Vikas Bharati Public School
Sample Paper
Periodic Test 2 (2017-2018)
Class – X
Subject : Mathematics
Time: 3 hrs. MM:80
Section –A
Questions 1 to 6 carry 1 mark each. (6 x 1 = 6)
Q1 Find a quadratic polynomial with √2 and 1/3 as sum and product of zeroes respectively.
Q2 A letter is chosen at random from the word TRIANGLE. What is the probability that it is a
vowel.
Q3 Find the value of p for which the equation px2 – 5x + p = 0 has equal roots.
Q4 Find the probability of getting 53 Sundays in a leap year.
Q5 Find the angle of elevation of the top of 15 m high tower at a point 15 m away from the base of
the tower.
Q6 If sin A = 1/3 , then find the value of (2 cot2 A + 2 )
Section – B
Questions 7 to 12 carry 2 marks each. (6 x 2 = 12)
Q7 If tan (A-B) = 1/√3 and sin A = 1/√2 , find A and B.
Q8 Represent the following situation in the form of a quadratic equation:
Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from
now will be 360 . We would like to find Rohan’s present age.
Q9. Check whether 301 is a term of the list of numbers 5,11,17,23,………
Q10 Find the point on x axis which is equidistant from (2,-5) and (-2,9).
Q11 There are 40 students in class X of a school of whom 25 are girls and 15 are boys . The class teacher has to select one student as a class representative. She writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of a (1) girl ? (2) a boy.
Q12. Find the roots of the following quadratic equation by using quadratic formula :
2x2 - 2√2 x + 1 = 0
Section – C
Questions 13 to22 carry 3 marks each. (10 x 3 = 30)
Q13 Prove that 3 + √2 is irrational.
Q14 Without using trigonometric tables , evaluate the following :
Sin 750 cos 150 + cos750 sin150
______
Cot 50 cot 300 cot 350 cot 550 cot 850
OR
Without using trigonometric tables , evaluate :
Cos 700 4 (sec2 590 – cot2 310 )
______+ ______- _2_ sin 900
3 sin 200 3 3
Q15 If the 3rd and the 9th terms of an A.P. are 4 and - 8 respectively , which term of this A.P. is
zero?
Q16 From a point on the ground , the angles of elevation of the bottom and the top of a transmission
tower fixed at the top of a 20 m high building are 450 and 600 respctively. Find the height of
the tower.
Q17 Find the sum of first 40 positive integers divisibl by 6.
OR
Which term of the A.P. : 3, 15 , 27 , 39 , ……… will be 132 more than its 54th term?
Q18 Evaluate : 5 cos2 600 + 4 sec2 300 – tan2 450
______
Sin2 300 + cos2 300
OR
Find the value of cos 300 geometrically.
Q19 Draw the graph of 2x + y = 6 and 2x – y + 2 = 0 . Shade the region bounded by these lines and
the x axis . Find the area of the shaded region.
Q20 If sinⱷ and cosⱷ are the roots of the equation ax2 + bx + c = 0 , prove that a2 – b2 + 2ac = 0
Q21 Find the coordinates of the points of trisection of the line segment joining (4,-1) and (-2,-3)
Q22 If m sinⱷ + n cosⱷ = p and m cosⱷ - n sinⱷ = q , then prove that m2 + n2 = p2 + q2
Section – D
Questions 23 to 30 carry 4 marks each. (8 x 4 = 32)
Q23 If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138 x – 35 are 2 + √3 and 2 - √3 , find other
zeroes.
OR
If the polynomial x4 – 6x3 – 25x + 10 is divided by another polynomial x2 – 2x + k , the remainnder comes out to be x + a , find k and a.
Q24 Two water taps together can fill a tank in 75/8 hours. The tap of larger diameter takes 10 hours
less than the smaller one to fill the tank separately. Find the time in which each tap can
separately fill the tap.
Q25 In a single throw of two dice , find the probability of :
(1) getting a total of more than 7 (2) getting the sum as perfect square
(2) getting same number on the two dice. (4) getting a prime numbers on both the dice
OR
A number x is selected at random from the numbers 1,2,3and 4 and number y is selected
at random from the numbers 1,4,9,16 . Find the probability that the value of xy is more than 16.
Q26 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work and also that by 1 man alone.
Q27 The shadow of a tower standing on a level ground is found to be 40 m longer when the sun’s altitude is 300 than when it is 600. Find the height of the tower.
OR
From a point on a bridge across a river , the angles of depression of the banks on opposite sides
of the river are 300 and 450 , respectively. If the bridge is at a height of 3 m from the banks ,
find the width of the river.
Q28 A straight highway leads to the foot of a tower. A man standing at the top of the tower observes
a car at an angle of depression of 300 , 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 600. Find the
time taken by the car to reach the foot of the tower from this point.
Q29 Pradeep repays the total loan of ₹1,18,000 by paying every month starting with the first
instalment of ₹1000 . He increases the instalment by ₹100 every month.
(a) What amount will he pays as the last instalment of loan.
(b) On 5th of every month the amount of instalment is directly transferred from his bank account.Therefore ,Pradeep ensures sufficient funds in his bank account before 5th of every month. What values are depicted by Pradeep in this act?
Q30. A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m
from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is
600 . After some time , the angle of elevation reduces to 300. Find the distance travelled by the
balloon during the interval.