Chapter 2

${\log }_{a}1$ is equal to (a) 0 (b) 1 (c) $\mathrm{\infty }$ (d) 10

Characteristic of $\log 0.5828$ is (a) $-2$ (b) 1 (c) $\bar{2}$ (d) $\overline{I}$

For the curve $y=x^3+1$, the values of $y$ corresponding to values of $x$ as $-2$ and 2 are (a) $7,-9$ (b) $-3,6$ (c) $-7,9$ (d) $6,-3$

Slope of the line $2x-y=3$ is (a) $-2$ (b) $-1/2$ (c) $1/2$ (d) 2

Derivative of $x+\frac{1}{x}$ w.r.t. $x$ is (a) $1-\frac{1}{x^2}$ (b) $1+\frac{1}{x^2}$ (c) $-1+\frac{1}{x^2}$ (d) $-1-\frac{1}{x^2}$

Expression for $\sin C-\sin D$ is (a) $2\cos \frac{C-D}{2}\sin \frac{C+D}{2}$ (b) $2\cos \frac{C+D}{2}\sin \frac{C-D}{2}$ (c) $2\sin \frac{C+D}{2}\sin \frac{C-D}{2}$ (d) $2\cos \frac{C+D}{2}\cos \frac{C-D}{2}$

Integration of $x$ w.r.t. $x$ within the limits $x=2$ to $x=4$ has the value (a) 60 (b) 40 (c) 20 (d) 10

The value of $\frac{8!}{6!}$ is (a) 224 (b) 28 (c) 112 (d) 56

The number of ways 5 English books and 4 Hindi books can be placed on a shelf so that the books on the same language always remain together is (a) $5!4!3!$ (b) $5!4!2!$ (c) $4!3!2!$ (d) $5!3!2!$

The decimal equivalent of $(11001{)}_2$ is (a) 25 (b) 50 (c) 35 (d) 15