Mathematics questions
18011 published questions with worked solutions.
- (2 ^ -1 (1/5) + ^ -1 ( 5 /2) + 2 ^ -1 (1/8)) is equal to :
- The statement (~(p ~q)) q is :Not in JEE syllabus
- If for some p, q, r R, not all have same sign, one of the roots of the equation (p^ 2 + q^ 2 )x^ 2 - 2q(p + r)x + q^ 2 + r^ 2 = 0...
- The number of 5-digit natural numbers, such that the product of their digits is 36, is _____.
- The series of positive multiples of 3 is divided into sets: 3 , 6, 9, 12 , 15, 18, 21, 24, 27 , _____ Then the sum of the...
- If the coefficients of x and x^ 2 in the expansion of (1 + x)^p(1 − x)^q, p, q 15, are −3 and −5 respectively, then the...
- Let the function f(x) = 2x^ 2 − log_e x, x > 0, be decreasing in (0, a) and increasing in (a, 4). A tangent to the parabola y^ 2...
- Let Q and R be two points on the line (x + 1)/2 = (y + 2)/3 = (z − 1)/2 at a distance 26 from the point P(4, 2, 7). Then the...
- Let f : ℝ ℝ be defined by f(x) = x − 1 and g : ℝ − 1, −1 ℝ be defined by g(x) = x^ 2 /(x^ 2 - 1). Then the function f∘g is:
- If the system of equations x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = has infinitely many solutions, then the ordered pair ( ,...
- If A = _ n=1 ^ 1 (3+(-1)^n)^n and B = _ n=1 ^ (-1)^n (3+(-1)^n)^n , then A/B is equal to :
- _ x 0 ( x) - x x^4 is equal to -
- Let f(x) = min 1, 1 + x sin x , 0 x 2 . If m is the number of points, where f is not differentiable and n is the number of...
- The area of the region bounded by y^ 2 = 8x and y^ 2 = 16(3 - x) is equal to
- If 1x 1-x 1+x dx = g(x) + c, g(1) = 0, then g(1/2) is equal to
- If the solution of the differential equation dy/dx + e^ x (x^ 2 - 2)y = (x^ 2 - 2x)(x^ 2 - 2)e^ 2x satisfies y(0) = 0, then the...
- If m is the slope of a common tangent to the curves x^ 2 /16 + y^ 2 /9 = 1 and x^ 2 + y^ 2 = 12, then 12m^ 2 is equal to :
- The locus of the mid-point of the line segment joining the point (4, 3) and the points on the ellipse x^ 2 + 2y^ 2 = 4 is an...
- The normal to the hyperbola x^ 2 /a^ 2 - y^ 2 /9 = 1 at the point (8, 3 3 ) on it passes through the point :
- If the plane 2x + y − 5z = 0 is rotated about its line of intersection with the plane 3x − y + 4z − 7 = 0 by an angle of /2, then...