Practice questions
88551 published questions with worked solutions.
- If x_1, x_2, , x_n and 1 h_1 , 1 h_2 , , 1 h_n are two A.P's such that x_3 = h_2 = 8 and x_8 = h_7 = 20, then x_5 h_ 10 equals
- The mean of a set of 30 observations is 75. If each other observation is multiplied by a non-zero number and then each of them is...
- If n is the degree of the polynomial, [ 1 5x^3 + 1 - 5x^3 - 1 ]^8 + [ 1 5x^3 + 1 + 5x^3 - 1 ]^8 and m is the coefficient of x^n...
- Let S be the set of all real values of k for which the system of linear equations x + y + z = 2 2x + y - z = 3 3x + 2y + kz = 4...
- The value of the integral _ - /2 ^ /2 ^4 x (1 + ( 2 + x 2 - x ) )dx is
- An angle between the plane x + y + z = 5 and the line of intersection of the planes, 3x + 4y + z - 1 = 0 and 5x + 8y + 2z + 14 =...
- If a right circular cone having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm²) of...
- If tan A and tan B are the roots of the quadratic equation, 3x^2 - 10x - 25 = 0 then the value of 3 ^2(A + B) - 10 (A + B) (A +...
- Two parabolas with a common vertex and with axes along x-axis and y-axis, respectively, intersect each other in the first...
- Let y = y(x) be the solution of the differential equation dy dx + 2y = f(x), where f(x) = cases 1, & x [0, 1] 0, & otherwise...
- The area (in sq. units) of the region x R : x 0, y 0, y x - 2 and y x , is
- If is one of the angles between the normals to the ellipse, x^2 + 3y^2 = 9 at the points (3 , 3 ) and (-3 , 3 ); (0, 2 ); then 2...
- If (p q) (p r) p q is false, then the truth values of p, q and r are respectivelyNot in JEE syllabus
- The set of all R , for which w = 1 + (1 - 8 )z 1 - z is a purely imaginary number, for all z C satisfying |z| = 1 and Re (z) 1, is
- If a , b and c are unit vectors such that a + 2 b + 2 c = 0 , then | a c | is equal to
- An aeroplane flying at a constant speed, parallel to the horizontal ground, 3 km above it, is observed at an elevation of 60°...
- Let S = ( , ) R R : f(t) = (| |e^ |t| - ) (2|t|), t R , is a differentiable function . Then S is a subset of
- n-digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be...
- A box 'A' contains 2 white, 3 red and 2 black balls. Another box 'B' contains 4 white, 2 red and 3 black balls. If two balls are...
- A body of mass 2kg slides down with an acceleration of 3m/s² on a rough inclined plane having a slope of 30°. The external force...