Mathematics questions
18011 published questions with worked solutions.
- A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8, and B wins if he throws a...
- Consider the region R = (x, y): x y 9 - 11 3 x^2, x 0 . The area, of the largest rectangle of sides parallel to the coordinate...
- The area of the region (x, y) : x^2 + 4x + 2 y |x + 2| is equal to
- For a statistical data x_1, x_2, ..., x_ 10 of 10 values, a student obtained the mean as 5.5 and _ i=1 ^ 10 x_i^2 = 371. He later...
- For some n 10, let the coefficients of the 5th, 6th and 7th terms in the binomial expansion of (1 + x)^ n+4 be in A.P. Then the...
- The product of all the rational roots of the equation (x^2 - 9x + 11)^2 - (x - 4)(x - 5) = 3, is equal to :
- Let the line passing through the points (–1, 2, 1) and parallel to the line x-1 2 = y+1 3 = z 4 intersect the line x+2 3 = y-3 2...
- Let the lines 3x - 4y - = 0, 8x - 11y - 33 = 0, and 2x - 3y + = 0 be concurrent. If the image of the point (1, 2) in the line 2x...
- If the system of equations 2x – y + z = 4 5x + λy + 3z = 12 100x – 47y + μz = 212, has infinitely many solutions, then μ – 2λ is...
- Let f be a differentiable function such that 2(x + 2)^2 f(x) - 3(x + 2)^2 = 10 _0^x (t+2)f(t) , dt, x 0. Then f(2) is equal to...
- Let A be a 3 × 3 matrix such that X^T AX = O for all non-zero 3 × 1 matrices X = pmatrix x pmatrix . If A pmatrix 1 1 1 pmatrix =...
- Let S = p_1, p_2, ...., p_ 10 be the set of first ten prime numbers. Let A = S P, where P is the set of all possible products of...
- The equation of the chord, of the ellipse x^2 25 + y^2 16 =1, whose mid-point is (3,1) is :
- The function f : (- , ) (-1,1), defined by f(x)= 2^x-2^ -x 2^x+2^ -x is :
- If > > > 0, then the expression ^ -1 + (1+ ^2) ( - ) + ^ -1 + (1+ ^2) ( - ) + ^ -1 + (1+ ^2) ( - ) is equal to :
- Let f : (0, ) R be a function which is differentiable at all points of its domain and satisfies the condition x^2f'(x) = 2xf(x) +...
- Let A = x (0, )- 2 : _ (2/ ) | x| + _ (2/ ) | x| = 2 and B = x 0 : x ( x -4)-3| x -2|+6=0 . Then n(A B) is equal to :
- Let [x] denote the greatest integer function, and let m and n respectively be the numbers of points, where the function f(x) =...
- In an arithmetic progression, if S_ 40 = 1030 and S_ 12 = 57, then S_ 30 - S_ 10 is equal to :
- If 7 = 5 + 1 7 (5+ ) + 1 7^2 (5+2 ) + 1 7^3 (5+3 ) + , then the value of is :