Model Question Paper 10th Class Mathematics Time : 3 Hrs M.M: 80
General Instruction :
1. Question No.1 to 16 are of MCQ type and carry 1 mark for each question.
2. Question No. 17 to 25 are of short type questions and each carry 2 marks.
3. Question No. 26 to 32 are of long type questions and each carry 3 marks.
4. Question No. 33 to 37 are application based question and each carry 5 marks.
Section-A (1 x 16 = 16)
M.C.Q (Choose the right option)
1. HCF of 17,23 and 29 is
(a) 17 (b) 23 (c) 1 (d) 0
2. Product of two numbers = _____________
(a) LCM + HCF (b) LCM X HCF (c) LCM ÷ HCF (d) None of above
3. How many zeroes will quadratic equation \(4x^2-4x-1= 0\) have:
(a) 1 (b) 2 (c) 3 (d) 4
4. P(E) + P(E) = …………..
(a) 0 (b) -1 (c) 1 (d) 2
5. The roots of quadratic equation will be equal if
(a) \(b^2=4ac<0 \) (b) \(b^2 -4ac=0 \) (c) \(b^2-4ac>0\) (d) \(b^2-4ac<0\)
6. Next term in the A.P -5, -1,3 ………..
(a) 2 (b) 7 (c) 6 (d) -7
7. In Trigonometric Identify: \(1 + \tan^2 \theta\) = ………
(a)\(\sin^2 𝜃\) (b) sec\(^2 𝜃\) (c)\(\cot^2 𝜃\) (d)None of these.
8. According to Pythagoras theorem \((8)^2 + (15)^2 =\) ………….
(a) \((16)^2\)
(b) \((17)^2\)
(c) \((18)^2\)
(d) \((19)^2\)
9. A Line intersecting a circle in two points is called a ……………..
(a) Chord (b) Secant line (c) Tangent line (d) Radius
10. Volume of cylinder
(a) \(𝜋rh\) (b) \(𝜋r2h\) (c) \(2𝜋rh\) (d) \(𝜋r^2h\)
11. nth Term of an A.P.
(a) a+(n-1)d (b) a-(n-1)d (c) (n-1)d (d) (n+1)d
12. If \( \sin A ={3 \over 4}\),then value of Cosec A?
(a) \({ 25\over 4}\)
(b) \({ 7\over 4}\)
(c) \({ 9\over 16}\)
(d) \({ 4\over 3}\)
13. All Squares are ………….
(a) Similar (b) Congruent (c) Always equal (d) all of above
14. Tangent to circle make an angle of …………. With the radius of circle.
(a) \(60^0\)
(b) \(70^0\)
(c) \(90^0\)
(d) \(180^0\)
15. Volume of two spheres are in ratio 64 : 27 then the ratio of their surface area is
(a) 3:4 (b) 16:9 (c) 9:16 (d) 27:64
16. Sum of zeroes in the polynomial \(5y^2- 14y + 8\) is
(a) \({5 \over 2}\)
(b) \({-5 \over 2}\)
(c) \({14 \over 5}\)
(d) \({8 \over 5}\)
Section-B (9 x 2 = 18)
17. Express 336 as a product of its prime factor
18. The coordinates of Ram’s house are (6,0) and coordinates of shyam’s house are (0,8),find the distance between houses of Ram and shyam.
19. Find the Value of : \(\sin 60^\circ \cos 30^\circ + \sin 60^\circ \cos 60^\circ \)
20. Solve the pair of linear equation by the substitution method
x + y = 14
x – y = 4
21. Find the roots of the equation:\(\sqrt 2 x^2 + 7x + 5√2 = 0\).
22. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that ball drawn is red?
23. Prove that the perpendicular at the point of contact to the tangent of circle passes through the centre.
OR
The length of the minute hand of a clock is 6cm. Find the area swept by it when it moves from 9:10 a.m. to 9:20 a.m.
24. Show that 5 - √3 is irrational
25. Determine the A.P whose third term is 16 and 7th term exceeds the 5th term by 12
Section-C (7 x 3 = 21)
26. Solve the pair of linear equations graphically.
2x + y = 6
4x – 2y = 4
27. Find a relation between x and y such that the point (x,y) is equidistant from the point (3,6) and (-3,4)
OR
A cottage industry produces a certain number of pottery articles in a day. It was observed that on a particular day the cost of production of each article (In Rs was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90 , find the number of articles produced and the cost of
each article.
28. Prove that:
\[{1+ sec \theta \over sec \theta}={\sin^2 \theta \over 1-\cos \theta}\]
29. A Chord of circle of radius 10cm subtends a right angle at the centre. Find the area of the corresponding (i) minor Segment (ii) Major Sector (use 𝜋 = 3.14)
30. If \(\cot \theta ={7 \over 8}\) , evaluate :\[{(1+\sin \theta)(1-\sin \theta) \over (1+\cos \theta)(1-\cos \theta)}\]
31. Find two numbers whose sum is 27 and product is 182.
32. The length of tangent from a point A at distance 5cm from the centre of the circle is 4 cm. Find the radius of circle.
Section-D (5 x 5 = 25)
33. Prove that a line is drawn parallel to any one sides of the triangle that intersects the other two sides in two distinct points, then the line divides those two sides in the same ratio.
34. A tree breaks due to storm and the broken part bends so that top of the tree touches the ground making an angle of 300 with it. The distance between the food of the tree to the point whose top of tree touches the ground is 8 m. Find the height of tree.
OR
The Taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 Km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and charge per KM? How much does a person have to pay for travelling a distance of 25 Km.
35. Radha has a doll in the shape of cone of radius 3.5cm mounted on hemisphere of same radius the total height of doll is 15.5cm. Radha wants to color her doll. Find the total area of doll to be colored.
OR
A wooden toy rocket is in the shape of a cone mounted on cylinder, as shown in figure. The height of the entire rocket is 26cm, while the height of the conical part is 6cm. the base of the conical portion has diameter of 5cm, while the base diameter of cylindrical portion is 3cm if conical portion is to be painted orange and the cylinder portion yellow, find the area of the rocket painted with each of these colors.(Take \(\pi = 3.14)\)
36. Five years ago, Nuri was thrice as old as sonu. Ten years later, Nuri will be twice as old as sonu. How old are Nuri and Sonu?
37. The following data gives the information on the observed lifetimes (in hours) of 225 electrical components.
Lifetimes(in Hrs) 0-20 20-40 40-60 60-80 80-100 100-120
Freq 10 35 52 61 38 29
Determine the modal lifetimes of the components.
0 Comments