VITEEE Maths Test - 7

If 1 + i is the conjugate of (x+iy)(1-2i), then

where [x] denotes the greatest integer less than or equal to x, is continuous at x = 2, then the value of a is equal to

=

The real part of  is

If y' = x-y/x+y, then its solution is

The solution of the equation cosylog(secx+tanx)dx=cosxlog(secy+tany)dy is

(d²y/dx²)² + x(dy/dx)³ is a differential equation of

If and f 0 = 0 then f ′ 0 is

Integrating factor of dy/dx+y/x=x³-3 is

For real values of x the minimum value of [(1-x+x²)/(1+x+x²)] is

If ∫e^xsinx dx =(1/2)e^x(a+c), then a=

∫ (sin ^-1 x + cos⁻¹ x)   d x = ?

The solution of sin^-1(2a/1 + a²) - cos^-1 (1 - b²/1 + b²) = tan^-1(2x/1 - x²) is :

The value of  

If

 and  , then which one of the following is true ?

If , then the values of k, a, b are respectively

If ²ⁿC₃:ⁿC₂=44:3.For which value of r, ⁿC_r=15?

One hundred identical coins, each with probability p, of showing up heads are tossed. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of the heads showing in 51 coins, then the value of p is

India plays two matches each with Australia and Pakistan. The probability of India getting points 0,1,2 are 0.45, 0.05, 0.50 . Find the probability of India getting at least 7 points in the series

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is

If in a , then

The sum of the series 0.4 + 0.004 + 0.00004 + .... ∞ is

Consider the following statements:
1. Mode can be computed from histogram
2. Median is not independent of change of scale
3. Variance is independent of change of origin and scale.
Which of these is/are correct?

Covariance (x, y) between x and y if ∑x = 15, ∑y = 40, ∑xy = 110, n = 5 is

If the product of roots of the equation mx²+6x+(2m-1)=0 is -1, then the value of m is

If x²+2x+2xy+my-3 has two rational factors the value of m is

The direction cosines of the normal to the plane 6x-3y-2z=1 are

If P be the (2,6,3), then the equation of the plane thro' P at right angles to OP,O being the origin, is

The equation
3(x² + y²) + 5x - 7y - 2 = 0 is represents

The general solution of tan3x=1 is

The radius of the circle inscribed in the triangle formed by lines x = 0, y = 0,
4x + 3y - 24 = 0 is

The median AD of the triangle ABC is bisected at E, BE meets AC in F, than AF:AC =

If p=i-2j+3k and q=3i+j+2k, then a vector r which is a linear combination of p and q and perpendicular to q is