Mathematics questions
18011 published questions with worked solutions.
- The square of the distance of the point ( 15 7 , 32 7 ,7 ) from the line x+1 3 = y+3 5 = z+5 7 in the direction of the vector i...
- The area of the region bounded by the curves x(1+y^2)=1 and y^2=2x is :
- Let A= bmatrix 1 2 & -2 0 & 1 bmatrix and P= bmatrix & - & bmatrix , θ > 0. If B=PAP^T, C=P^TB^ 10 P and the sum of the diagonal...
- If f(x) = 1 x^ 1/4 (1+x^ 1/4 ) dx, f(0) = –6, then f(1) is equal to:
- Let f : R → R be a twice differentiable function such that f(2) = 1. If F(x) = xf(x) for all x ∈ R, _0^2 xF'(x)dx = 6 and _0^2...
- Let [x] denote the greatest integer less than or equal to x. Then domain of f(x)= ^ -1 (2[x]+1) is :
- If _ r=1 ^ 13 1 ( 4 +(r-1) 6 ) ( 4 + r 6 ) =a 3+b, a, b ∈ Z, then a^2+b^2 is equal to:
- Two equal sides of an isosceles triangle are along – x + 2y = 4 and x + y = 4. If m is the slope of its third side, then the sum,...
- Let the coefficients of three consecutive terms T_r, T_ r+1 and T_ r+2 in the binomial expansion of (a+b)^ 12 be in a G.P. and...
- If A and B are the points of intersection of the circle x^2+y^2-8x=0 and the hyperbola x^2 9 - y^2 4 =1 and a point P moves on...
- Let f(x)= _ n _ r=0 ^n ( (x/2^ r+1 )+ ^3(x/2^ r+1 ) 1- ^2(x/2^ r+1 ) ). Then _ x 0 e^x-e^ f(x) (x-f(x)) is equal to ____.
- The interior angles of a polygon with n sides, are in an A.P. with common difference 6°. If the largest interior angle of the...
- If y = y(x) is the solution of the differential equation, 4-x^2 dy dx = ( ( ^ -1 ( x 2 ) )^2-y ) ^ -1 ( x 2 ), -2 x 2, y(2)= (...
- Let the line x + y = 1 meet the circle x^2 + y^2 = 4 at the points A and B. If the line perpendicular to AB and passing through...
- Let M and m respectively be the maximum and the minimum values of f(x) = vmatrix 1+ ^2 x & ^2 x & 4 4x ^2 x & 1+ ^2 x & 4 4x ^2 x...
- Let ABC be a triangle formed by the lines 7x – 6y + 3 = 0, x + 2y –31 = 0 and 9x –2y–19 = 0, Let the point (h,k) be the image of...
- Let a = 2 i - j + 3 k , b = 3 i - 5 j + k and c be a vector such that a c = c b and ( a + c ).( b + c ) = 168. Then the maximum...
- Let P be the set of seven digit numbers with sum of their digits equal to 11. If the numbers in P are formed by using the digits...
- Let the area of the region (x, y) : 2y x^2 + 3, y + |x| 3, y |x - 1| be A. Then 6A is equal to :
- The least value of n for which the number of integral terms in the Binomial expansion of ( [3] 7 + [12] 11 )^n is 183, is :