Mathematics questions
18011 published questions with worked solutions.
- Perpendiculars are drawn from points on the line x + 2 2 = y + 1 -1 = z 3 to the plane x + y + z = 3. The feet of perpendiculars...
- Let PR = 3 i + j - 2 k and SQ = i - 3 j - 4 k determine diagonals of a parallelogram PQRS and PT = i + 2 j + 3 k be another...
- Let S_n = _ k=1 ^ 4n (-1)^ k(k+1) 2 k^2. Then S_n can take value(s)
- For 3 × 3 matrices M and N, which of the following statement(s) is (are) **NOT** correct ?
- Let f(x) = x x, x > 0. Then for all natural numbers n, f'(x) vanishes at
- A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular...
- A line l passing through the origin is perpendicular to the lines l_1 : (3 + t) i + (-1 + 2t) j + (4 + 2t) k, - < t < l_2 : (3 +...
- The coefficients of three consecutive terms of (1 + x)^ n+5 are in the ratio 5 : 10 : 14. Then n =
- A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and the sum of the numbers...
- A vertical line passing through the point (h, 0) intersects the ellipse x^2 4 + y^2 3 = 1 at the points P and Q. Let the tangents...
- Consider the set of eight vectors V = a i + b j + c k : a, b, c -1, 1 . Three non-coplanar vectors can be chosen from V in 2^p...
- Let w = 3 + i 2 and P = w^n : n = 1, 2, 3, . Further H_1 = z C : Re z > 1 2 and H_2 = z C : Re z < -1 2 , where C is the set of...
- If 3^x = 4^ x-1 , then x =
- Let ω be a complex cube root of unity with ω ≠ 1 and P = [p_ ij ] be a n × n matrix with p_ ij = ^ i+j . Then P^2 0, when n =
- The function f(x) = 2|x| + |x + 2| - ||x + 2| - 2|x| | has a local minimum or a local maximum at x =
- For a R (the set of all real numbers), a ≠ −1, _ n (1^a + 2^a + + n^a) (n + 1)^ a-1 [(na + 1) + (na + 2) + + (na + n) ] = 1 60...
- Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length 2 7 on y-axis is (are)
- Two lines L_1 : x = 5, y 3 - = z -2 and L_2 : x = , y -1 = z 2 - are coplanar. Then α can take value(s)
- In a triangle PQR, P is the largest angle and P = 1 3 . Further the incircle of the triangle touches the sides PQ, QR and RP at...Not in JEE syllabus
- A line L : y = mx + 3 meets y-axis at E(0, 3) and the arc of the parabola y^2 = 16x, 0 y 6 at the point F(x_0, y_0). The tangent...