Mathematics questions
18011 published questions with worked solutions.
- _ x /4 (8 2 - ( x + sin x)^ 7 )/( 2 - 2 sin 2x) is equal to
- _ n (1/2^ n )(1/ 1 - 1/2^ n + 1/ 1 - 2/2^ n + 1/ 1 - 3/2^ n + ... + 1/ 1 - (2^ n - 1)/2^ n ) is equal to
- If A and B are two events such that P(A) = 1/3, P(B) = 1/5 and P(A B) = 1/2, then P(A|B') + P(B|A') is equal to
- Let the point P( , ) be at a unit distance from each of the two lines L_ 1 : 3x − 4y + 12 = 0 and L_ 2 : 8x + 6y + 11 = 0. If P...
- Let a smooth curve y = f(x) be such that the slope of the tangent at any point (x, y) on it is directly proportional to (−y)/x....
- If the ellipse x^ 2 /a^ 2 + y^ 2 /b^ 2 = 1 meets the line x/7 + y/(2 6 ) = 1 on the x-axis and the line x/7 − y/(2 6 ) = 1 on the...
- The tangents at the points A(1, 3) and B(1, −1) on the parabola y^ 2 - 2x - 2y = 1 meet at the point P. Then the area (in unit^ 2...
- Let the foci of the ellipse x^ 2 /16 + y^ 2 /7 = 1 and the hyperbola x^ 2 /144 - y^ 2 / = 1/25 coincide. Then the length of the...
- A plane E is perpendicular to the two planes 2x − 2y + z = 0 and x − y + 2z = 4, and passes through the point P(1, −1, 1). If the...
- The shortest distance between the lines (x + 7)/(−6) = (y − 6)/7 = z and (7 − x)/2 = y − 2 = z − 6 is
- Let a = i - j + 2 k and let b be a vector such that a b = 2 i - k and a b = 3. Then the projection of b on the vector a - b is
- If the mean deviation about median for the number 3, 5, 7, 2k, 12, 16, 21, 24 arranged in the ascending order, is 6 then the...
- 2 ( /22) (3 /22) (5 /22) (7 /22) (9 /22) is equal to
- Let A = 1, 2, 3, 4, 5, 6, 7 . Define B = T ⊆ A : either 1 ∉ T or 2 T and C = T ⊆ A : T the sum of all the elements of T is a...
- Let f(x) be a quadratic polynomial with leading coefficient 1 such that f(0) = p, p 0, and f(1) = 1/3. If the equations f(x) = 0...
- The sum of the maximum and minimum values of the function f(x) = |5x − 7| + [x^ 2 + 2x] in the interval [5/4, 2], where [t] is...
- Let the area enclosed by the x-axis, and the tangent and normal drawn to the curve 4x^ 3 - 3xy^ 2 + 6x^ 2 - 5xy - 8y^ 2 + 9x + 14...
- The total number of functions, f : 1, 2, 3, 4 1, 2, 3, 4, 5, 6 such that f(1) + f(2) = f(3), is equal to :
- For n N, let S_n = z C : |z − 3 + 2i| = n/4 and T_n = z C : |z − 2 + 3i| = 1/n . Then the number of elements in the set n N : S_n...
- The number of (0, 4 ) for which the system of linear equations 3( 3 )x - y + z = 2 3( 2 )x + 4y + 3z = 3 6x + 7y + 7z = 9 has no...