| Part (a) | Part (b) |
| 1. $\begin{array}{l}\text { Value of }(1+i)\left(1+i^2\right) \left(1+i^3\right)\left(1+i^4\right)\end{array}$ | (a) 0 |
| 2. $a=1+i$ then value of $a^2$ | (b) $-i$ |
| 3. Square root of $-i$ | (c) $2 i$ |
| 4. $i^{135}$ | (d) $\pm \frac{1}{\sqrt{2}}(1-i)$ |
| 5. $i^{-999}$ | (e) $i$ |
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| Part (A) | Part (B) |
| 1. $\frac{d}{d x}(\sin \sqrt{x})$ | (a) $\frac{e^{\sqrt{2 x}}}{\sqrt{2 x}}$ |
| 2. $\frac{d}{d x}(x+2)^3$ | (b) $\frac{\sec ^2 \sqrt{x}}{2 \sqrt{x}}$ |
| 3. $\frac{d}{d x}\left(\frac{1}{\sqrt{x}}\right)$ | (c) $3(x+2)^2$ |
| 4. $\frac{d}{d x} e^{\sqrt{2 x}}$ | (d) $\frac{\cos \sqrt{x}}{2 \sqrt{x}}$ |
| 5. $\frac{d}{d x} \tan \sqrt{x}$ | (e) $-\frac{1}{2} x^{-3 / 2}$ |
| Part (A) | Part (B) |
| 1. Probability of obtaining three heads on tossing three coins | (a) $\frac{1}{6}$ |
| 2. Probability of obtaining at least two heads on tossing three coins | (b) $\frac{5}{6}$ |
| 3. Probability of getting a number less than 6 on throwing one dice | (c) $\frac{1}{8}$ |
| 4. Probability of getting a sum of 5 on throwing two dice | (d) $\frac{1}{9}$ |
| 5. Probability of getting a sum of 7 on throwing two dice | (e) $\frac{1}{2}$ |
| Part (a) | Part (b) |
| 1. If $\frac{2 x+4}{x-1} \geq 5$, then | (a) $x \in(4, \infty)$ |
| 2. If $3 x-7>x+1$, then | (b) $x \in\left(-\frac{1}{4}, \frac{5}{6}\right)$ |
| 3. If $\frac{5 x}{2}+\frac{3 x}{4} \geq \frac{39}{4}$, then | (c) $x \in(-\infty,-5) \cup(5, \infty)$ |
| 4. If $\frac{6 x-5}{4 x+1}<0$, then | (d) $x \in[3, \infty)$ |
| 5. If $\frac{x}{x-5}>\frac{1}{2}$, then | (e) $x \in(1,3]$ |
| Part (A) | Part (B) |
| 1. The angle between the lines$2 x-y+3=0$ and $x+2 y+3=0$ | (a) $-\frac{7}{2}$ |
| 2. The image of point $(4,-13)$ in line $5 x+y+6=0$ | (b) $(-1,-14)$ |
| 3. Point at equal distance from lines $4 x+3 y-10-0$, $5 x-12 y+26=0$ and $7 x+24 y-50=0$ | (c) $90^{\circ}$ |
| 4. If slope of line passing through points $(2,5)$ and $(x, 3)$ is 2 , then the value of $x$ is | (d) $(0,0)$ |
| 5. The slope of line passing through points $(3,-5)$ and $(1,2)$ | (e) 1 |
| Part (A) | Part (B) |
| 1. There are three red, four white and five blue balls in a bag. On taking out two balls from the bag, the probability of their being of different colours is | (a) $\frac{3}{7}$ |
| 2. 6 girls and 6 boys are sitting in a row. The probability of all girls sitting together is | (b) $\frac{47}{66}$ |
| 3. The probability of getting 1 on both dice when thrown together is | (c) $\frac{1}{132}$ |
| 4. Probability of 53 Fridays or 53 Saturdays in a leap year is | (d) $\frac{6}{216}$ |
| 5. Probability of obtaining same number on throwing 3 dice is | (e) $\frac{1}{36}$ |
| Part (A) | Part (B) |
| 1. The coordinates of focus of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=-1$ | (a) $(-g,-f)$ |
| 2. The equation of major axis of ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$ | (b) $(0, \pm b e)$ |
| 3. The length of latus rectum of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=-1$ | (c) $y=0$ |
| 4. The coordinates of centre of circle $x^2+y^2+2 g x+2 f y+c=0$ | (d) $2 b$ |
| 5. The length of major axis of ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a<b$ | (e) $\frac{2 a^2}{b}$ |
| Part (A) | Part (B) |
| 1. $\frac{d}{d x}\left(\log _e x\right)$ | (a) $-\frac{2}{x^3}$ |
| 2. $\frac{d}{d x}\left(\log _a x\right)$ | (b) $(x+1) e^x$ |
| 3. $\frac{d}{d x}\left(\frac{1}{x^2}\right)$ | (c) $\frac{1}{x}$ |
| 4. $\frac{d}{d x} \sqrt{a x+b}$ | (d) $\frac{a}{2 \sqrt{a x+b}}$ |
| 5. $\frac{d}{d x}\left(x e^x\right)$ | (e) $\frac{1}{x \log _e a}$ |
| Part (A) | Part (B) |
| 1. Distance between points $P(1,2,3)$ and $Q(-1,-1,-1)$ | (a) $x-2 y-z+1=0$ |
| 2. The locus of a point equidistant from points $A (0,2,3)$ and $B (2,-2,1)$ | (b) $\sqrt{29}$ |
| 3. Point on $y$-axis which is equidistant from points $(3, 1, 2)$ and $(5, 5, 2)$ | (c) $(0,0,7)$ |
| 4. Point on the $z$-axis which is at a distance of $\sqrt{21}$ unit from point $(1,2,3)$ | (d) $(0,5,0)$ |
| Part (a) | Part (b) |
| 1. Number of terms in the expansion of $\left(4 x^2+12 x y+9 y^2\right)^9$ | (a) $\sum_{r=0}^n{ }^n C _r x^{n-r} y^r$ |
| 2. $(2+\sqrt{5})^5+(2-\sqrt{5})^5$ | (b) 9 |
| 3. $999^3$ | (c) 1364 |
| 4. Number of terms in the expansion of $(a+b x)^{17} -(a-b x)^{17}$ | (d) 19 |
| 5. $(x+y)^{ n }$ | (e) 997002999 |
| Part (a) | Part (b) |
| 1. ${ }^{20} C _r={ }^{20} C _{r-10}$, then the value of ${ }^{18} C _r$ | (a) 3 |
| 2. ${ }^{15} C _{3 r}={ }^{15} C _{r+3}$, then the value of $r$ | (b) 816 |
| 3. ${ }^n C _{12}={ }^n C _8$, then the value of $n$ | (c) 0 |
| 4. ${ }^{\left(a^2-a\right)} C _2={ }^{\left(a^2-a\right)} C _4$, then the value of $a$ | (d) 3 |
| 5. $[\lfloor\underline{n+1}]$ $= 90[\lfloor\underline{n-1}]$, then the value of $n$ | (e) 20 |