Jkbose previous year question paper 2023 set Z class 11

Y-12-Z
{XIARJKUT23}
9212-Z
{MATHEMATICS}
[Time : 3.00 Hours ]
[Maximum Marks : 100]
{Section-A}
{(Objective Type Questions)}

1. Domain of the function $$f(x)=\frac{1}{x}$$ is :
(A) $$(0, \infty)$$
(B) $$(-\infty, 0)$$
(C) $$(-\infty, \infty)$$
(D) All real numbers except for zero
2. Z-coordinate in xy-plane is zero.
(True/False)
3. Imaginary part of -2 = $$\qquad$$
4. If a die is thrown once, find probability of getting an even number.

XIARJKUT23-9212-Z
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{Section-B}

{(Very Short Answer Type Questions)}
5. Draw Venn diagram of each of following $$(A \cup B)^{\prime}$$ and $$(A \cap B)^{\prime}$$.
6. Find the value of $$\tan \frac{19 \pi}{3}$$.
7. Find the solution of linear inequation $$2(2 x+3)-10<6(x-2)$$.
8. Evaluate: $$\lim _{x \rightarrow-2} \frac{\frac{1}{x}+\frac{1}{2}}{x+2}$$
9. Find the derivative of $$x^{-4}\left(3-6 x^{5}\right)$$ w.r.t. $$x$$.
10. Using binomial theorem evaluate (99) $${ }^{5}$$.
11. Find the equation of a straight line which makes intercepts -3 and 2 on the $$x$$ and y-axes respectively.
12. If the sum of a certain number of terms of an A.P. 25, 22, 19……… is 116, find the number of terms.

XIARJKUT23-9212-Z
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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. Find the equation of the line passing through the point (2, 2) and cutting Off intercepts on the axes whose sum is 9.
17. If $$(x+iy)^{3}=u+i v$$, then show that:
$$
\frac{u}{x}+\frac{v}{y}=4\left(x^{2}-y^{2}\right)
$$

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18. Find the equation of parabola having vertex $$(0,0)$$, passing through $$(5,2)$$ and symmetric with respect to $$y$$-axis.
19. Find the ratio in which the yz-plane divides the line segment formed by joining the points $$(-2,4,7\rangle$$ 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.

XIARJKUT23-9212-Z
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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) $$\mathrm{P}(\mathrm{E}$$ 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

XIARIKUT23-9212-Z
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Or
Let $$f$$ be a subset of $$z \times z$$ delined by $$f:((a b, a+b): a, b \in z)$$ where $$z$$ is a set of inleger. Is $$f$$ a function from $$z$$ to $$z$$ ? Justify your answer.
Section-D
(Long Answer Type Questions) ….. 6 each
24. If $$\cot x=\frac{3}{4}, x$$ lies in 3rd quadrant find the values of other five frigonometric 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 $$5 .{ }^{4} P_{r}=6 .{ }^{5} P_{r-1}$$.
$$
\mathrm{Or}
$$

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

XIARJKUT23-9212-Z
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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.
$$
O r
$$

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 $$f(x)=\frac{x+1}{x-1}$$ 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 $$(0,±6)$$.

Or

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

XIARJKUT23-9212-Z
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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

XIARJKUT23-9212-Z
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