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 Z Class 10
A-3-Z
Roll No.
[Total No. of Questions: 40$$] \quad$$ [Total No. of Printed Pages : 15 ]
$$10^{\text {th }}$$ ARM(SZ)JKUT20248
1003-Z
{MATHEMATICS}
Section A
1. The number 0.10110111011110 ……………… is :
(A) Even number
(B) Rational number
(c) Irrational number
(D) None of these
A-3-Z
2. Product of zeroes of the polynomial $$4 x^{2}+8 x$$ is :
(A) 2
(B) 0
(C) 4
(D) None of these
3. The pair of linear equations $$x+2 y-4=0$$ and $$2 x+4 y-12=0$$ are :
(A) Coincident
(B) Intersecting
(C) Parallel
(D) None of these
$$10^{\text {th }}$$ ARM(SZ)JKUT2024-1003-Z
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4. $$\quad \sin 2 \mathrm{~A}=2 \sin \mathrm{~A}$$ is true when $$\mathrm{A}=$$
(A) $$0^{\circ}$$
(B) $$45^{\circ}$$
(C) $$30^{\circ}$$
(D) None of these
5. $$11^{\text {th }}$$ term of the A.P. : $$-3,-\frac{1}{2}, 2 . \ldots \ldots \ldots$$. is :
(A) 28
(B) 22
(C) $$\quad-38$$
(D) None of these
$$10^{\text {th }}$$ ARM(SZ)JKUT2024-1003-Z
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6. The abscissa of any point on y-axis is :
(A) 1
(B) 0
(C) -1
(D) None of these
7. H.C.F. of 26 and 91 is :
(A) 26
(B) 13
(C) 14
(D) None of these
10 thaRM(SZ)JKUT2024-1003-Z
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8. Getting a natural number greater than zero is an example of :
(A) Impossible event
(B) Simple event
(if Sure event
(D) None of these
9. Volume of sphere is :
(A) $$\frac{4}{3} \pi r^{2}$$
(B) $$\frac{3}{4} \pi r^{3}$$
(C) $$\frac{4}{3} \pi r^{3}$$
(D) None of these
10. Discriminant of the quadratic equation $$x^{2}+5 \sqrt{5} x-70=0$$ is :
(A) 280
(D) 405
(C) 504
(D) None of these
11. Prime factorization of 3825 is $$3 \times 3 \times 5 \times 7 \times 17$$. (True/False)
12. The sum of first 1000 positive integers is :
(A) 500500
(B) 500005
(C) 100100
(D) None of these
$$10^{\text {th }}$$ ARM(SZ)JKUT2024-1003-Z
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13. $$\frac{1}{2}$$ can be the probability of an event.
14. All triangles are similar. (isosceles/ equilateral)
15. Number of tangents that can be drawn on the circle is $$\qquad$$
16. If $$a_{n}=(n-1)(2-n)$$, then find $$a_{4}$$.
17. $$x=3, y=-2$$ is a solution of equation $$2 x-3 y=12$$. (True/False)
18. The value of $${cosec} \mathrm{A}$$ is always greater than or equal to 1 .
(True/False)
Or
$$
\sec ^{2} \mathrm{~A}=1+\ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \text { for } 0^{\circ} \leq \mathrm{A} \leq 90^{\circ}
$$
$$10^{\text {th }}$$ ARM(SZ)JKUT2024-1003-Z
Turn Over
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19. Calculate mean of first 7 even numbers.
20. Write the formula for mean of grouped data.
Or
Median of 6, 10, 14, 18, 22, 26, 30 is………..
Section-B
21. Solve the pair of linear equations $$3 x+4 y=10$$ and $$2 x-2 y=2$$ by
elimination method.
22. Find the roots of the quadratic equation $$2 x^{2}-x+\frac{1}{8}=0$$ 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.
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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
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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.
$$10^{\text {th ARM(SZ)JKUT2024-1003-Z }}$$
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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
