Let z₁ and z₂ be nth roots of unity which subtend a right angle at the origin, then n must be of the form :
The area bounded by the curve y = 4x - x2 and x-axis is
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 ∫exsinx dx =(1/2)ex(a+c), then a=
The solution of sin-1(2a/1 + a2) - cos-1 (1 - b2/1 + b2) = tan-1(2x/1 - x2) is :
∫ (sin -1 x + cos−1 x) d x = ?
The value of
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, nCr=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
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
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
If in a , then
or 2 sin A cos B = cos A sin B + sin A cos B = sin A + B = sin C .
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
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