A ball of mass 100 g is projected with velocity \(20 \mathrm{~m} / \mathrm{s}\) at \(60^{\circ}\) with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is

A disc is rolling without slipping on a surface. The radius of the disc is \(R\). At \(t=0\), the top most point on the disc is \(A\) as shown in figure. When the disc completes half of its rotation, the displacement of point \(A\) from its initial position is

In a Young's double slit experiment, the slits are separated by \(0.3\, {mm}\) and the screen is \(1.5\, {m}\) away from the plane of slits. Distance between fourth bright fringes on both sides of central bright is \(2.4\, {cm}\). The frequency of light used is \(..........\,\times 10^{14} {Hz}\)

Two \(4\) bits binary numbers, \(A = 1101\) and \(B = 1010\) are given in the inputs of a logic circuit shown in figure below. The output \((Y)\) will be:

A car \(P\) travelling at \(20\,ms ^{-1}\) sounds its horn at a frequency of \(400\,Hz\). Another car \(Q\) is travelling behind the first car in the same direction with a velocity \(40\,ms ^{-1}\). The frequency heard by the passenger of the car \(Q\) is approximately \(.......\,Hz\) [Take, velocity of sound \(=360\,ms ^{-1}\) ]

pendulum made of a uniform wire of cross sectional area \(A\) has time period \(T\). When an additional mass \(M\) is added to its bob, the time period changes to \(T_M\). If the Young's modulus of the material of the wire is \(Y\) then \(\frac{1}{Y}\) is equal to : (\(g\) = gravitational acceleration)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Consider a ferromagnetic material :
Assertion (A) : The individual atoms in a ferromagnetic material possess a magnetic dipole moment and interact with one another in such a way that they spontaneously align themselves forming domains.
Reason (R) : At high enough temperature, the domain structure of ferromagnetic material disintegrates. Thus, magnetization will disappear at high enough temperature known as Curie temperature.
In the light of the above statements, choose the correct answer from the options given below :

The surface tension of a soap solution is \(3.5 \times 10^{-2}\) N/m. The work required to increase the radius of a soap bubble from \(1\) cm to \(2\) cm is \(\alpha \times 10^{-6}\) J. The value of \(\alpha\) is _____. (\(\pi = 22/7\))

Two long current carrying conductors are placed parallel to each other at a distance of \(8 \,cm\) between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is \(300 \,\mu T\). The equal current flowing in the two conductors is ...............

Let \(\alpha=8-14 i , A=\left\{ z \in C : \frac{\alpha z -\bar{\alpha} \overline{ z }}{ z ^2-(\overline{ z })^2-112 i }=1\right\}\) and \(B =\{ z \in C :| z +3 i |=4\}\) Then \(\sum_{z \in A \cap B}(\operatorname{Re} z-\operatorname{Im} z)\) is equal to \(...............\).

If \(y=y(x)\) is the solution of the differential equation \(\frac{5+ e ^{ x }}{2+ y } \cdot \frac{ dy }{ dx }+ e ^{ x }=0\) satisfying \(y (0)=1,\) then a value of \(y \left(\log _{ e } 13\right)\) is 

A body of mass \(m\)  starts moving from rest along \(x-\) axis so that its velocity varies as \(v = a\sqrt s\) where \(a\) is a constant and \(s\)  is the distance covered by the body. The total work done by all the forces acting on the body in the first second after the start of the motion is

Math List \(I\) with List \(II\) Choose the correct answer from the option given below: