Mathematics questions
18011 published questions with worked solutions.
- Let a = i + j + k, b = - i - 8 j + 2 k and c = 4 i + c_2 j + c_3 k, be three vectors such that b a = c a. If the angle between...
- If dx dy = 1 + x - y^2 y , x(1) = 1, then 5x(2) is equal to ______.
- Let f : (0, ∞) → R and F(x) = _0^xtf(t)dt. If F(x^2) = x^4 + x^5, then _ r=1 ^ 12 f(r^2) is equal to __________ .
- Three points O(0, 0), P(a, a²), Q(−b, b²), a > 0, b > 0, are on the parabola y = x². Let S_1 be the area of the region bounded by...
- Let S = z ∈ C : |z − 1| = 1 and ( 2 - 1)(z + z) - i(z - z) = 2 2 . Let z_1, z_2 ∈ S be such that |z_1| = _ z S |z| and |z_2| = _...
- Let x^2 a^2 + y^2 b^2 = 1, a > b be an ellipse, whose eccentricity is 1 2 and the length of the latusrectum is 14 . Then the...
- For 0 < θ < π/2, if the eccentricity of the hyperbola x^2 - y^2 ^2 = 5 is 7 times eccentricity of the ellipse x^2 ^2 + y^2 = 5,...
- 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...