CBSE 10th Class Sample paper 4

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 n is Natural number then 9²ⁿ-4²ⁿ is always divisible by
(a) 5
(b) 13
(c) 5 and 13
(d) none of these
2. If the mean of the following distribution is 2.6 , then the value of y is

a) 3
b) 8
c) 13
d) 24
3.If the difference between the circumference and radius of a circle is 37 cm then the circumference (in cm) of the circle is
a) 7
b) 14
c) 44
d) 154
4. If am≠bl, then the system of equations ax+ by= c and Ix+ my= n
(a) has a unique solution
(c) has infinitely many solutions
(b) has no solution
(d) may or may not have solution
5. The value of k for which the quadratic equation x²- kx +4= 0 have equal roots.
6. The sum of three consecutive terms of an increasing A.P. is 51 and the products of 1st and 3rd of these terms is 273, then the third term is......
(a) 13
(b) 9
C) 21
D) 17
7. If (k +1)=sec²θ(1 +sinθ )( 1-sinθ) find k.
8. If ( cosecθ + cotθ ) = x , find cosecθ - cotθ
9. If a pole 6 m high casts a shadow of 2√3 long on the ground then what is the sun's elevation?
10. State true or false and justify
"If a die is thrown, there are two possible outcomes an odd number or an even number. Therefore the probability of getting an odd numbers is 1/2."
11.State true or false and justify
"A driver attempts to start a car. The car starts or doesnot start is an equally likely outcome. "
12. In an equilateral triangle, the lengths of the median is √3 cm. then find the length of the side of this equilateral triangle.
13. In the given figure of ABC, D and E are points on CA and CB respectively such that DE|| AB, AD= 2x, DC=x+3.BE=2x-1, CE=x find x.

14. Find the altitude of an equilateral triangle of side 8 cm.
15. Fill in the blanks If P(2, 4), Q(0, 3), R (3, 6) and S(a, b) are vertices of a parallelogram then the value of a+b is...........
16. Find K if the point P(2, 4) is equidistant from A(5, K) and B(K, 7).
17. Two tangents making an angle of 60° between them, are drawn to a circle of radius √2 cm, then find the length of each tangent.
18. If the sum and product of the zeros of the polynomial ax² -5x +c is 10. find a and c.
19. If a, b are zeros of 2x² -5x + 1 find a quadratic polynomial whose zeroes are 2a and 2b.
20. If radii of two concentric circles are 4 cm and 5 cm, then find the length of the chord of one circle, which is tangent to the other circle.

Section B

21. Given that √2 is irrational, prove that (5+3√2) is an irrational number.
22. For what value of k the system of equations kx + 3y = 1 , 12x + ky =2 has no solution.
23. The length of minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
24. Two cubes each of volume 27 cm³ are joined end to end to form a solid cuboid. Find the surface area of the resulting cuboid.
25. The following distribution table shows the marks scored by 140 students in an examination:

Calculate the mode of the distribution.
26. An integer is chosen at random between 1 and 100. Find the probability that it is:
(i) divisible by 8.
(ii) not divisible by 8.

Section C

27. Evaluate :
(cos² 20° + cos² 70°) + cot 25°/tan 65° + cot5°cot 10°cot 60°cot 80°cot85°
28. QT and RS are medians of a triangle PQR right angled at P. Prove that 4(QT² +RS²) = 5QR²
29. If a and b are zeroes of the polynomial p(x) = 2x² + 11x + 5 , find the value of 1/a + 1/b - 2ab.
30. Prove that: sinθ/(1-cosθ) + tanθ/(1+cosθ) = cosθcosecθ + cotθ
31. Find the roots of the equation
1/(X + 4) + 1/(X-7) = 11X /30 , X ≠ -4,7
32. Show that one and only one out of n, n+2, n+ 4 is divisible by 3, where 'n' is any positive integer.
33. The sum of first six terms of an A.P. is 42. The ratio of its 10th term to 30 term is 1:3. Calculate the first and 13 term of the A.P.
34. In figure, AB is chord of a circle, with centre O, such that AB=16 cm and radius of circle is 10 cm. Tangents at A and B intersect each other at P. Find the length of PA.

Section D

35. On selling a tea set at 5% loss and a lemon set at 15% gain, a crockery dealer gains 7 $ . If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains 13 $. Find the actual price of the tea-set and the lemon-set.
36. Point P divides the line segment joining the points A (2, 1) and B(5,-8) such that AP/AB = 1/3. If P lies on the line 2x-y+k = 0, find the value of k. Also find the distance between AP.
37. Draw an isosceles triangle ABC in which AB=AC=6 cm and BC=5 cm. Construct a triangle PQR similar to ABC in which PQ = 8cm. Also justify the construction.
38. A person observes the elevation of a cloud from a point 60 metres above a lake as 30° and the angle of depression of its reflection in the lake as 60°. Find the height of the cloud.
39. Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?
40. If the median of the following frequency distribution is 525. on the table given below, find the value of x and y, if total frequency is 100.