Jkbose previous year question paper 2023 set X class 11

[Total No. of Questions: 29]
[ Total No. of Printed Pages : 8]
XIARJKUT23 9212-X

MATHEMATICS

[Time: 3.00 Hours ]
[ Maximum Marks : 100

Section-A

(Objective Type Questions)
1 each
1. Domain of the function $$f(x)=\sqrt{9-x^{2}}$$ is:
(A) $$(-3,3)$$
(B) $$(-3,0)$$
(C) $$(0,3)$$
(D) $$[-3,3]$$
2. $$y$$-coordinate in $$y z$$-plane is zero.
(True/False)
3. Imaginary part of $$-i=$$ $$\qquad$$
4. If $$P(A)=\frac{2}{5}$$, find $$P({not} A)$$.

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{Section-B}

5. If $$U=\{1,2,3,4,5,6,7,8,9\}, A=\{2,4,6,8\}, B=\{2,3,5,7\}$$, verify $$(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$$.
6. Find the value of $$\sin 765^{\circ}$$.
7. Find the solution of linear inequation $$3(2-x) \geq 2(1-x)$$.
8. Evaluate :
$$
{Lt}_{x \rightarrow 0} \frac{a x+x \cos x}{b \sin x}
$$
9. Find the derivative of $$x^{3}(5+3 x)$$ w.r.t. $$x$$.
10. Using binomial theorem evaluate (102) $${ }^{5}$$.
11. Find the equation of straight line intersecting the $$x$$-axis at a distance of 3 units to the left of origin with slope -2 .
12. If the sum of a certain number of terms of the A.P. $$25,22,19, \ldots \ldots \ldots \ldots .$$. is 116, find the number of terms.

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{Section-C}

{(Short Answer Type Questions)}
13. In a group of 400 people, 250 can speak Hindi and 200 can speak

English. How many people can speak both Hindi and English?
14. Prove the following by using the principle of Mathematical induction for all $$n \in N:$$
$$
1^{2}+3^{2}+5^{2}+\ldots \ldots \ldots+(2 n-1)^{2}=\frac{n(2 n-1)(2 n+1)}{3}
$$
15. Find the general solution of the trigonometric equation:
$$
\sin x+\sin 3 x+\sin 5 x=0
$$
16. Two lines passing through the point $$(2,3)$$ intersects each other at an angle of $$60^{\circ}$$. If the slope of one line is 2 , find the equation of the other line.

17. If $$x-i y=\sqrt{\frac{a-i b}{c-i d}}$$, prove that :
$$
\left(x^{2}+y^{2}\right)^{2}=\frac{a^{2}+b^{2}}{c^{2}+d^{2}}
$$

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18. Find the equation of parabola whose form is $$(0,-3)$$ and directrix is $$y=3$$.
19. Find the ratio in which the $$y z$$-plane divides the line segment formed by joining the points $$(-2,4,7)$$ and $$(3,-5,8)$$.
20. (a) Write the negation of the following statements :
(i) Chennai is the capital of Tamil Nadu.
(ii) The number 2 is greater than 7 .
(b) Write each of the following statements in the form ‘if-then’:
(i) You get a job implies that your credertials are good.
(ii) A quadrilateral is a parallelogram if its diagonals bisect each other.
21. A card is selected from a pack of 52 cards :
(a) Find the probability that the card is an ace of spade.
(b) Find the probability that the card is an ace.
(c) Find the probability that the card is a black.

{Or}

If $$E$$ and $$F$$ are events such that $$P(E)=\frac{1}{4}, P(F)=\frac{1}{2}$$ and $$P(E$$ and $$F)=\frac{1}{8}$$,
find :
(i) $$\mathrm{P}(\mathrm{E}$$ or F$$)$$
(ii) P (not E and not $$F)$$

22.In the expansion of $$(1+a)^{m+n}$$, prove that coefficients of $$a^{m}$$ and $$a^{n}$$ are equal.

{Or}

Find the 13th term in the expansion of :
$$
\left(9 x-\frac{1}{3 \sqrt{x}}\right)^{18}, \quad x \neq 0
$$
23. Let $$A=\{1,2,3,4,6\}$$ and $$R$$ be the relation on $$A$$ defined as $$R=\{(a, b)$$ :
$$a, b \in A, b$$ is exactly divisible by a\}:
(i) Write R in roaster form
(ii) Find the domain of R
(iii) Find the range of $$R$$

{Or}

Let $$f$$ be a subset of $$z \times z$$ defined by $$f:\{(a b, a+b): a, b \in z\}$$ where $$z$$ is a set of integer. Is $$f$$ a function from $$z$$ to $$z$$ ? Justify your answer.

{Section-D}
(Long Answer Type Questions)
24. If $$\cot x=\frac{3}{4}, x$$ lies in 3rd quadrant find the values of other five trigonometric functions.
Or

Prove that :
$$
2 \cos \frac{\pi}{13} \cos \frac{9 \pi}{13}+\cos \frac{3 \pi}{13}+\cos \frac{5 \pi}{13}=0
$$
25. Find $$r$$, if $$5 .{ }^{4} \mathrm{P}_{r}=6.5 \mathrm{P}_{r-1}$$.

Or
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

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26. Find sum of $$n$$ terms of two A.P’s are in the ratio $$5 n+4: 9 n+6$$. Find the ratio of their 18th terms.
Or

In $$a, b, c, d$$ are in G.P., show that :
$$
\left(a^{2}+b^{2}+c^{2}\right)\left(b^{2}+c^{2}+d^{2}\right)=(a b+b c+c d)^{2}
$$
27. Find the derivative of the function $$f(n)=\frac{x+1}{x-1}$$ from first principle.
Or

If $$f(x)=\frac{4 x+5 \sin x}{3 x+7 \cos x}$$, find $$f^{\prime}(x)$$.
28. Find the equation of ellipse with length of minor axis 16 and foci $$(0, \pm 6)$$.

{Or}
$$
\quad
$$

Find the coordinates of the foci, vertices, the eccentricity and the length of the latus rectum of the hyperbola $$5 y^{2}-9 x^{2}=36$$.

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29. Find the mean and variance for the following frequency distribution :
Classes & Frequencies
$$0-10$$ & 5
$$10-20$$ & 8
$$20-30$$ & 15
$$30-40$$ & 16
$$40-50$$ & 6