Practice questions
88551 published questions with worked solutions.
- If the plane 2x - y + 2z + 3 = 0 has the distances 1 3 and 2 3 units from the planes 4x - 2y + 4z + = 0 and 2x - y + 2z + = 0,...
- Let f(x) = _e( x), (0 < x < ) and g(x) = ^ -1 (e^ -x ), (x 0). If α is a positive real number such that a = (f g)'( ) and b = (f...
- The angles A, B and C of a triangle ABC are in A.P. and a : b = 1 : 3. If c = 4 cm, then the area (in sq. cm) of this triangle is:Not in JEE syllabus
- Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is:
- Let λ be a real number for which the system of linear equations x + y + z = 6, 4x + y - z = - 2, 3x + 2y - 4z = -5 has infinitely...
- If z and w are two complex numbers such that |zw| = 1 and (z) - (w) = 2 , then:
- The smallest natural number n, such that the coefficient of x in the expansion of (x^2 + 1 x^3 )^n is ^nC_ 23 , is:
- The sum of the real roots of the equation vmatrix x & -6 & -1 2 & -3x & x-3 -3 & 2x & x+2 vmatrix = 0, is equal to:
- If 5x + 9 = 0 is the directrix of the hyperbola 16x^2 - 9y^2 = 144, then its corresponding focus is:
- The area (in sq. units) of the region bounded by the curves y = 2^x and y = |x + 1|, in the first quadrant is:
- If the line ax + y = c, touches both the curves x^2 + y^2 = 1 and y^2 = 4 2 ,x, then |c| is equal to:
- The integral _ /6 ^ /3 ^ 2/3 x , cosec ^ 4/3 x ,dx is equal to:
- Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar...
- If x^5e^ -x^2 dx = g(x)e^ -x^2 + c, where c is a constant of integration, then g(−1) is equal to:
- Let y = y(x) be the solution of the differential equation, dy dx + y x = 2x + x^2 x, x (- 2 , 2 ), such that y(0) = 1. Then:
- The tangent and normal to the ellipse 3x^2 + 5y^2 = 32 at the point P(2, 2) meet the x-axis at Q and R, respectively. Then the...
- If the tangent to the curve y = x x^2-3 , x R , (x 3), at a point (α, β) ≠ (0, 0) on it is parallel to the line 2x + 6y - 11 = 0,...
- Lines are drawn parallel to the line 4x - 3y + 2 = 0, at a distance 3 5 from the origin. Then which one of the following points...
- The negation of the Boolean expression s ( r s) is equivalent to:Not in JEE syllabus
- If both the mean and the standard deviation of 50 observations x_1, x_2, , x_ 50 are equal to 16, then the mean of (x_1 - 4)^2,...