The amplitude and the time period in a $S.H.M.$ are $0.5 \, cm$ and $0.4 \, s$ respectively. If the initial phase is $\pi / 2 \, rad$,then the equation of $S.H.M.$ will be

An $LCR$ series circuit with a resistance of $100\,\Omega$ is connected to an ac source of $200\,V$ (r.m.s.) and angular frequency $300\,rad/s$. When only the capacitor is removed,the current lags behind the voltage by $60^\circ$. When only the inductor is removed,the current leads the voltage by $60^\circ$. The average power dissipated is......$W$.

According to the kinetic theory of gases,when two molecules of a gas collide with each other,then:

Let the three sides of a triangle be on the lines $4x - 7y + 10 = 0$,$x + y = 5$,and $7x + 4y = 15$. Then the distance of its orthocentre from the orthocentre of the triangle formed by the lines $x = 0$,$y = 0$,and $x + y = 1$ is

Let $2 \sin^2 x + 3 \sin x - 2 > 0$ and $x^2 - x - 2 < 0$. ($x$ is measured in radians). The $x$ lies in the interval

If $P(A \cup B)=0.8$ and $P(A \cap B)=0.3$,then $P(\bar{A})+P(\bar{B})$ is equal to: