Mathematics questions
18011 published questions with worked solutions.
- Let f : S S where S = (0, ) be a twice differentiable function such that f(x + 1) = xf(x). If g : S R be defined as g(x) =...
- Let P(x) = x^2 + bx + c be a quadratic polynomial with real coefficients such that _0^1P(x)dx=1 and P(x) leaves remainder 5 when...
- If the foot of the perpendicular from point (4, 3, 8) on the line L_1: x-a = y-2 3 = z-b 4 , 0 is (3, 5, 7), then the shortest...
- Let C_1 be the curve obtained by the solution of differential equation 2xy dy dx =y^2-x^2, x > 0. Let the curve C_2 be the...
- Let a = i +2 j -3 k and b =2 i -3 j +5 k . If r a = b r , r .( i +2 j + k )=3 and r .(2 i +5 j - k )=-1, R, then the value of +|...
- If the distance of the point (1, –2, 3) from the plane x + 2y – 3z + 10 = 0 measured parallel to the line, x-1 3 = 2-y m = z+3 1...
- Consider the statistics of two sets of observations as follows : Observation I : Size 10, Mean 2, Variance 2 Observation II :...
- For real numbers , , and , if (x^2-1)+ ^ -1 ( x^2+1 x ) (x^4+3x^2+1)+ ^ -1 ( x^2+1 x ) dx= _e ( ^ -1 ( x^2+1 x ) )+ ^ -1 (...
- Let f : R R and g : R R be defined as f(x)= cases x+a, & x<0 |x-1|, & x 0 cases and g(x)= cases x+1, & x<0 (x-1)^2+b, & x 0 cases...
- Let 1 16 , a and b be in G.P. and 1 a , 1 b , 6 be in A.P., where a, b > 0. Then 72(a + b) is equal to ________.
- In , the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of is 30 cm ^2 and R and r are respectively the...Not in JEE syllabus
- Let c be a vector perpendicular to the vectors a = i + j - k and b = i +2 j + k . If c .( i + j +3 k )=8 then the value of c .( a...
- Let S_n(x)= _ a^ 1/2 x+ _ a^ 1/3 x+ _ a^ 1/6 x+ _ a^ 1/11 x+ _ a^ 1/18 x+ _ a^ 1/27 x+ up to n-terms, where a > 1. If S_ 24...
- The number of elements in the set x R:(|x|.3)|x+4|=6 is equal to :
- Let a vector i + j be obtained by rotating the vector 3 i + j by an angle 45° about the origin in counterclockwise direction in...
- If for a > 0, the feet of perpendiculars from the points A(a, –2a, 3) and B(0, 4, 5) on the plane x+my+nz=0 are points C(0, –a,...
- Consider three observations a, b and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of...
- If for x (0, 2 ), _ 10 x+ _ 10 x=-1 and _ 10 ( x+ x)= 1 2 ( _ 10 n-1), n > 0, then the value of n is equal to :
- Let, A= bmatrix i&-i -i&i bmatrix , i= -1 . Then the system of linear equations A^8 bmatrix x bmatrix = bmatrix 8 64 bmatrix has -
- If the three normals drawn to the parabola, y^2=2x pass through the point (a, 0) a 0, then 'a' must be greater than :