Which of the following compound will undergo self aldol condensation in the presence of cold dilute alkali

Which of the following compounds containing carbonyl group will give coloured crystalline compound with

If then the equation with roots and

If then  is equal to

If , then

In this question, we have to find the range of function from k to K. Here we know that sin^-1x + cos^-1x = and it only defines if -1 ≤ x ≤ 1 . And tan^-1x lines in () to ( ) .

In an experiment with a beam balance an unknown mass m is balanced by two known masses of 16 kg and 4 kg as shown in figure. The value of the unknown mass m is :–

A particle starts from the point (0m, 8m) and moves with uniform velocity of m/s After 5 seconds, the angular velocity of the particle about the origin will be

A particle of mass M is at a distance a from surface of a thin spherical shell of equal mass and having radius a

There is a concentric hole of radius R in a solid sphere of radius 2R. Mass of the remaining portion is M. What is the gravitational potential at centre ?

A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as shown in figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is

A non uniform rod OA of liner mass density (= const.) is suspended from ceiling with hinge joint O & light string as shown in figure. Find the angular acceleration of rod just after the string is cut

A particle of mass m moves with a constant velocity. Which of the following statements is not correct about its angular momentum:

In the figure (A) half of the meter scale is made of wood while the other half of steel. The wooden part is pivoted at O. A force F is applied at the end of steel part. In figure (B) the steel part is pivoted at O and the same force is applied at the wooden end:–

A person supports a book between finger and thumb as shown (the point of grip is assumed to be at the corner of the book). If the book has a weight of W then the person is producing a torque on the book of

A string is wrapped around the rim of a wheel of moment of inertia 0.20 kg- and radius 20 cm. The wheel is free to rotate about its axis and initially the wheel is rest. The string is now pulled by a force of 20N. The angular velocity of the string after 5 seconds will be:–

In figure, the winch is mounted on an axle, and the 6-sided nut is welded to the winch. By turning the nut with a wrench, a person can rotate the winch. For instance, turning the nut clockwise lifts the block off the ground, because more and more rope gets wrapped around the winch. Three students agree that using a longer wrench makes it easier to turn the winch. But they disagree about why. All three students are talking about the case where the winch is used, over a 10 s time interval, to lift the block one metre off the ground.
Student 1 By using a longer wrench, the person decreases the average force he must exert on the wrench, in order to lift the block one metre in 10s.
Student 2 : Using a longer wrench reduces the work done by the person as he uses the winch to lift the block 1m in 10s.
Student 3 : Using a longer wrench reduces the power that the person must exert to lift the block 1m in 10s.Which of the following is true about student 2 and 3 :-