SUBJECT: MATHEMATICS
CLASS $$10^{\text {TH }}$$

TIME: 3 HOURS
MAX MARKS: $$\mathbf{8 0}$$

General Instructions:
i. This question paper comprises of four sections A, B, C \& D and carries 40 questions of 80 marks. All questions are compulsory.
ii. Section-A-Q No. 1 to Q 20 comprises of 20 questions of one mark each.
iii. Section-B-Q No. 21 to Q 26 comprises of 6 questions of two marks each.
iv. Section-C-Q No. 27 to Q 34 comprises of 8 questions of three markseach.
v. Section-D-Q No. 35 to Q 40 comprises of 6 questions of four marks each.
vi. There is no overall choice in the question paper. However, choice has been provided in 2 questions of one mark, 2 questions of two marks, 2 questions of three marks and 4 questions of four marks. Student has toattempt only one of the choice in such questions.

Jkbose previous year question paper 2024 set Y Class 10

[Total No. Of Question 40 ]
[Total No. Of Printed Pages 15]
$$10^{th}$$ ARM(SZ)JKUT2024
1003-Y
MATHEMATICS

Time: 3 Hours
Maximum Marks 80

Section-A
1. The number $$\sqrt{3} \ldots$$.
(A) Odd number
(B) Rational number
(C) Real number
(D) None of these

10 thARM(SZ)JKUT2024-1003-Y
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2. Zeroes of the polynomial $$3 x^{2}+5 x-2$$ are :
(A) $$\frac{1}{3},-2$$
(B) $$-\frac{1}{3}, 2$$
(C) $$3 . \frac{1}{2}$$
(D) None of these
3. The pair of linear equations $$x-2 y=0$$ and $$3 x+4 y-20=0$$ are :
(A) Parallel
(B) Intersecting
(C) Coincident
(D) None of these
10thARM(SZ)JKUT2024-1003-Y
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4. 15th term of the A.P. 2, 7, 12, …….. is :
(A) 62
(B) 27
(C) 172
(D) None of these
5. $$\sin ^{2} 30^{\circ}+\cos ^{2} 60^{\circ}$$ is equal to :
(A) $$\frac{3}{4}$$
(B) 1
(C) $$\frac{1}{4}$$
(D) None of these
6. The distance of a point from y-axis is called its:
(A) Ordinate
(B) Cooordinate
(C) Abscissa
(D) None of these
7. L.C.M. of 6 and 20 is :
(A) 120
(B) 60
(C) 20
(D) None of these

8. The probability of a leap year selected it randon contains 53 Sundays is :
(A) $$\frac{53}{36}$$
(B) $$\frac{1}{7}$$
(C) $$\frac{53}{365}$$
(D) None of these
9. A cylindrical pencil sharpened at one edge is a combination of :
(A) A cone and a cylinder
(B) A hemisphere and a cylinder
(C) Four cylinders
(D) None of these

10 AnARM(SZ)JKUT2024-1003-Y
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10. Discriminant of the quadratic equation $$x^{2}+5 x+5=0$$ is :
(1) 25
(P) -5
(E) 5
(D) None of these
11. Prime factorization of 5313 is $$3 \times 7 \times 11 \times 23$$. (T̂rue/false)
12. The sum of first 100 positive integers is :
(A) 5000
(B) 5050
(C) 5005
(D) None of these

ARM(SZ)JKUT2024-1003-Y

13. $$\frac{3}{2}$$ can be the probability of an event.(True/False)
14. All squares are…….. (Similar/congruent)
15. Two tangents drawn at the end points of diameter of a given circle are always ……
16. Write formula for $$n^{\text {th }}$$ terms of an A.P.
17. $$x=2, y=3$$ is a solution of equation $$3 x+4 y=18$$.
18. The value of $$\sin \mathrm{A}$$ never exceeds 1 .[True/False]

Or
$$
{cosec}^{2} \mathrm{~A}-\ldots . . . . . . . . . . . . . . . .
$$

JthARM(SZ)JKUT2024-1003-Y
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19. Calculate mean of first 8 natural numbers.
20. Write the formula for mode of grouped data.

Or

If mean $$=20$$. mode $$=18$$. then median $$=$$

Section B
21. Solve the pair of linear equations $$\frac{x}{2}+\frac{2 y}{3}=-1$$ and $$x-\frac{y}{3}=3$$ by elimination method.
22. Find the roots of the quadratic equation $$\sqrt{2} x^{2}+7 x+5 \sqrt{2}=0$$ by factorisation.

23. Given $$\sec \theta=\frac{13}{12}$$. calculate all other trigonometric ratios.

$$10^{\text {th }}$$ ARM(SZ)JKUT2024-1003-Z
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24. Find volume of sphere of radius 3 cm .
Or

Calculate the curved surface area of cylinder of radius 2 cm and height 7 cm.
25. Find the values of $$y$$ for which the distance between the points $$P(2,-3)$$ and $$Q(10, y)$$ is 10 units.

Or

Check whether $$(5,-2),(6,4)$$ and $$(7,-2)$$ are the vertices of an isosceles triangle.
26. Find a quadratic polynomial, the sum and product of whose zeroes are $$\sqrt{2}$$ and $$\frac{1}{3}$$. respectively.

A-3-Z

Section-C
27. Find the coordinates of the points which divide the linesegment joining $$A(-2,2)$$ and $$B(2,8)$$ into four equal parts.
28. Find the area of a quadrant of a circle whose circumference is 22 cm .
29. Prove that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
$$
\mathrm{Or}
$$

Two tangents TP and TQ are drawn to a cricle with centre O from an external point T. Prove that :
$$
\angle \mathrm{PTQ}=2 \angle \mathrm{OPQ}
$$
$$10^{\text {th }}$$ ARM(SZ)JKUT2024-1003-Z
A-3-Z

30 E: is a point on the side $$A D$$ produced of a parallelogram $$A B C D$$ and BF intersects CD at F. Show that:

$$\triangle \mathrm{ABE} \sim \triangle \mathrm{CFB}$$
31. The diagonals of a quadrilateral ABCD intersect each other at the point $$O$$ such that $$\frac{A O}{B O}=\frac{C O}{D O}$$. Show that $$A B C D$$ is a trapezium.
32. Prove that $$6+\sqrt{2}$$ is irrational.

33. An AP consists of 50 terms of which $$3^{\text {rd }}$$ term is 12 and the last term is 106 . Find the $$29^{\text {th }}$$ term.
$$
O r
$$

Find the sum of the first 15 multiples of 8.

{A-3-Z}
34. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting :
(i) A face card
(ii) A spade

Section-D
35. A train travels a distance of 480 km at a uniform speed. If the speed had been $$8 \mathrm{~km} / \mathrm{h}$$ less, then it would have taken 3 hours more to cover the same distance. Find the speed of the train.
Or

Find the value of K so that the quadratic equation $$\mathrm{Kx}(x-2)+6=0$$ has equal roots.

$$10^{\text {th ARM(SZ)JKUT2024-1003-Z }}$$
A-3-Z
36 . A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm . which is surmounted by another cylinder of height 60 cm and radius 8 cm . Find the mass of the pole, given that $$1 \mathrm{~cm}^{3}$$ of iron has approximately 8 g mass. (Use $$\pi=3.14$$ )

{Or}

From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm .
a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest $$\mathrm{cm}^{2}$$.
37. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is $$60^{\circ}$$ and the angle of depression of its foot is $$45^{\circ}$$. Determine the height of the tower.
38. Evaluate :
$$
\begin{gathered}
\frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-\tan ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}} \\
O r
\end{gathered}
$$

Prove the identity :
$$
\frac{\sin \theta-2 \sin ^{3} \theta}{2 \cos ^{3} \theta-\cos \theta}=\tan \theta
$$
39. If a line intersects sides AB and AC of a $$\triangle \mathrm{ABC}$$ at D and E respectively and is parallel to BC , prove that :
$$
\frac{\mathrm{AD}}{\mathrm{AB}}=\frac{\mathrm{AE}}{\mathrm{AC}}
$$

{Or}

A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.
40. If the median of the distribution given below is 28.5 , find the value of $$x$$ and $$y$$ :
Class Interval Frequency
0-10 ……. 5
10-20 …… $$x$$
20-30 ….. .20
30-40 ….. .15
40-50……..$$y$$
50-60 ……. 5
Total……….. 60