Mathematics questions
18011 published questions with worked solutions.
- Let S = x^3+ax^2+bx+c : a,b,c N and a,b,c 20 be a set of polynomials. Then the number of polynomials in S, which are divisible by...
- A bag contains 10 balls out of which k are red and (10-k) are black, where 0 k 10. If three balls are drawn at random without...
- If , , where < , are the roots of the equation x^2 - ( +3)x + 3 = 0 such that 1 - 1 = 1 3 , then the sum of all possible values...
- If ( 1-5 ^2 x ^5 x ^2 x )dx = f(x) + C where C is the constant of integration, then f ( 6 ) - f ( 4 ) is equal to
- Let f be a polynomial function such that f(x^2+1) = x^4+5x^2+2, for all x R. Then _0^3 f(x)dx is equal to
- The area of the region R = (x,y): xy 8, 1 y x^2, x 0 is
- The value of _ x 0 _e ( (ex) (e^2x) (e^ 10 x) ) e^2 - e^ 2 x is equal to
- The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2,3,5,10,11,13,15,21, then...
- Let A,B and C be three 2 2 matrices with real entries such that B = (I+A)^ -1 and A+C = I. If BC = bmatrix 1 & -5 -1 & 2 bmatrix...
- The common difference of the A.P.: a_1,a_2, ,a_m is 13 more than the common difference of the A.P.: b_1,b_2, ,b_n. If b_ 31 =...
- If the distances of the point (1,2,a) from the line x-1 1 = y 2 = z-1 1 along the lines L_1: x-1 3 = y-2 4 = z-a b and L_2: x-1 1...
- For three unit vectors a , b , c satisfying | a - b |^2+| b - c |^2+| c - a |^2 = 9 and |2 a +k b +k c | = 3, the positive value...
- Let y=y(x) be the solution of the differential equation x dy dx - 2y = x^3(2-x^3) ^2 y, x 0. If y(2)=0, then (y(1)) is equal to
- In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms...
- For some (0, 2 ), let the eccentricity and the length of the latus rectum of the hyperbola x^2 - y^2 ^2 = 8 be e_1 and _1,...
- The value of _ r=1 ^ 20 ( ( _0^r x| x|dx ) ) is _____.
- Let PQR be a triangle such that PQ = -2 i - j +2 k and PR = a i +b j -4 k , a,b Z. Let S be the point on QR, which is equidistant...
- Given below two statements : Statement I : 13^ 13 25^ 13 20^ 13 8^ 13 3 is divisible by 7. Statement II : The integral part of...
- Let A be the focus of the parabola y^2 = 8x. Let the line y = mx+c intersect the parabola at two distinct points B and C. If the...
- The probability distribution of a random variable X is given below : | X | 4k | 30 7 k | 32 7 k | 34 7 k | 36 7 k | 38 7 k | 40 7...