| 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) $\frac{1}{x \log _e a}$ |
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| 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. ${ }^{20} C _r={ }^{20} C _{r-10}$, 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 |
| Part (A) | Part (B) |
| 1. The length of latus rectum of parabola $x^2=4 a y$ | (a) $2 a$ |
| 2. The length of major axis of ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$ | (b) $( \pm a, 0)$ |
| 3. The coordinates of vertex of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ | (c) $y=b / e, y=-b / e$ |
| 4. The equation of directrix of ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a < b$ | (d) $(-a, 0)$ |
| 5. The coordinates of focus of parabola $y^2=-4 a x$ | (e) $4 a$ |
| Part (a) | Part (b) |
| 1. ${ }^n P _4=20 \times{ }^n P _2$, then the value of $n$ | (a) 14 |
| 2. ${ }^{2 n+1} P _{n-1}:{ }^{2 n-1} P _n=3: 5$, then the value of $n$ | (b) 5 |
| 3. ${ }^{15} P _{r-1}:{ }^{16} P _{r-2}=3: 4$, then the value of $r$ | (c) 7 |
| 4. ${ }^n P _5:{ }^n P _3=2: 1$, then the value of $n$ | (d) 91 |
| 5. If ${ }^n C _8={ }^n C _6$, then the value of ${ }^n C _2$ | (e) 4 |
| 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. If $|x+2| \leq 9$, then | (a) $x \in(2,4) \cup(4,6)$ |
| 2. If $|x-1|>5$, then | (b) $x \in(10, \infty)$ |
| 3. If $-3 x+17<-13$, then | (c) $x \in[-11,7]$ |
| 4. If $\left|\frac{2}{x-4}\right|>1, x \neq 4$, then | (d) $x \in(-\infty, 3.9) \cup(4, \infty)$ |
| 5. If $2(2 x+3)-10<$ $6(x-2)$, then | (e) $x \in(-\infty,-4) \cup(6, \infty)$ |
| Part (A) | Part (B) |
| 1 The 9th term of geometric progression $1,4,16,64, \ldots$ | (a) $\sqrt{3}\left(\frac{1}{3}\right)^{n-1}$ |
| 2. The 10 th term of geometric progression $-\frac{3}{4}, \frac{1}{2},-\frac{1}{3}, \frac{2}{9}, \ldots \ldots$ is | (b) $4^8$ |
| 3. The $n$th term of geometric progression $\sqrt{3}, \frac{1}{\sqrt{3}}, \frac{1}{3 \sqrt{3}}, \ldots \ldots $ is | (c) 2186 |
| 4. The sum of seven terms of geometric progression $2,6,8$,$\ldots$ is | (d) $\sqrt{7}\left(\frac{3^{n / 2}-1}{\sqrt{3}-1}\right)$ |
| 5. The sum of 10 terms of geometric progression $4,2,1,1 / 2$, $\ldots$ is | (e) $8\left(1-\frac{1}{1024}\right)$ |
| (f) $\frac{1}{2}\left(\frac{2}{3}\right)^8$ |
| 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 slope of line passing through points $(3,-5)$ and $(1,2)$ | (a) $x=2$ |
| 2. Equation of line parallel to $x$-axis and passing through point $(3,-5)$ | (b) $-\frac{7}{2}$ |
| 3. Equation of line parallel to $x$-axis and is at equal distance from lines $x=-2$ and $x=6$ | (c) $y=2 x+3$ |
| 4. Equation of line having slope 2 and which cuts $y$-intercept as 3 . | (d) $y=-5$ |
| 5. Equation of line passing through point $(6,2)$ having slope -3 | (e) $3 x+y-20=0$ |
| 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) $\frac{2 a^2}{b}$ |