Mathematics questions
18011 published questions with worked solutions.
- Let C be a circle passing through the points A(2, −1) and B(3, 4). The line segment AB is not a diameter of C. If r is the radius...
- Let the normal at the point P on the parabola y^ 2 = 6x pass through the point (5, −8). If the tangent at P to the parabola...
- If the two lines _ 1 : (x − 2)/3 = (y + 1)/(−2), z = 2 and _ 2 : (x − 1)/1 = (2y + 3)/ = (z + 5)/2 are perpendicular, then an...
- Let the plane 2x + 3y + z + 20 = 0 be rotated through a right angle about its line of intersection with the plane x − 3y + 5z =...
- If a b = 1, b c = 2 and c a = 3, then the value of [ a ( b c ), b ( c a ), c ( b a )] is
- Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then...
- The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean,...
- Let f(x) = 2 ^ -1 x + 4 ^ -1 x - 3x^ 2 - 2x + 10, x [−1, 1]. If [a, b] is the range of the function f then 4a − b is equal to :
- The sum of the cubes of all the roots of the equation x^ 4 - 3x^ 3 - 2x^ 2 + 3x + 1 = 0 is _____.
- There are ten boys B_ 1 , B_ 2 , ..., B_ 10 and five girls G_ 1 , G_ 2 , ..., G_ 5 in a class. Then the number of ways of forming...
- Let the common tangents to the curves 4(x^ 2 + y^ 2 ) = 9 and y^ 2 = 4x intersect at the point Q. Let an ellipse, centered at the...
- Let f(x) = max |x + 1|, |x + 2|, ......., |x + 5| . Then _ -6 ^0f(x)dx is equal to _____.
- Let the solution curve y = y(x) of the differential equation (4 + x^ 2 )dy - 2x(x^ 2 + 3y + 4)dx = 0 pass through the origin....
- If ^ 2 (10^ ) (20^ ) (40^ ) (50^ ) (70^ ) = − (1/16)sin(10°), then 16 + ^ -1 is equal to _____.
- Let A = n ℕ : H.C.F. (n, 45) = 1 and let B = 2k : k 1, 2, …, 100 . Then the sum of all the elements of A B is _____.
- The value of the integral 48 ^4 _0^ ( 3 x^2 2 - x^3 ) x 1 + ^2x dx is equal to _____.
- Let A = _ i=1 ^ 10 _ j=1 ^ 10 i, j and B = _ i=1 ^ 10 _ j=1 ^ 10 i, j . Then A + B is equal to _____.
- Let S = (0, 2 ) - /2, 3 /4, 3 /2, 7 /4 . Let y = y(x), x S, be the solution curve of the differential equation dy/dx = 1/(1 + sin...
- If + + =2 , then the system of equations x + (cos ) y + (cos ) z = 0, (cos ) x + y + (cos ) z = 0, (cos ) x + (cos ) y + z = 0...
- Let a , b , c be three vectors mutually perpendicular to each other and same magnitude. If a vector r satisfies, a ( r - b ) a +...