KENDRIYA VIDYALAYA SANGATHAN
HYDERABAD REGION
SAMPLE PAPER - 16
TIME: 3 hours MAX.MARKS: 80
General Instructions:
Read the following instructions carefully and follow them:
1. This question paper contains 38 questions.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (MCQ’s) and questions no. 19 and
20 are Assertion- Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02
marks each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions,
carrying 05 marks each.
7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks
each with sub parts of the values of 1, 1 and 2 marks each respectively.
8. All Questions are compulsory. However, an internal choice in 2 questions of section A,
2 Questions of section B and 2 Questions of section C has been provided. An internal choice has
been provided in the all 2 marks questions of Section E.
9. Draw neat and clean figures wherever required.
10. Take π =22/7 wherever required if not stated.
11. Use of calculators is not allowed.
SECTION A
1 Given that HCF (26,169) = 13, then LCM (26, 169) is 1
A) 26 B)52 C) 338 D)13
2 The fathers age is six times his sons age. Four years hence , the age of father will be 1
four times his son . The present ages of the son and the father are
A)4 and 24 B) 5 and 30 C) 6 and 36 D) 3 and 24
2
3 What is the discriminant of the equation x – 3x – 10 = 0 ? 1
A)14 B) -31 C) 31 D) 49
4 If P(-1,1)is mid point of the line segment joining A(-3,b) and 1
B (1, b+4) then b=
A)1 B) -1 C)2 D) 0
5 If angle between two radii of a circle is 1300 , then the angle between the two 1
tangents at the ends of the radii is
(A) 900 ( B) 500 (C) 700 (D) 400
6 In triangles ABC and DEF ∠B= ∠E, ∠F= ∠C and AB=3DE. Then the two triangles are 1
A) Congruent but not similar B) similar but not congruent
C) neither congruent nor similar D) congruent and similar
7 In a triangle ABC right angled at B, sin A = 7/25, then the value of cos C is 1
A) 7/25 B)24/25 C) 7/24 D)24/7
8 In triangles ABC and DEF , AB/EF = AC/DE, then they will be similar when 1
A) ∠A=∠D B) ∠A=∠E C) ∠B=∠E D) ∠C = ∠F
3 2 2
9 What is the LCM of 3 x 5 and 3 x 5 ? 1
A) 45 B) 675 C) 135 D) 225
10 Which term of the AP : 21, 42, 63, 84, …. Is 210 1
A) 9th B)10th C)11th D)12th
11 The shadow of a 5m long stick is is 2m long. At the same time the length of the 1
shadow of a 12.5 m high tree is
A) 3m B)3.5m C) 4.5 m D)5 m
12 If radii of two concentric circles are 4 cm and 5 cm , then the length of each chord 1
of one circle which is tangent to other circle is
A) 3 cm (B) 6 cm (C) 9 cm (D) 1 cm
13 If a triangle ABC is right angled at C, then the value of cos (A+B) is 1
A) 0 B) 1 C) 1/2 D)1/3
14 The volume of the largest right circular cone that can be cut out from a cube of 1
edge 4.2 cm is
A)9.7cm3 B) 77.6 cm3 C) 58.2 cm3 D) 19.4 cm3
15 The probability that a non leap year selected at random will contain 53 Sundays is 1
A) 1/7 B) 2/7 C)3/7 D) 5/7
2
16 Find the value of k for 2X -kx+k = 0 so that it has two equal roots. 1
A)0 B)4 C) 8 D)0 and 8
17 If the mode of the distribution is8 and its mean is also 8, then the median is 1
A) 12 B) 16 C) 0 D) 8
18 A quadratic polynomial in which the sum and product of whose zeroes are 3 and 2 1
respectively is
A) x2+3x-2) B) x2-3x+2 C) x2-2x+3) D) x2-2x-3
DIRECTION: In the question number 19 and 20, a statement of Assertion (A) is
followed by a statement of Reason (R).
Choose the correct option
A) Both assertion (A) and reason (R) are true and reason (R) is the correct
explanation of assertion (A)
B) Both assertion (A) and reason (R) are true and reason (R) is not the correct
explanation of assertion (A)
C) Assertion (A) is true but reason (R) is false.
D) Assertion (A) is false but reason (R) is true.
19 (A) Assertion: Common difference of AP -5, -1, 3, 7, ….is 4. 1
(R). Reason: Common difference of AP is given by d=2nd term – 1st term
20 (A )Assertion : √a is an irrational number , where a is a prime number. 1
(R). Reason: Square root of any prime number is an irrational number.
SECTION B
21 Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9). 2
OR
If Q (0, 1) is equidistant from P (5, -3), and R (x, 6), find the values of x. Also, find
the distances QR and PR.
22 Prove that the angle between the two tangents drawn from an external point to a 2
circle is supplementary to the angle subtended by the line segment joining the
points of contact at the centre.
23 Find the sum of first 51 terms of an AP whose second and third terms are 14 and 2
18 respectively.
OR
Find the sum of the first 40 positive integers divisible by 6.
24 Evaluate: 2
25 A survey was conducted by a group of students as a part of their environment 2
awareness programme, in which they collected the following data regarding the
number of plants in 20 houses in a locality. Find the mean number of plants per
house.
SECTION C
26 Prove that 3+2√5 is irrational. 3
27 Find the ratio in which the line segment joining A(1,-5) and B(-4,5) is divided by the 3
x-axis. Also find the coordinates of the point of division.
OR
If the points A(6,1), B(8, 2),C (9, 4) and D(p, 3) are the vertices of a parallelogram
taken in order, find p.
28 Prove that cos A/(1+sin A) + (1+sin A)/cos A =2 sec A 3
29 A life insurance agent found the following data for distribution of ages of 100 3
policy holders. Calculate the median age, if policies are given only to persons
having age 18 years onwards but less than 60 years.
30 Prove that the tangent of a circle is perpendicular to the radius at the point of 3
contact.
OR
Prove that opposite sides of a quadrilateral circumscribing a circle subtend
supplementary angles at the centre of the circle.
31 Meena went to a bank to withdraw ₹2000. She asked the cashier to give her ₹50 3
and ₹100 notes only. Meena got 25 notes in all. Find how many notes of ₹50 and
₹100 she received.
SECTION D
32 A) To fill a swimming pool two pipes are to be used. If the pipe of larger 5
diameter is used for 4 hours and the pipe of smaller diameter for 9 hours,
only half the pool can be filled. Find, how long it would take for each pipe to
fill the pool separately, if the pipe of smaller diameter takes 10 hours more
than the pipe of larger diameter to fill the pool.
OR
B) A rectangular park is to be designed whose breadth is 3 m less than its
length. Its area is to be 4 square metres more than the area of a park that
has already been made in the shape of an isosceles triangle with its base as
the breadth of the rectangular park and of altitude 12 m. Find the length
and breadth of the rectangular park.
33 The diagonals of a quadrilateral ABCD intersect each other at the point O such 5
that AO/BO=CO/DO∙ Show that ABCD is a trapezium.
34 A chord of a circle of the radius 12 cm subtends an angle of 120° at the centre. Find 5
the area of the corresponding segment of the circle. (Use π = 3.14 and √3 = 1.73).
35 A straight highway leads to the foot of a tower. A man standing at the top of the 5
tower observes a car at an angle of depression of 30°, which is approaching the
foot of the tower with a uniform speed. Six seconds later, the angle of depression
of the car is found to be 60°. Find the time taken by the car to reach the foot of the
tower from this point.
OR
As observed from the top of a 75 m high lighthouse from the sea-level, the angles
of depression of two ships are 30° and 45°. If one ship is exactly behind the other
on the same side of the lighthouse, find the distance between the two ships.
SECTION E
36 Rahul and Ravi planned to play Business ( board game) in which they were
supposed to use two dice.
i Ravi got first chance to roll the dice. What is the probability that he got the sum of 1
the two numbers appearing on the top face of the dice is 8?
ii Rahul got next chance. What is the probability that he got the sum of the two 1
numbers appearing on the top face of the dice is 13?
iii Now it was Ravi’s turn. He rolled the dice. What is the probability that he got the 2
sum of the two numbers appearing on the top face of the dice is less than or equal
to 12?
OR
Rahul got next chance. What is the probability that he got the sum of the two
numbers appearing on the top face of the dice is equal to 7?
37 In a soccer match the path of the soccer ball in a kick is recorded as shown in the
following figure
i Based on the above information, answer the following questions. 1
(i) The shape of path of the soccer ball is a
(a) Circle (b) Parabola (c) Line (d) None of these
ii The zeroes of the polynomial, represented in the given graph, are 1
(a) -1,7 (b) 5,-2 (c) -2,7 (d) -3,8
iii Which of the following polynomial has -2 and -3 as its zeroes? 2
A) X2-5x-6 B) x2+5x+6 C) x2-5x+6 D) x2+5x-6
38 Arun a 10th standard student makes a project on coronavirus in science for an
exhibition in his school. In this project, he picks a sphere that has volume 38808
cm3 and 11 cylindrical shapes, each of volume 1540 cm3 with a length of 10 cm
Based on the above information, answer the following questions:
i The diameter of the base of the cylinder is 1
(a) 7 cm (b) 14 cm (c) 12 cm (d) 16 cm
Ii The diameter of the sphere is 1
(a) 40 cm (b) 42 cm (c) 21 cm (d) 20 cm
iii The total volume of the shape formed is 2
(a) 85541 cm3 (b) 45738 cm3 (c) 24625 cm3 (d) 55748 cm3
OR
The curved surface area of the one cylindrical shape is
(a) 850 cm2 (b) 221 cm2 (c) 440 cm2 (d) 540 cm2
THE END
