Mathematics questions
18011 published questions with worked solutions.
- Let n ≥ 2 be a natural number and 0 < < 2. Then ( ^n - )^ 1/n ^ n+1 d is equal to: (where C is a constant of integration)
- If the system of equations x + y + z = 5, x + 2y + 3z = 9, x + 3y + αz = β has infinitely many solutions, then β − α equals:
- An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained...
- Let f: R R be a function such that f(x) = x^3 + x^2f'(1) + xf''(2) + f'''(3), x ∈ R. Then f(2) equals:
- The equation of a tangent to the hyperbola 4x^2 - 5y^2 = 20 parallel to the line x − y = 2 is:
- A point P moves on the line 2x − 3y + 4 = 0. If Q(1, 4) and R(3, −2) are fixed points, then the locus of the centroid of ΔPQR is...
- The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is:
- If _ i=1 ^ 20 ( , ^ 20 C_ i-1 , ^ 20 C_i + ^ 20 C_ i-1 )^3 = k 21 , then k is equal to:
- Consider the quadratic equation (c - 5)x^2 - 2cx + (c - 4) = 0, c ≠ 5. Let S be the set of all integral values of c for which one...
- If the area enclosed between the curves y = kx^2 and x = ky^2, (k > 0), is 1 square unit. Then k is:
- Consider a triangular plot ABC with sides AB = 7 m, BC = 5 m and CA = 6 m. A vertical lamp-post at the mid point D of AC subtends...Not in JEE syllabus
- The shortest distance between the point ( 32, 0 ) and the curve y = x, (x > 0), is:
- Let I = _a^b(x^4 - 2x^2) ,dx. If I is minimum then the ordered pair (a, b) is:
- For each t ∈ R, let [t] be the greatest integer less than or equal to t. Then _ x 1^+ (1 - |x| + |1 - x|) ( 2[1 - x] ) |1 - x|...
- If the line 3x + 4y − 24 = 0 intersects the x-axis at the point A and the y-axis at the point B, then the incentre of the...
- The sum of all values of (0, 2 ) satisfying ^22 + ^42 = 34 is:Not in JEE Main syllabus
- Let A be a point on the line r = (1 - 3 ) i + ( - 1) j + (2 + 5 ) k and B(3, 2, 6) be a point in the space. Then the value of μ...
- Let d ∈ R, and A = bmatrix -2 & 4 + d & ( ) - 2 1 & ( ) + 2 & d 5 & (2 ) - d & (- ) + 2 + 2d bmatrix , θ ∈ [0, 2π]. If the...
- Let f(x) = cases |x|, x^2 , & |x| 2 8 - 2|x|, & 2 < |x| 4 cases . Let S be the set of points in the interval (−4, 4) at which f...
- If the third term in the binomial expansion of (1 + x^ _2x )^5 equals 2560, then a possible value of x is: