Mathematics questions
18011 published questions with worked solutions.
- The line y = x + 1 meets the ellipse x^ 2 /4 + y^ 2 /2 = 1 at two points P and Q. If r is the radius of the circle with PQ as...
- Let A = bmatrix 2 & -2 1 & -1 bmatrix and B = bmatrix -2 & 2 -1 & 1 bmatrix , Then the number of elements in the set (n, m) : n,...
- Let f(x) = [2x^ 2 + 1] and g(x) = 2x − 3 for x < 0 and 2x + 3 for x 0. Where [t] is the greatest integer t. Then, in the open...
- The value of b > 3 for which 12 _3^b dx (x^2-1)(x^2-4) = _e ( 49 40 ), is equal to _____.
- If the sum of the co-efficients of all the positive even powers of x in the binomial expansion of (2x^ 3 + 3/x)^ 10 is 5^ 10 - 3^...
- If the mean deviation about the mean of the numbers 1, 2, 3, ......., n, where n is odd, is 5(n + 1)/n, then n is equal to _____.
- Let b = i + j + k , ℝ. If a is a vector such that a b = 13 i - j - 4 k and a b + 21 = 0, then ( b - a ) ( k - j ) + ( b + a ) ( i...
- The total number of three-digit numbers, with one digit repeated exactly two times, is _____.
- Let f(x) = |(x − 1)(x^ 2 - 2x − 3)| + x − 3, x ℝ. If m and M are respectively the number of points of local minimum and local...
- Let the eccentricity of the hyperbola x^ 2 /a^ 2 - y^ 2 /b^ 2 = 1 be 5/4. If the equation of the normal at the point (8/ 5 ,...
- Let l_ 1 be the line in xy-plane with x and y intercepts 1/8 and 1/(4 2 ) respectively and l_ 2 be the line in zx-plane with x...
- Let a circle C touch the lines L_ 1 : 4x - 3y + K_ 1 = 0 and L_ 2 : 4x - 3y + K_ 2 = 0, K_ 1 , K_ 2 ℝ. If a line passing through...
- The value of _0^ e^ x x (1+ ^2x)(e^ x + e^ - x ) dx is equal to :
- Let a, b and c be the length of sides of a triangle ABC such that (a + b)/7 = (b + c)/8 = (c + a)/9. If r and R are the radius of...Not in JEE syllabus
- Let f : ℕ ℝ be a function such that f(x + y) = 2f(x)f(y) for natural numbers x and y. If f(1) = 2, then the value of for which _...
- Let A be a 3 3 real matrix such that A(1, 1, 0)ᵀ = (1, 1, 0)ᵀ, A(1, 0, 1)ᵀ = (−1, 0, 1)ᵀ and A(0, 0, 1)ᵀ = (1, 1, 2)ᵀ. If X = (x_...
- Let f : ℝ ℝ be defined as f(x) = x^ 3 + x - 5. If g(x) is a function such that f(g(x)) = x, ∀ 'x' ℝ, then g'(63) is equal to...
- Consider the following two propositions: P_ 1 : ~(p ~q), P_ 2 : (p ~q) ((~p) q). If the proposition p ((~p) q) is evaluated as...Not in JEE syllabus
- If 1/(2 3^ 10 ) + 1/(2^ 2 3^ 9 ) + … + 1/(2^ 10 3) = K/(2^ 10 3^ 10 ), then the remainder when K is divided by 6 is -
- Let f(x) be a polynomial function such that f(x) + f'(x) + f″(x) = x^ 5 + 64. Then, the value of _ x 1 f(x) x-1 is equal to :