Mathematics questions
18011 published questions with worked solutions.
- The slope of the line touching both the parabolas y^2 = 4x and x^2 = -32y is
- If [ a b b c c a ] = [ a b c ]^2 then is equal to:
- Let A and B be two events such that P( A B ) = 1 6 , P(A B) = 1 4 and P( A ) = 1 4 , where A stands for the complement of the...
- The locus of the foot of perpendicular drawn from the centre of the ellipse x^2 + 3y^2 = 6 on any tangent to it is:
- If f and g are differentiable functions in [0, 1] satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6, then for some c ]0, 1[:
- Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the...
- If g is the inverse of a function f and f'(x) = 1 1 + x^5 , then g'(x) is equal to:
- If , 0, and f(n) = ^n + ^n and vmatrix 3 & 1 + f(1) & 1 + f(2) 1 + f(1) & 1 + f(2) & 1 + f(3) 1 + f(2) & 1 + f(3) & 1 + f(4)...
- If (10)^9 + 2(11)^1(10)^8 + 3(11)^2(10)^7 + + 10(11)^9 = k(10)^9, then k is equal to:
- The angle between the lines whose direction cosines satisfy the equations + m + n = 0 and ^2 = m^2 + n^2 is -
- The variance of first 50 even natural numbers is:
- If X = 4^n - 3n - 1 : n N and Y = 9(n - 1) : n N , where N is the set of natural numbers, then X Y is equal to:
- If f(x) + 2f ( 1 x ) = 3x, x ≠ 0, and S = x ∈ R : f(x) = f(–x) ; then S :
- A value of θ for which 2 + 3i 1 - 2i is purely imaginary, is :
- If A = bmatrix 5a & -b 3 & 2 bmatrix and A adj A = AA^T, then 5a + b is equal to
- The system of linear equations x + λy – z = 0 λx – y – z = 0 x + y – λz = 0 has a non-trivial solution for
- If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a...
- If the 2^ nd , 5^ th and 9^ th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is
- If the sum of the first ten terms of the series (1 3 5 )^2 + (2 2 5 )^2 + (3 1 5 )^2 + 4^2 + (4 4 5 )^2 + , is 16 5 m, then m is...
- Let p = _ x 0^+ (1 + ^2 x )^ 1 2x then log p is equal to