class 12

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JEE Main

The major product expected from the following reaction is :

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At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by \displaystyle\frac{{{d}{P}}}{{{\left.{d}{x}\right.}}}={100}-{12}\sqrt{{{x}{\dot}}}If the firm employs 25 more workers, then the new level of production of items is

For a simle pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly ? (Graphs are schematic and not drawn to scale)

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

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is :

The sum of coefficients of integral powers of x in the binomial expansion of $(1−2x )_{50}$ is:

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

The period of oscillation of a simple pendulum is $T=2πgL .$ Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using wrist watch of 1 s resolution. The accuracy in the determination of g is :

Let $T_{n}$be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $T_{n+1}−T_{n}=10$, then the value of n is