Mathematics questions
18011 published questions with worked solutions.
- Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables X and Y respectively...
- The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which...
- If the range of f( ) = ^4 + 3 ^2 ^4 + ^2 , θ ∈ R is [α, β], then the sum of the infinite G.P., whose first term is 64 and the...
- Let = _ r=0 ^ n (4r^2 + 2r + 1) nr and = ( _ r=0 ^ n nr r + 1 ) + 1 n + 1 . If 140 < 2 < 281, then the value of n is ______.
- Let a = 9 i - 13 j + 25 k, b = 3 i + 7 j - 13 k and c = 17 i - 2 j + k be three given vectors. If r is a vector such that r a = (...
- Let the area of the region enclosed by the curve y = min sin x, cos x and the x-axis between x = −π to x = π be A. Then A² is...
- The value of _ x 0 2 ( 1 - x 2x [3] 3x [10] 10x x^2 ) is ________.
- Let a = i + 2 j + 3 k, b = 2 i + 3 j - 5 k and c = 3 i - j + k be three vectors. Let r be a unit vector along b + c. If r a = 3,...
- In an increasing geometric progression of positive terms, the sum of the second and sixth terms is 70 3 and the product of the...
- The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not...
- The sum of all possible values of θ ∈ [−π, 2π], for which 1 + i 1 - 2i is purely imaginary, is equal to:
- If the system of equations x + 4y − z = λ, 7x + 9y + μz = −3, 5x + y + 2z = −1 has infinitely many solutions, then (2μ + 3λ) is...
- If the shortest distance between the lines x - 2 = y - 4 3 = z - 3 4 and x - 2 4 = y - 4 6 = z - 7 8 is 13 29 , then a value of λ...
- If the value of 3 36° + 5 18° 5 36° - 3 18° is a 5 - b c , where a, b, c are natural numbers and gcd(a, c) = 1, then a + b + c is...
- Let y = y(x) be the solution curve of the differential equation sec y dy dx + 2x sin y = x³ cos y, y(1) = 0. Then y(√3) is equal...
- The area of the region in the first quadrant inside the circle x² + y² = 8 and outside the parabola y² = 2x is equal to:
- If the line segment joining the points (5, 2) and (2, a) subtends an angle 4 at the origin, then the absolute value of the...
- Let a = 4 i - j + k, b = 11 i - j + k and c be a vector such that ( a + b) c = c (-2 a + 3 b). If (2 a + 3 b) c = 1670, then |...
- If the function f(x) = 2x³ − 9ax² + 12a²x + 1, a > 0 has a local maximum at x = α and a local minimum x = α², then α and α² are...
- There are three bags X, Y and Z. Bag X contains 5 one-rupee coins and 4 five-rupee coins; Bag Y contains 4 one-rupee coins and 5...