Jkbose previous year question paper 2023 set Y class 11

{Y-12-Y}

Roll No
[Tolal No. of Printed Pages : 8]
[Tolal No. of Questions : 29]
XIARJKUT23
9212-Y

{MATHEMATICS}

Time: $$\mathbf{3 . 0 0}$$ Hours ]

[Maximum marks : 100]

Section-A
(Objective Type Questions)
1. Domain of the funclion $$\Lambda(x)=-|x|$$ is :
(A) (0,7)
(B) (-∞, 0)
(C) $$(-∞,∞)$$
(D) None of these
2. $$y$$-coordinate in $$z x$$-plane is zero.
(True/False)
3. Real part of $$-i=$$ $$\qquad$$
4. If $$P($$ not $$A)=\frac{1}{3}$$, find $$P(A)$$.

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{Section-B}
(Very Short Answer Type Question)
5. IF U = {1,2,3,4,5,6,7,8,9} A={1,2,3,4} B={2,4,6} verify $$(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$$.

6. Find the value of $${cosec}(-1410)$$
7. Find the solution of linear inequation 3(X- 1) > 2(X – 3)

8. Evaluate the given limit:
$$
\lim _{x \rightarrow \pi} \frac{\sin (\pi-x)}{\pi(\pi-x)}
$$

9. Find the derivative of $$x^{5}\left(3-6 x^{-9}\right)$$ w.r.t x.
10. Using binomial theorem evaluate $$(101)^3$$
11. Find the equation of straight Line passing through the points (-1, 1) and (2, -4).

12. It the sum of a certain number of terms of an A P. 25, 22, 19,……is 116. Find the number of terms.

V1NAAt:
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{Sectlon-C}
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 nEN:
$$
n^{2}+3^{2}+5^{2}+\ldots \ldots \ldots+(2 n-1)^{2}-\frac{n(2 n-1)(2 n-1)}{3}
$$
15. Find the general solution of the trigonometric equation :
$$
\sin x+\sin 3 x+\sin 5 x=0
$$
16. Find the coordinates of the foot of perpendicular from the point $$(-1,3)$$ to the line $$3 x-4 y-16=0$$.
17. Convert the complex number $$Z=\frac{1+7 i}{(2-i)^{2}}$$ in polar form.

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18. Find the equation of parabola having vertex ( 0,0 ), passing through (2,3) and axis is along $$x$$-axis.
19. Find the ratio in which the $$yz$$-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 credentials 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.

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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) $$P(E$$ or $$F)$$
(ii) P (not E and not F )
22. In the expansion of $$(1+a)^{m+n}$$. prove that coficients of $$a^{m}$$ and $$a^{n}$$ are equal.

Or

Find the 13 th term in the expansion of :
$$
\left(9 x-\frac{1}{3 \sqrt{x}}\right)^{18}, x≠0
$$
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

Turn over
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Or

Let f be a subset of $$\mathbf{z \times z}$$ defined by $$f:((a b, a+b): a, b \in z \mid$$ where $$z$$ is a set of integer. Is f a function trom $$\mathbf{z}$$ to $$\mathbf{z}$$ ? Justily your answer.
Section-D
(Long Answer Type Ouestions)
24. If $$\cot x=\frac{3}{4}, x$$ lies in 3 rd quadrant find the values of other five trigonometric functions.
$$
0r
$$

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 $$5 .{ }^{4} P_{r}=6 .{ }^{5} P_{r-1}$$.
$$
\alpha
$$

In how many ways can one select a crickel team of eleven from 17 players in which only $$\mathbf{5}$$ players can bowl if each cricket leam 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 :
$$
\left(a^{2}+b^{2}+c^{2}\right)\left(b^{2}+c^{2}+d^{d}\right)=(a b+b c+c a)^{2}
$$
27. Find the derivative of the function $$f(x)=\frac{x+1}{x-1}$$ from first principle.
$$
0r
$$

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 ( $$0,±
6$$ ).

Or

Find the coordinales 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 of the following frequency distribution
Classes & Frequencies
$$0-10$$ & 5
$$10-20$$ & 8
$$20-30$$ & 15
$$30-40$$ & 16
$$40-50$$ & 6

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