Mathematics questions
18011 published questions with worked solutions.
- If A(1, −1, 2), B(5, 7, −6), C(3, 4, −10) and D(−1, −4, −2) are the vertices of a quadrilateral ABCD, then its area is:
- If the line 2 - x 3 = 3y - 2 4 + 1 = 4 - z makes a right angle with the line x + 3 3 = 1 - 2y 6 = 5 - z 7 , then 4λ + 9μ is equal...
- If the constant term in the expansion of (1 + 2x - 3x^3) ( 32x^2 - 1 3x )^9 is p, then 108p is equal to
- The area of one region enclosed by the parabolas y = x² − 5x and y = 7x − x² is __________.
- Let f be a differentiable function in the interval (0, ∞) such that f(1) = 1 and _ t x t^2f(x) - x^2f(t) t - x = 1 for each x >...
- Let a_1, a_2, a_3, be in an arithmetic progeression of positive terms. Let A_k = a_1^2 - a_2^2 + a_3^2 - a_4^2 + + a_ 2k-1 ^2 -...
- Let a = i - 3 j + 7 k, b = 2 i - j + k and c be a vector such that ( a + 2 b) c = 3( c a). If a c = 130, then b c is equal to...
- The number of distinct real roots of the equation |x||x + 2| − 5|x + 1| − 1 = 0 is __________.
- Suppose AB is a focal chord of the parabola y² = 12x of length l and slope m < √3. If the distance of the chord AB from the...
- Let f : [−1, 2] → R be given by f(x) = 2x² + x + [x²] − [x], where [t] denotes the greatest integer less than or equal to t. The...
- The differential equation of the family of circles passing the origin and having center at the line y = x is:
- Let S_1 = z ∈ C : |z| ≤ 5 , S_2 = z C : Im ( z + 1 - 3i 1 - 3i ) 0 and S_3 = z ∈ C : Re(z) ≥ 0 . Then the area of region S_1 ∩...
- The area enclosed between the curves y = x|x| and y = x − |x| is:
- Let a = 2 i + 5 j - k, b = 2 i - 2 j + 2 k and c be three vectors such that ( c + i) ( a + b + i) = a ( c + i), a c = -29, then c...
- Consider three vectors a, b, c. Let | a| = 2, | b| = 3 and a = b c. If α ∈ [0, 3 ] is the angle between the vectors b and c, then...
- Let A(−1, 1) and B(2, 3) be two points and P be a variable point above the line AB such that the area of ΔPAB is 10. If the locus...
- Let (α, β, γ) be the image of the point (8, 5, 7) in the line x - 1 2 = y + 1 3 = z - 2 5 . Then α + β + γ is equal to
- If the constant term in the expansion of ( [5] 3 x + 2x [3] 5 )^ 12 , x ≠ 0, is α × 2⁸ × [5] 3 , then 25α is equal to:
- Let f, g : R → R be defined as: f(x) = |x − 1| and g(x) = cases e^x, & x 0 x + 1, & x 0 cases . Then the function f(g(x)) is
- Let the circle C_1: x² + y² − 2(x + y) + 1 = 0 and C_2 be a circle having centre at (−1, 0) and radius 2. If the line of the...