Practice questions
88551 published questions with worked solutions.
- Let f:R R be such that for all x R (2^ 1+x +2^ 1-x ), f(x) and (3^x+3^ -x ) are in A.P., then the minimum value of f(x) is -
- _ x 0 ( 3x^2+2 7x^2+2 )^ 1/x^2 is equal to -
- If a , b and c are the greatest values of ^ 19 C_p, ^ 20 C_q and ^ 21 C_r respectively, then -
- The number of all 3 × 3 matrices A, with enteries from the set –1, 0, 1 such that the sum of the diagonal elements of AA^T is 3,...
- An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so...
- The sum _ k=1 ^ 20 (1+2+3+ +k) is ___________________.
- The least positive value of 'a' for which the equation, 2x^2+(a-10)x+ 33 2 =2a has real roots is ______________.
- Let the normal at a point P on the curve y^2-3x^2+y+10=0 intersect the y-axis at (0, 3 2 ). If m is the slope of the tangent at P...
- A Carnot engine having an efficiency of 1 10 is being used as a refrigerator. If the work done on the refrigerator is 10 J, the...
- A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00...
- Consider two charged metallic spheres S_1 and S_2 of radii R_1 and R_2, respectively. The electric fields E_1 (on S_1) and E_2...
- Consider a mixture of a n moles of helium gas and 2n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its C_P...
- A particle moves such that its position vector r (t)= t , i + t , j where is a constant and t is time. Then which of the...
- An electron (mass m) with initial velocity v =v_0 i +v_0 j is in an electric field E =-E_0 k . If _0 is initial de-Broglie...
- A simple pendulum is being used to determine the value of gravitational acceleration g at a certain place. The length of the...
- A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown...
- A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 10^4 N. When the tension is...
- A galvanometer having a coil resistance 100 gives a full scale deflection when a current of 1 mA is passed through it. What is...
- In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is 1 8 th of...
- The series combination of two batteries, both of the same emf 10 V, but different internal resistance of 20 and 5 , is connected...