Practice questions
88551 published questions with worked solutions.
- Let f : R → R and g : R → R be defined as f(x) = cases _e x, & x > 0 e^ -x , & x 0 cases and g(x) = cases x, & x 0 e^x, & x < 0...
- Let the median and the mean deviation about the median of 7 observation 170, 125, 230, 190, 210, a, b be 170 and 205 7...
- If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any...
- If the system of equations 2x + 3y − z = 5, x + αy + 3z = −4, 3x − y + βz = 7 has infinitely many solutions, then 13αβ is equal...
- A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found...
- The value of the integral _0^ /4 x ,dx ^4(2x) + ^4(2x) equals:
- Let 3, a, b, c be in A.P. and 3, a − 1, b + 1, c + 9 be in G.P. Then, the arithmetic mean of a, b and c is:
- If 5f(x) + 4f ( 1x ) = x^2 - 2, ∀ x ≠ 0 and y = 9x²f(x), then y is strictly increasing in:
- Let a = -5 i + j - 3 k, b = i + 2 j - 4 k and c = ((( a b) i) i) i. Then c (- i + j + k) is equal to:
- If A = bmatrix 2 & 1 -1 & 2 bmatrix , B = bmatrix 1 & 0 1 & 1 bmatrix , C = ABA^T and X = A^TC^2A, then det X is equal to:
- The area enclosed by the curves xy + 4y = 16 and x + y = 6 is equal to:
- If the shortest distance between the lines x - -2 = y - 2 1 = z - 1 1 and x - 3 1 = y - 1 -2 = z - 2 1 is 1, then the sum of all...
- Let f : R → R be define as: f(x) = cases a - b 2x x^2 , & x < 0 x^2 + cx + 2, & 0 x 1 2x + 1, & x > 1 cases . If f is continuous...
- Let y = y(x) be the solution of the differential equation dy dx = 2x(x + y)^3 - x(x + y) - 1, y(0) = 1. Then ( 1 2 + y ( 1 2 )...
- Let C : x² + y² = 4 and C′ : x² + y² − 4λx + 9 = 0 be two circles. If the set of all values of λ so that the circles C and C′...
- If x = x(t) is the solution of the differential equation (t + 1)dx = (2x + (t + 1)^4)dt, x(0) = 2, then, x(1) equals _____.
- Let P = z ∈ C: |z + 2 − 3i| ≤ 1 and Q = z ∈ C: z(1 + i) + z(1 − i) ≤ −8 . Let in P ∩ Q, |z − 3 + 2i| be maximum and minimum at...
- The number of elements in the set S = (x, y, z) : x, y, z ∈ ℤ, x + 2y + 3z = 42, x, y, z ≥ 0 equal ______.
- Let 3, 7, 11, 15, …, 403 and 2, 5, 8, 11, …, 404 be two arithmetic progressions. Then the sum of the common terms in them, is...
- Let A = 1, 2, 3, …, 20 . Let R_1 and R_2 two relation on A such that R_1 = (a, b) : b is divisible by a , R_2 = (a, b) : a is an...