Mathematics questions
18011 published questions with worked solutions.
- The set of all values of k for which ( ^ -1 x)^ 3 + ( ^ -1 x)^ 3 = k ^ 3 , x ℝ, is the interval :
- Let S = n : 1 n 50 and n is odd . Let a S and A = vmatrix 1&0&a -1&1&0 -a&0&1 vmatrix . If _ a S ( adj A) = 100 , then is equal...
- For the function f(x) = 4 _ e (x - 1) - 2x^ 2 + 4x + 5, x > 1, which one of the following is NOT correct ?
- If the tangent at the point (x_ 1 , y_ 1 ) on the curve y = x^ 3 + 3x^ 2 + 5 passes through the origin, then (x_ 1 , y_ 1 ) does...
- The sum of absolute maximum and absolute minimum values of the function f(x) = |2x^ 2 + 3x − 2| + sin x cos x in the interval [0,...
- If a_ i _ i=1 ^ n , where n is an even integer, is an arithmetic progression with common difference 1, and _ i=1 ^na_i = 192, _...
- If x = x(y) is the solution of the differential equation y dx/dy = 2x + y^ 3 (y + 1)e^ y , x(1) = 0 ; then x(e) is equal to
- Let x - 2y = be a tangent to the hyperbola a^ 2 x^ 2 - y^ 2 = b^ 2 . Then ( /a)^ 2 - ( /b)^ 2 is equal to :
- Let a , b be unit vectors. If c be a vector such that the angle between a and c is /12, and b = c + 2( c a ), then |6 c |^ 2 is...
- If a random variable X follows the Binomial distribution B(33, p) such that 3P(X = 0) = P(X = 1), then the value of P(X=15)...
- The domain of the function f(x) = ^ -1 ( x^2-5x+6 x^2-9 ) _e(x^2-3x+2) is -
- Let S = [- , ] - /2 : sin tan + tan = sin 2 . If T = _ S cos 2 , then T + n(S) is equal to -Not in JEE Main syllabus
- The number of choices for , , , , such that (p q) ((p ~q) ((~p) q)) is a tautology, is -Not in JEE syllabus
- In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks...
- Let A(3/ a , a ), a > 0, be a fixed point in the xy-plane. The image of A in y-axis be B and the image of B in x-axis be C. If...
- Let a line having direction ratios 1, −4, 2 intersect the lines (x − 7)/3 = (y − 1)/−1 = (z + 2)/1 and x/2 = (y − 7)/3 = z/1 at...
- The number of points where the function f(x) = cases |2x^2 - 3x - 7|, & x -1 [4x^2 - 1], & -1 < x < 1 |x+1| + |x-2|, & x 1 cases...
- Let _ 0 x 2 9 - x^2 5 - x = and _ 0 x 2 9 - x^2 5 - x = . If _ - 83 ^ 2 -1 9-x^2 5-x , x dx = _1 + _2 _e ( 8 15 ) then _ 1 + _ 2...
- If two tangents drawn from a point ( , ) lying on the ellipse 25x^ 2 + 4y^ 2 = 1 to the parabola y^ 2 = 4x are such that the...
- Let S be the region bounded by the curves y = x^ 3 and y^ 2 = x. The curve y = 2|x| divides S into two regions of areas R_ 1 and...