Jkbose previous year question paper 2023 set C class 11
X-60-C
[Total No. of Questions: 29]
[Totai No. of Printed Pages : 7]
{$$11^{\text {th }}$$ ARJKLK23 9560-C}
{MATHEMATICS}
[Time : 3 Hours]
[Maximum Marks : 100]
Section-A
(Objective Type Questions)
1.Let $$A=\{1,2,3\}$$ and $$B=\{4,5,6\}$$, then the number of relations from $$A$$
to B will be $$2^{9}$$.
(True/False)
2.A function $$f$$ defined by $$f(x)=2 x-5$$, then $$f(5)=$$ $$\qquad$$…..
(Fill in the blank)
3. $$\lim _{x \rightarrow 0} \frac{\tan x}{x}=$$
(Fill in the blank)
4.Define Polynomial Function.
$$11^{\text {th }}$$ ARJKLK $$23-9560-\mathrm{C}$$
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{(very Short Answer Type Questions)}
5. Let $$X=\{a, b, c, d\}$$, and $$Y=\{f, b, d, g\}$$, find:
(i) $$X-Y$$
(ii) $$X \cap Y$$
6. Express $$Z=(1-i)^{4}$$ in the form of $$a+i b$$.
7.Evaluate:
$$
\lim _{x \rightarrow 2} \frac{x^{3}-2 x^{2}}{x^{2}-5 x+6}
$$
8. Find the derivative of $$f(x)=\frac{x+1}{x-1}$$.
9. Find the equation of the line through the points $$(1,-1)$$ and $$(3,5)$$.
10. Expand $$(2 x-3)^{5}$$ by using Binomial Theorem.
11. Find $$24^{\text {th }}$$ term of the sequence whose $$n^{\text {th }}$$ term is defined by $$a_{n}=4 n-3$$.
12. If $$2 / 11$$ is the probability of an event, what is the probability of the event not $$A^{\prime}$$ ?
X-60-C
{Section-C}
{(Short Answer Type Question)}
13.In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?
14. Let $$f(x)=x+1, g(x)=2 x-3$$ be two real functions. Find:
(i) $$(f+g)(x)$$
(ii) $$(f-g)(x)$$
(iii) $$(f / g)(x)$$
15.Prove by using the principle of Mathematical Induction for all $$n$$ E N :
$$
1^{2}+2^{2}+3^{2}+\ldots \ldots \ldots \ldots+n^{2}=\frac{n(n+1)(2 n+1)}{6}
$$
16.Find the coordinates of the foci, the vertices, the length of major axis, the
minor axis, the eccentricity and the latus rectum of the ellipse $$\frac{x^{2}}{25}+\frac{y^{2}}{8}=1$$.
17. Find the multiplicative inverse of $$2-3i$$.
$$11^{\text {th }}$$ ARJKLK $$23-9560-\mathrm{C}$$
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X-60-C
18.Find the derivative of $$f(x)=\tan x$$ from first principle.
{or}
Find the derivative of the function:
$$
f(x)=\frac{4 x+5 \sin x}{3 x+7 \cos x}
$$
19.Find the distance of the point $$(3,-5)$$ from the line $$3 x-4 y-26=0$$.
20. A coin is tossed twice, what is the probability that at least one tail occurs.
21. Find a positive value of $$m$$ for which the coefficient of $$x^{2}$$ in the expansion
$$(1+x)^{m}$$ is 6.
22.Using Section formula, prove that the three points $$(-4,6,10),(2,4,6)$$ and (14, $$0,-2$$ ) are collinear.
23.Find the component statements of the following compound statements :
(i) The sky is blue and the grass is green.
(f) It is raining and it is cold.
$$11^{\text {th }}$$ ARJKLK23-9560-C
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{(Long Answer Type Questions)}
24.Solve :
$$
2 \cos ^{2} x+3 \sin x=0
$$
{Or}
Prove that :
$$
\cos 6 x=32 \cos ^{6} x-48 \cos ^{4} x+18 \cos ^{2} x-1
$$
25. Prove that :
$$
{ }^{n} C_{r}+{ }^{n} C_{r-1}={ }^{n+1} C_{r}
$$
Or
In how many ways can a student choose a programme of 5 courses if 9
courses are available and 2 specific courses are compulsory for every
student?
26.Show that :
$$\tan 3 x \tan 2 x \tan x=\tan 3 x-\tan 2 x-\tan x$$
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$$11^{\text {th }}$$ ARJKLK23-9560-C
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27.Find the equation of the ellipse, with major axis along the $$x$$-axis and passing through the points (4, 3) and (-1, 4).
28. Calculate Mean, Variance and Standard Deviation for the following distribution:
Classes & Frequencies
$$30-40$$ & 3
$$40-50$$ & 7
$$50-50$$ & 12
$$60-70$$ & 15
$$70-80$$ & 8
$$80-90$$ & 3
$$11^{\text {th ARJKLK23-9560-C }}$$
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29. If the first and the nth terms of a G.P. are $$a$$ and $$b$$, respectively and if $$P$$ is the product of $$n$$ terms, prove that :
$$
\mathrm{P}^{2}=(a b)^{n}
$$
{Or}
Find the sum to $$n$$ terms of the series :
$$
5+11+19+29+41+\ldots \ldots \ldots \ldots .
$$
$$11^{\text {th }}$$ ARJKLK $$23-9500-C$$
$$X-60-C$$
