Mathematics questions
18011 published questions with worked solutions.
- Among the statements (S1) : If A(5,-1) and B(-2,3) are two vertices of a triangle, whose orthocentre is (0,0), then its third...
- Let a = 2 i - j + k and b = j +2 k , Z be two vectors, Let c = a b and d be a vector of magnitude 2 in yz-plane. If | c | = 53 ,...
- If X= bmatrix X bmatrix is a solution of the system of equations AX=B, where adj A = bmatrix 4 & 2 & 2 -5 & 0 & 5 1 & -2 & 3...
- Let L be the line x+1 2 = y+1 3 = z+3 6 and let S be the set of all points (a,b,c) on L, whose distance from the line x+1 2 = y+1...
- Let P(10,2 15 ) be a point on the hyperbola x^2 a^2 - y^2 b^2 =1, whose foci are S and S'. If the length of its latus rectum is...
- Let , be the roots of the quadratic equation 12x^2-20x+3 =0, Z. If 1 2 | - | 3 2 , then the sum of all possible values of is :
- Let the domain of the function f(x) = _3 _5(7- _2(x^2-10x+85)) + ^ -1 ( | 3x-7 17-x | ) be ( , ]. Then + is equal to :
- Let [ ] denote the greatest integer function, and let f(x) = 2 x, x^2 . Let S = x (-2,2): the function g(x)=|x|[x^2] is...
- Let S and S' be the foci of the ellipse x^2 25 + y^2 9 =1 and P( , ) be a point on the ellipse in the first quadrant. If...
- Let C_r denote the coefficient of x^r in the binomial expansion of (1+x)^n, n N , 0 r n. If P_n = C_0 - C_1 + 2^2 3 C_2 - 2^3 4...
- Let a vector a = 2 i - j + k , >0, make an obtuse angle with the vector b =- ^2 i +4 2 j +4 2 k and an angle , 6 < < 2 , with the...
- Let [ ] be the greatest integer function. If = _0^ 64 (x^ 1/3 -[x^ 1/3 ] )dx, then 1 _0^ ( ^2 ^6 + ^6 )d is equal to ____ .
- Let ( + ) = - 1 10 and ( - ) = 3 8 , where 0< < 3 and 0< < 4 . If 2 = 3(1-r 5 ) 11 (s+ 5 ) , r,s N, then r+s is equal to ____ .
- Suppose a,b,c are in A.P. and a^2, 2b^2, c^2 are in G.P. If a<b<c and a+b+c=1, then 9(a^2+b^2+c^2) is equal to ____ .
- Let S be the set of the first 11 natural numbers. Then the number of elements in A = B S: n(B) 2 and the product of all elements...
- Let the domain of the function f(x) = _3 _5 _7(9x - x^2 - 13) be the interval (m, n). Let the hyperbola x^2 a^2 - y^2 b^2 = 1...
- Let f(x) = (2-x^2) e^x ( 1+x )(1-x)^ 3/2 dx. If f(0) = 0, then f ( 1 2 ) is equal to :
- Let a = - i + j +2 k , b = i - j -3 k , c = a b and d = c a . Then ( a - b ) d is equal to :
- A rectangle is formed by the lines x=0, y=0, x=3 and y=4. Let the line L be perpendicular to 3x+y+6=0 and divide the area of the...
- Let the line y-x=1 intersect the ellipse x^2 2 + y^2 1 =1 at the points A and B. Then the angle made by the line segment AB at...