Jkbose previous year question paper 2024 set X, Class 11

Roll No. $$\qquad$$

[Total No: of Questions: 31]
[ Total No. of Printed Pages: 8]
$$11^{\text {th }}$$
ARM(SZ)JKUT2024 \\ 1207-X

MATHEMATICS
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[Time: $$\mathbf{3 . 0 0}$$ Hours ]
[ Maximum Marks : $$\mathbf{8 0}$$ ]

{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 $$\mathbf{1 0}$$ comprises of 10 questions of 1 mark each.
(iii) Section-B : Q. No. $$\mathbf{1 1}$$ to $$\mathbf{2 0}$$ comprises of 10 Very Short Answer (V.S.A.) type questions of 2 marks each.
(iv) Section-C : Q. No. $$\mathbf{2 1}$$ to $$\mathbf{2 8}$$ 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.

{Section-A}
1. Subsets of set $$\{-1,1\}$$ are :
(A) $$\phi,\{-1\}$$
(B) $$\phi$$ only
(C) $$\phi,\{-1\},\{1\},\{-1,1\}$$
(D) 0
2. Let :
$$
f(x)=\frac{x^{2}}{2}
$$
then $$f(2)$$ is equal to :
(A) 2
(B) 4
(C) 6
(D) 8
3. $$\sin (x+y)$$ is equal to :
(A) $$\sin x+\sin y$$
(B) $$\sin x-\sin y$$
(C) $$\sin x \cos y+\cos x \sin y$$
(D) None of these

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4. The value of $$(\sqrt{3} i)^{2}$$ is equal to :
(A) 3
(B) -3
(C) 9
(D) 18
5. The value of
$$
\frac{n!}{(n-r)!}
$$
when $$n=6, r=2$$ is equal to :
(A) 6
(B) 8l
(C) 15
(D) 30
6. $$\quad e$$ (eccentricity) of ellipse is :
(A) $$e<1$$
(B) $$e=1$$
(C) $$e>1$$
(D) $$e=2$$
7. Equation of circle with centre $$(0,2)$$ and radius 2 is equal to :
(A) $$x^{2}+y^{2}-6 y=0$$
(B) $$x^{2}+y^{2}-4 y=0$$
(C) $$x^{2}+2 y^{2}-3=0$$
(D) $$2 x^{2}+y^{2}+3 y=0$$
8. The value of $$-12 x>30$$ when $$x$$ is a natural number is :
(A) 3
(B) $$<3$$
(C) No solution
(D) 0
9. Mean of first 4 natural numbers is :
(A) 4
(B) 2.5
(C) 0
(D) -4
10. Sample space of a coin when tossed twice is :
(A) $$\{\mathrm{H}, \mathrm{H}\}$$
(B) $$\{\mathrm{HH}, \mathrm{HT}, \mathrm{TH}, \mathrm{TT}\}$$
(C) $$\{\mathrm{HH}, \mathrm{TT}\}$$
(D) $$\{\mathrm{TH}, \mathrm{HT}\}$$

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$${ }^{11^{\text {th }} \text { ARM(SZ)JKUT2024-1207-X }}$$
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{Section-B}

11. Write down all the subsets of set $$\{1,2,3\}$$.

12. Find the Union of sets A={X|X is a natural number and 1<X<6}, B={X|X is a natural number and 6<X<10}

13.Reduce the equation $$3 x+2 y-12=0$$ into intercept form and find its intercepts on the axes.

14. Find the centre and radius of the circle $$(x+5)^{2}+(y-3)^{2}=36$$.
15. Find the coordinates of focus and the equation of the directrix of the parabola $$y^{2}=12 x$$.

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16. Find the degree measure of the angle subtended at the centre of circle of radius 100 cm by an arc of length 22 cm . (Use $$\pi=\frac{22}{7}$$ )
17. Write down the sample space when a die is thrown twice.
$$
11^{\text {th }} A R M(\mathrm{SZ}) J K U T 2024-1207-X
$$

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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 $$\frac{1}{6!}+\frac{1}{7!}=\frac{x}{8!}$$ find $$x$$.

20. Which term of the sequence $$\sqrt{3}, 3,3 \sqrt{3}$$…………is 729?
{Section-C}

{(Short Answer Type Questions)}

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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 $$\sqrt{5}$$+$$3 i$$.
24.Solve the given inequality and show the graph of the solution on number line:
$$
\frac{x}{2} \geq \frac{(5 x-2)}{3}-\frac{(7 x-3)}{5}
$$

25. If $$p$$ is the length of perpendicular from the origin to the line whose intercepts on the lies 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
$$
\begin{gathered}
{ }^{n-1} p_{3}:{ }^{n} p_{4}=1: 9 . \\
\text { Section-D }
\end{gathered}
$$
(Long Answer Type Questions)

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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.