Mathematics questions
18011 published questions with worked solutions.
- Let A = (x,y) R R|2x^2+2y^2-2x-2y=1 , B = (x,y) R R|4x^2+4y^2-16y-7=0 and C = (x,y) R R|x^2+y^2-4x-2y+5 r^2 . Then the minimum...
- For real numbers and , consider the following system of linear equations : x+y-z=2, x+2y+ =1, 2x-y+z= . If the system has...
- Let a = i + j + k , b and c = j - k be three vectors such that a b = c and a . b =1. If the length of projection vector of the...
- If _3 2, _3(2^x-5), _3 (2^x- 7 2 ) are in an arithmetic progression, then the value of x is equal to _____.
- Let the domain of the function f(x)= _4( _5( _3(18x-x^2-77))) be (a, b). Then the value of the integral _a^b ^3x ( ^3x+...
- Let f(X)= vmatrix ^2x&-2+ ^2x& 2x 2+ ^2x& ^2x& 2x ^2x& ^2x&1+ 2x vmatrix , x [0, ]. Then the maximum value of f(X) is equal to...
- Let F : [3, 5] R be a twice differentiable function on (3, 5) such that F(X)=e^ -X _3^x(3t^2+2t+4F'(t))dt. If F'(4)= e^ -224 (e^...
- Let a plane P pass through the point (3, 7, –7) and contain the line, x-2 -3 = y-3 -3 = z+2 1 . If distance of the plane P from...
- If y = y(x), y [0, 2 ) is the solution of the differential equation sec y dy dx – sin(x+y) – sin(x–y) = 0, with y(0)=0, then 5y'...
- Let f : [0, 3] R be defined by f(x) = min x–[x], 1+[x]–x where [x] is the greatest integer less than or equal to x. Let P denote...
- The point P(a,b) undergoes the following three transformations successively : (a) reflection about the line y = x. (b)...
- Let ^ 10 C_s(25^ (s-1) +7)×(5^ (s-1) +1)^ -1 = 180, is: A possible value of 'x', for which the ninth term in the expansion of 3^...
- For real number and 0, if the point of intersection of the straight lines x- 1 = y-1 2 = z-1 3 and x-4 = y-6 3 = z-7 3 , lines on...
- Let C be the set of all complex numbers. Let S_1 = z : |z-2| 1 and S_2 = z : z(1-i) + z(1-i) 4 . Then, the maximum value of |z- 5...
- A student appeared in a examination consisting of 8 true–false type question. The student guesses the answers with equal...
- If ( 9 ), x, ( 7 18 ) are in arithmetic progression and ( 9 ), y, ( 5 18 ) are also in arithmetic progression, then |x – 2y| is...
- Let the mean and variance of the frequency distribution x: x_1=2, x_2=6, x_3=8, x_4=9 f: 4, 4, , be 6 and 6.8 respectively. If...
- The area of the region bounded by y – x = 2 and x^2 = y is equal to :-
- Let y = y(x) be the solution of the differential equation (x-x^3)dy=(y+yx^2-3x^4)dx, x > 2. If y(3) = 3, then y(4) is equal to :
- The value of _ x 0 ( x [8] 1- x - [8] 1+ x ) is equal to :