A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is 1/2, 1/3 and 1/4. Probability that the problem is solved is
Events A, B, C are mutually exclusive events such that P(A) = (3x + 1)/3, P(B) = (x - 1)/4, P(C) = (1 - 2x)/4. The set of possible values of x are in the interval
The number of solution of tan x + sec x = 2 cos x in [0, 2π) is
The negation of the statement "If I become a teacher, then I will open a school" is
A triangle with vertices (4, 0), (-1, -1), (3, 5) is
If the two circles (x-1)2 + (y-3)2 = r2 and x2 + y2 - 8x + 2y + 8 = 0 intersect in two distinct point, then
A plane which passes through the point (3, 2, 0) and the line (x-4)/1 = (y-7)/5 = (z-4)/4 is
The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is:
If 2+3i is one of the roots of the equation 2x3 – 9x2 + kx – 13 = 0, k ∈ R, then the real root of this equation:
Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is:
If the coefficients of the three successive terms in the binomial expansion of (1+x)n are in the ratio 1:7:42, then the first of these terms in the expansion is:
What is the sum of the squares of the roots of the equation x2 + 2x - 143 = 0?
If the difference between the roots of ax2 + bx + c = 0 is 1, then which one of the following is correct?
If α and β are the roots of the equation x2 - q(1+x) - r = 0, then what is (1+α)(1+β) equal to?
A and B are two matrices such that AB = A and BA = B then what is B2 equal to?
If the 2nd, 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:
Let P be the point on the parabola, y2 = 8x which is at a minimum distance from the centre C of the circle, x2 + (y + 6)2 = 1. Then the equation of the circle, passing through C and having its centre at P is:
The system of linear equations
x + λy – z = 0
λx – y – z = 0
x + y – λz = 0
has a non-trivial solution for:
The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal half of the distance between its foci, is:
If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?
If the line, (x-3)/2 = (y+2)/-1 = (z+4)/3, lies in the plane, lx + my – z = 9, then l2 + m2 is equal to:
If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation
cosx + cos2x + cos3x + cos4x = 0 is: