$A$ police party is moving in a jeep at a constant speed $v$. They see a thief at a distance $x$ on a motorcycle which is at rest. The moment the police see the thief,the thief starts moving with a constant acceleration $a$. Which of the following relations is true if the police are able to catch the thief?

An archaeologist analyses the wood in a prehistoric structure and finds that the ratio of ${C^{14}}$ (half-life $= 5700 \, years$) to ${C^{12}}$ is only one-fourth of that found in the cells of living plants. The age of the wood is about ........ $years$.

If the coefficients $a$ and $b$ of a quadratic expression $x^2+ax+b$ are chosen from the sets $A=\{3,4,5\}$ and $B=\{1,2,3,4\}$ respectively, then the probability that the equation $x^2+ax+b=0$ has real roots is

If $t_n$ denotes the number of triangles formed with $n$ points in a plane,no three of which are collinear,and if $t_{n+1}-t_n=36$,then $n$ is equal to

Which of the following halides is most acidic?

$A$ ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards the right as shown. Relative to its initial position with respect to the table,the ball :-
$(A)$ Remains stationary if there is no friction between the paper and the ball.
$(B)$ Moves to the left and starts rolling backwards,i.e.,to the left if there is friction between the paper and the ball.
$(C)$ Moves forward,i.e.,in the direction in which the paper is pulled if there is friction between the paper and the ball.
Here,the correct statement$(s)$ is/are :-