Question
| Column-I | Column-II |
| (a) $\log _{10} 1000000$ | (i) 0 |
| (b) $\log _e 1$ | (ii) 6 |
| (c) $\log _{32}\left(\frac{1}{4}\right)$ | (iii) 10 |
| (d) $\log _2 1024$ | (iv) $-\frac{2}{5}$ |
| Column-I | Column-II |
| (a) $\log _{10} 1000000$ | (i) 0 |
| (b) $\log _e 1$ | (ii) 6 |
| (c) $\log _{32}\left(\frac{1}{4}\right)$ | (iii) 10 |
| (d) $\log _2 1024$ | (iv) $-\frac{2}{5}$ |
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| Column - I | Column - II |
| (a) How many km apart will they be at the end of $2 \frac{1}{2}$ hours, If they walk in opposite direction? | (i) 32 hours |
| (b) How many km apart will they be at the end of $2 \frac{1}{2}$ hours, if the walk in same direction? | (ii) $1 \frac{1}{4} km$ apart |
| (c) What time will they take to be 16 km apart if they walk in opposite directions. | (iii) $2 \frac{6}{13}$ hours |
| (d) What time will they take to be 16 km apart if they walk in same direction? | (iv) $16 \frac{1}{4} km$ apart |
| Column-I | Column-II |
| (a) Parallel to y-axis is | (i) $\lambda=-\frac{3}{4}$ |
| (b) Perpendicular to 7x + y -4 = 0 is | (ii) $\lambda=-\frac{1}{3}$ |
| (c) Passes through (1, 2) is | (iii) $\lambda=-\frac{17}{41}$ |
| (d) Parallel to x-axis is | (iv) $\lambda=3$ |
| Column 1 | Column 2 |
| (a) $\sum_{i=1}^n \frac{\left|x_i-\bar{x}\right|}{n}$ | (i) Mean Deviation about median |
| (b) $\sum_{i=1}^n \frac{\left|x_i-M_d\right|}{n}$ | (ii) Mean deviation for discrete frequency distribution |
| (c) $\sum_{i=1}^n \frac{f_i\left|x_i-A\right|}{N}$ | (iii) Mean deviation about mean |
| (d) $\frac{\Sigma f_i x_i}{N}$ | (iv) Mean |
| Column - I | Column - II |
| (a) $1^2+2^2+3^2+\ldots+n^2$ | (i) $\left(\frac{n(n+1)}{2}\right)^2$ |
| (b) $1^3+2^3+3^3+\ldots+n^3$ | (ii) n(n+1) |
| (c) $2+4+6+\ldots+2 n$ | (iii) $\frac{n(n+1)(2 n+1)}{6}$ |
| (d) $1+2+3+\ldots+n$ | (iv) $\frac{n(n+1)}{2}$ |
| (a) $f o g(2)$ | (i) 38 |
| (b) $g o f(2)$ | (ii) 2 |
| (c) $f o f(2)$ | (iii) 6 |
| (d) $g o g(2)$ | (iv) $\frac{6}{5}$ |
| (a) $\{2,3\}$ | (i) $\quad\{x: x \in N$ and is divisor of 6$\}$ |
| (b) $\{5,-5\}$ | (ii) $\{x: x \in N$ and prime is divisor of 6$\}$ |
| (c) $\{1,3,5\}$ | (iii) $\{x: x$ is an odd number less than 6$\}$ |
| (d) $\{1,2,3,6\}$ | (iv) $\left\{x: x\right.$ is the root of equation $x^2-25$ $=0\}$ |
| Column-I | Column-II |
| (a) Decimal equivalent of $(1011)_2$ is | (i) 1000000 |
| (b) Binary equivalent of decimal 64 is | (ii) 14 |
| (c) Decimal equivalent of $(1110)_2$ | (iii) 11 |
| (d) Binary equivalent of octal 76 is | (iv) 1001100 |
| Column - l | Column - ll |
| (a) Equation of circle whose centre is at $x$-axis and origin is not on the circumference of the circle. | (i) $x^2+y^2-2 x y=0$ |
| (b) Equation of circle whose centre is at $y$-axis and origin is not on the circumference of the circle. | (ii) $x^2+(y-k)^2=a^2$ |
| (c) Equation of circle whose centre is on the $x$-axis and origin is on the circumference of the circle. | (iii) $x^2+y^2-2 a x=0$ |
| (d) Equation of circle whose centre is on the $y$-axis and origin is on the circumference of the circle. | (iv) $(x-h)^2+y^2=a^2$ |
| Column I | Column II |
| (a) GST is a matter of jurisdiction of | (i) Goods are sold within a state |
| (b) Inter-state trade is presently subject to | (ii) Consumption based |
| (c) Goods and service tax is | (iii) Integrated GST |
| (d) SGST is applicable when | (iv) Both centre and state government |
| $C _1$ | $C _2$ |
| (a) Boys and girls alternate | (i) $5!\times 6$ ! |
| (b) No two girls sit together | (ii) $10!-5! 6$ ! |
| (c) All the girls sit together | (iii) $(5!)^2+(5!)^2$ |
| (d) All the girls are never together | (iv) $5!\times 6$ ! |