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A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90s, 91s, 95s and 92s. If the minimum division in the measuring clock is 1s, then the reported mean time should be :

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The area (in sq. units) of the region described by ${(x,y):y_{2}≤2x$and $y≥4x−1}$is :

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, .. , is

$(lim)_{x→0}x_{2}sin(πcos_{2}x) $ is equal to

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$and $l_{2}=m_{2}+n_{2}$is

Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and touching the circle C externally, then the radius of T is equal to

The rate of a reaction doubles when its temperature changes from 300K to 310K. Activation energy of such a reaction will be: $(R=8.314JK_{−1}mol_{−1}andg2=0.301)$

If $∫f(x)dx=ψ(x)$, then $∫x_{5}f(x_{3})dx$is equal to

In the following sequence of reactions : Toluene $→KMnO_{4}A→SOCl_{2}BBaSO_{4}→ H_{2}/Pd C,$ The product C is :