Mathematics questions
18011 published questions with worked solutions.
- Each of the angles and that a given line makes with the positive y and z-axes, respectively, is half of the angle that this line...
- If the four distinct points (4, 6), (–1, 5), (0, 0) and (k, 3k) lie on a circle of radius r, then 10k + r^2 is equal to
- The sum 1 + 1+3 2! + 1+3+5 3! + 1+3+5+7 4! + upto terms, is equal to
- The number of solutions of the equation (4- 3 ) x - 2 3 ^2 x = -4 1+ 3 , x [-2 , 5 2 ] isNot in JEE Main syllabus
- Let A = –2, –1, 0, 1, 2, 3 . Let R be a relation on A defined by xRy if and only if y = x, 1 . Let l be the number of elements in...
- The distance of the point (7, 10, 11) from the line x-4 1 = y-4 0 = z-2 3 along the line x-9 2 = y-13 3 = z-17 6 is
- Consider the lines x(3 + 1) + y(7 + 2) = 17 + 5, being a parameter, all passing through a point P. One of these lines (say L) is...
- If z_1, z_2, z_3 C are the vertices of an equilateral triangle, whose centroid is z_0, then _ k=1 ^ 3 (z_k - z_0)^2 is equal to
- The area of the region (x, y) : |x-y| y 4 x is
- Let y = y(x) be the solution of the differential equation dy dx + 3( ^2 x)y + 3y = ^2 x, y(0) = 1 3 + e^3. Then y ( 4 ) is equal...
- Let C be the circle of minimum area enclosing the ellipse E : x^2 a^2 + y^2 b^2 = 1 with eccentricity 1 2 and foci( 2, 0). Let...
- If the equation of the hyperbola with foci (4, 2) and (8, 2) is 3x^2 - y^2 - x + y + = 0, then + + is equal to _____.
- Let I be the identity matrix of order 3 × 3 and for the matrix A = bmatrix & 2 & 3 4 & 5 & 6 7 & -1 & 2 bmatrix , |A| = -1. Let B...
- If _ x 0 ( x x )^ 1 x^2 = p, then 96 _e p is equal to ______.
- Let a = i + 2 j + k , b = 3 i - 3 j + 3 k , c = 2 i - j + 2 k and d be a vector such that b d = c d and a . d = 4. Then | a d |^2...
- If _ r=1 ^ 9 ( r+3 2^r ). ^9C_r = ( 3 2 )^9 - , , N, then ( + )^2 is equal to
- Let a line passing through the point (4, 1, 0) intersect the line L_1 : x-1 2 = y-2 3 = z-3 4 at the point A(α, β, γ) and the...
- A line passing through the point P( 5, 5) intersects the ellipse x^2 36 + y^2 25 = 1 at A and B such that (PA).(PB) is maximum....
- Let A be a matrix of order 3 × 3 and |A| = 5. If |2 adj (3A adj (2A))| = 2^ .3^ .5^ , , , N, then + + is equal to
- Let f(x) = cases (1+ax)^ 1/x , & x<0 1+b, & x=0 (x+4)^ 1/2 -2 (x+c)^ 1/3 -2 , & x>0 cases be continuous at x = 0. Then e^abc is...