 is

The length of the intercept made by the circle x² + y² + 10x - 6y + 9 = 0 on the X-axis is

If  makes an acute angle with , then is equal to

If |a+b|=|a-b|, then the angle between a and b is