Jkbose previous year question paper 2024 set Y Class 11

Roll No.

[Total No. of Questions: 31]
[ Total No. of Printed Pages: 8]

$$11^{\text {th }}$$ ARM(SZ)JKUT2024

1207-Y

{MATHEMATICS}

[Time : $$\mathbf{3 . 0 0}$$ Hours ]
[ Maximum Marks : 80

{General Instructions:}
(i) This question paper contains 4 Sections A, B, C and D. Each Section is compulsory.
(ii) Section-A : Q. No. 1 to 10 comprises of 10 questions of 1 mark each.
(iii) Section-B : Q.iNo. 11 to $$\mathbf{2 0}$$ comprises of 10 Very Short Answer = (V.S.A.) type questions of 2 marks each.
(iv) Section-C : Q. No. 21 to 28 comprises of 8 Short Answer (S.A.) type questions of 4 marks each.
(v) Section-D : Q. No. 29 to 31 comprises of 3 Long Answer (L.A.) type questions of 6 marks each.
$$\left.11^{\text {th }} \mathrm{ARM(SZ}\right) J K U T 2024-1207-\mathrm{Y}$$

Section-A
(Objective Type Questions)
1.Set buider form of $$\{3,6,9,12\}$$ is :
(A) $$\{x :x=3 n, n \in N$$ and $$1 \leq n \leq 9\}$$
(B) $$\{x \mid x=4 n, n \in N$$ and $$1 \leq n \leq 6\}$$
(C) $$\{x \mid x=3 n, n \in N$$ and $$1 \leq n \leq 4\}$$
(D) $$\{x \mid x=2 n, n \in N$$ and $$1 \leq n \leq 4\}$$
2. Let $$f(x)=2 x-5$$, then $$f(7)$$ is equal to:
(A) 12
(B) 11
(C) 0
(D) 9
3. $$\sin 3 x$$ is equal to :
(A) $$4 \sin x-3 \cos ^{3} x$$
(B) $$3 \sin x-4 \sin ^{3} x$$
(C) $$4 \cos x-3 \sin ^{3} x$$
(D) $$4 \sin x-3 \cos x$$
$$11^{\text {th } \mathrm{ARM}(S Z) J K U T 2(24-1207-\mathrm{Y}}$$

4. The value of $$(5 i)(-3-5 i)$$ :
(A) $$-15 i+25$$
(B) $$-25+15 i$$
(C) $$3 i-15$$
(D) $$25-5 i$$
5. The value of :
$$
\frac{n!}{(n-r)!}
$$
when $$n=9, r=5$$ is :
(A) 1,300
(B) 2,400
(C) 15,120
(D) 12,560
6. The $$e$$ (eccentricity) of ellipse is equal to :
(A) $$e=1$$
(B) $$e<1$$(

C) $$e>1$$

(D) $$e=2$$
7. Equation of circle with centre $$(-a,-b)$$ is radius $$\sqrt{a^{2}-b^{2}}$$ is equal to
(A) $$x^{2}+y^{2}+2 a x+2 b y+2 b^{2}=0$$
(B) $$\quad x^{2}-y^{2}-a x-b y=0$$
(C) $$x^{2}+2 y^{2}-2 a x+4 a y=0$$
(D) $$x^{2}+y^{2}-2 a x+4 a y=0$$

8. The value of 5x-3<7 when x is an integer is:

(A) {………..-2,-1,0,1}
(B) {-2,-1,……………..}
(C) {-∞,∞}
(D) {1,2,3………………}

9. The mean of first $$n$$ natural number is :
(A) $$\frac{n\left(n^{2}+1\right)}{2}$$
(B) $$\frac{n(n+1)}{4}$$
(C) $$\frac{n(n+1)}{2}$$
(D) $$\frac{(n+1)}{2}$$
10. The probability of doublet in 2 throws of a dice is :
(A) $$\frac{1}{8}$$
(B) $$\frac{1}{6}$$
(C) $$\frac{1}{9}$$
(D) $$\frac{10}{21}$$
$$11^{\text {th }}$$ ARM(SZ)JKUT2024-1207-Y
Z-7-Y

{Section-B}

{(Very Short Answer Type Questions)}
11. Write down the subsets of $$\{a, b\}$$.
12. Find the union of set $$A=\{x / x$$ is natural number and multiple of 3$$\}$$ and $$B=\{x / x$$ is natural number less than 6$$\}$$.
13. Reduce the equation $$4 x-3 y=6$$ into intercept form and find its intercepts
on the axes.

14. Find the centre and radius of the circle $$x^{2}+y^{2}-4 x-8 y-45=0$$.
15. Find the equation of the parabola with vertex $$(0,0)$$ and focus $$(3,0)$$.
16. A wheel makes 360 revolution in 1 minute. Through how many radians does it turn in 1 second.
17. Write the sample space when a coin is tossed thrice.

18. Find the mean deviation about the median for the data as under : $$13,17,16,14,11,13,10,16,11,18,12,17$$.
19. If
$$
\frac{1}{6!}+\frac{1}{7!}=\frac{x}{8!}
$$
then find $$x$$.
20. Which term of the sequence $$\sqrt{3}, 3,3 \sqrt{3}$$ is 729.

{Section-C}

{(Short Answer Type Questions)}
21. Find the domain and range of the real function :
$$
f(x)=\sqrt{9-x^{2}}
$$
22. Prove that :
$$
\cos \left(\frac{\pi}{4}-x\right) \cos \left(\frac{\pi}{4}-y\right)-\sin \left(\frac{\pi}{4}-x\right) \sin \left(\frac{\pi}{4}-y\right)=\sin (x+y)
$$
23. Find the multiplicative inverse of $$\sqrt{5}+3 is$$.
24. Solve the inequality :
$$
\frac{x}{2} \geq \frac{5 x-2}{3}-\frac{7 x-3}{5}
$$
and show the graph of the solution on number line.
25. If $$p$$ is the length of perpendicular from the origin to the line whose intercepts on the axes are ‘ $$a$$ ‘ and ‘ $$b$$ ‘, then show that :
$$
\frac{1}{p^{2}}=\frac{1}{a^{2}}+\frac{1}{b^{2}}
$$
26. Find the derivative of :
$$
f(x)=\frac{2 x+3}{x-2}
$$
from the first principle.
27. Find the derivative of :
$$
\left(5 x^{3}+3 x-1\right)(x-1)
$$
28. Find $$n$$ if
$$
{ }^{n-1} p_{3}:{ }^{n} p_{4}=1: 9 .
$$
{Section-D}
(Long Answer Type Questions)
29. Prove that :
$$
\frac{\cos 4 x+\cos 3 x+\cos 2 x}{\sin 4 x+\sin 3 x+\sin 2 x}=\cot 3 x .
$$

Or
Prove that :
$$
\cos 4 x=1-8 \sin ^{2} x \cos ^{2} x
$$
30. In how many ways can one select a cricket team of 11 from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers.

{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.
31. Find the mean deviation about the mean for the following data :

Income Per Day (in ₹) & No. of Persons
$$0-100$$ & 4
$$100-200$$ & 8
$$200-300$$ & 9
$$300-400$$ & 10
$$400-500$$ & 7
$$500-600$$ & 5
$$600-700$$ & 4
$$700-800$$ & 3

or
In Class XI of a school 40% of the students study Mathematics and 30% students study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology or both.

$$
11^{\text {th }} \text { ARM (SZ)JKUT2024-1207-Y }
$$