CBSE 10th Class Sample paper 1

General Instruction

1. All the questions are compulsory
2. The question paper consists of 40 question and it is divided into four sections A,B , C and D. SECTION A Comprises of 20 questions carrying 1 mark each. Section B comprises of 6 questions carrying 2 marks each, Second C comprises of 8 questions carrying 3 marks cach. Section D comprises of 6 questions carrying 4 marks each.
3. There is no overall choice
4. Use of calculator is not permitted.

Section A

1. If p and q are co-prime, then p² and q² are ______________
2. If ∆ABC∼∆DEF, BC=3cm, EF= 4cm and ar( ∆ABC) = 54 cm² , then ar(∆DEF) =.....
3. If 5tanθ-4 =0 , then the value of (5sinθ -4cosθ)/( 5sinθ+ 4cosθ) is......
4. A die is thrown once. The probability of getting a prime number
(A) 2/3
(B) 1/3
(C) 1/2
(D) 1/6
5. the equation x² + 4x + k= 0 has real and distinct roots. then
(A) K<4
(B) k>4
(C) k <= 4
(D) k>= 4
6. If the circumference and the area of a circle are numerically equal, then diameter of the circle is
(A) π/2 units
(B) 2π units
(c) 2 units
(d) 4 units
7. The next term of the A.P. : √7, √28 , √63...
(A) √70
(B) √84
(C) √97
(D) √122
8. The distance between the points (acosθ + bsinθ, 0) and (0, asinθ - bcosθ) is
(A) a + b
(B) a² + b²
(C) a² - b²
(D)√(a² + b²)
9. If A quadratic polynomial f(x) is a square of a linear polynomial, then it's zeros are equal. (True/ False)
10. From a point lying on the circle, infinite number of tangents can be drawn (True/ False)
11. For What value of p,(-4) is a zero of the polynomial x² -2x -(7p+3)?
12. Find the number of solution of the following pair of linear equations

x+2y -8=0
2x +4y = 16

13. Find the area of a triangle with vertices (0,4),(0, 2) and (3.0).
14. If A(1, 2), B(4, 3) and C(0,0) are three vertices of parallelogram ABCD, find the coordinates of D.
15. In figure, PN || LM. Express x in terms of a b, and c where a b and c are length of LM, MN and NK respectively.

16. State Basic Proportionality Theorem.
17. What is the probability that a non leap year has 53 Mondays?
18. The total surface area of a solid hemisphere is 402 cm², find its diameter.
19. A Pole casts a shadow of length 2√3 m on the Ground, when the sun's elevation is 60^o, find the height of the pole.
20. IF E be an event such that P(E) =3/7, what is P (Not E) equal to?

Section B

21.On a square handkerchief, nine circular designs each of radius 7 cm are made Find the area of the remaining portion of the handkerchief.

22. Write a rational number between √2 and √3.
23. For what value of k, will the following system of equations have no solutions?

(3k+1)x + 3y = 2
(k2+1)x + (k - 2)y= 5

24. A cylindrical tub, whose diameter is 12 cm and height 15 cm is full of ice cream. The whole ice cream is to be divided into 10 children in equal ice-cream cones, with conical base surmounted by hemispherical top. If The height of conical portion is twice the diameter of base. Find the diameter of conical part of ice-cream cone.
25. Find the mean of the following frequency distribution:

26. Cards are marked with the numbers from 2 to 151 are placed in a box and mixed thoroughly. One card is drawn at random from this box. Find the probability that the number on the card is.
(i) a prime number less than 75
(ii) an odd number.

Section C

27. Prove that 2+ √3 is irrational.
28. If x=psecθ+ qtanθ and y=ptanθ+ qsecθ, then prove that x² - y²= p² -q²
29. A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, find the perimeter of ∆ABC.
30. Evaluate, without using trigonometric tables:
Cotθ tan( 90- θ) - secθ (90°-θ ) cosecθ + sin²2 65^o + sin² 25°+ √3 tan 5 tan 45 tan 85
31. If a and b are zeroes of the polynomial 6y² – 7y +2, find the quadratic polynomial whose zeroes are 1/a and 1/b.
32. Find a natural number whose square diminished by 10 is equal to five times of 8 more than the given number.
33. Prove that the area of the semi circle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the semi-circles drawn on the other two sides of the triangle.
34. An AP consists of 45 terms. The sum of the three middle most terms is 546 and the sum of the last three terms is 1050. Find the AP.

Section D

35.The angle of elevation of a cloud from a point 60 m above a lake is 30° and the angle depression of the reflection of cloud in the lake is 60^o. Find the height of the cloud.
36. The height of a cone is 30 cm. A small cone is cut off at the top of a plane parallel to the base. If Its volume is 1/ 27 of the volume of the given cone, at what height above the base is the section made?
37. Draw a ∆ABC, with side BC =7 cm, ∠B= 45°, ∠A=105. Then construct a triangle whose sides are 4/3 times the corresponding sides of ∆ABC.
38. The distribution given below show the marks of 100 students of a class

39. Find the value (s) of k for which the points (3k -1, k-2), (k, k-7) and (k-1,-k- 2) are collinear.
40. A motor boat whose speed is 18 km/hr in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.