Download Test Name:CBSE-X-Maths-SA1

Test Name:CBSE-Paper
Question numbers 1 to 8 carry one mark each. In each of these questions, four alternative choices have been provided of which
only one is correct. Select the correct choice.
1: Draw graph of the equation 3x + 4y = 11. Find the value of y when x = 1.
a) y = -2
b) y = 2
Correct Answer :
b) y = 2
2: Draw graph of the equation 5x + 3y = 6. From the graph, find the value of x when y = –3.
a) x = 3
b) x = -3
Correct Answer :
a) x = 3
3: All squares are -----a) similar
b) congruent
Correct Answer :
a) similar
4: The value of tan A is always less than 1
a) True
b) False
Correct Answer :
b) False
5:
a) cos 600
b) sin 600
c) tan 600
d) sin 300
Correct Answer :
c) tan 600
6: State whether true or false : cot A is not defined for A = 0 0
a) False
b) True
Correct Answer :
b) True
7: Choose the correct option and justify your choice:
a) tan 90°
b) 1
c) sin 45°
d) 0
Correct Answer :
d) 0
Explanation :
8: Choose the correct option and justify your choice:
a) cos 60°
b) sin 60°
c) tan 60°
d) sin 30°
Correct Answer :
b) sin 60°
Explanation :
Question Number 9 to 14 carry two marks each.
9: The LCM of two numbers is 64699, their HCF is 97 and one of the numbers is 2231. Find the other.
Explanation :
10: Mala purchased 5 chairs and 2 tables for Rs. 162.5 Reshma purchased 2 chairs and 1 table for Rs. 750. represent this situation
algebraically and graphically.
Explanation :
5x + 2y = 1625
2x + y = 750;
the two lines intersect at the point (125, 500)
11: Solve the following system of equations by substitution method:
3x + 4y = 10; 5x – 2y = 8
Explanation :
x = 2, y = 1
12: Prove the identity :
13: Prove that :
14: In triangle ABC, right angled at B,
if tan A =
, find the value of :
i) sin A cos C + cos A sin C
ii) cos A cos C – sin A sin C
Explanation :
Question Number 15 to 24 carry three marks each.
15: Find the HCF and LCM of the following positive integers by applying the prime factorization method: 35, 48, 56.
Explanation :
16: Find the LCM of the following polynomials :
Explanation :
17: Find the LCM of the following polynomials :
Explanation :
18: Find the LCM of the following polynomials :
Explanation :
12x2y2 (x + y)2 (x – y)
19: Find the zeroes of the given quadratic polynomial and verify the relationship between the terms and
their coefficients.
Explanation :
20: Form the pair of linear equations in the following problems, and find their solution (if they exist) by the elimination method:
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?
Explanation :
21: In ∆ ABC, ∠C > 90o and side AC is produced to D such that segment BD is perpendicular to segment AD.
Prove that
Explanation :
22: Prove the identity :
23:
24: Prove that
Explanation :
=
Question Number 25 to 34 carry four marks each.
25: Find the values of a and b so that the polynomials P(x) and Q(x) have
Explanation :
as their HCF, where
26: Solve the following pair of linear equations by substitution and cross multiplication methods.
8x + 5y = 9; 3x + 2y = 4
Explanation :
27: A motor boat takes 6 hours to cover 100 km downstream and 30 km upstream. If the boat goes 75 km downstream and returns
back to the starting point in 8 hours. Find the speed of the boat in still water and the speed of the stream.
Explanation :
28: One says, " Give me a hundred, friend! I shall become twice as rich as you". The other replies," If you give me ten, I shall be six
times as rich as you". Tell me what is the amount of their (respective) capital?
[Hint: x + 100 = 2(y – 100), y + 10 = 6(x – 10) ]
Explanation :
29: A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the
mess. When a student a takes food for 22 days, he has to play Rs. 1380 as hostel charges whereas a student B, who takes food for 28
days pay Rs. 1680 as hostel chareges. Find the fixed charges and the cost of food per days.
Explanation :
Rs. 280, Rs. 50
30: 7 audio cassettes and 3 video cassettes cost Rs. 1110 and 5 audio cassettes and 4 video cassettes cost Rs. 1350. find the cost of an
audio cassette and a video cassette.
Explanation :
Rs. 30, Rs. 300
31: Solve the system of equations by using cross multiplication method:
3x – 5y = 20; 7x + 2y = 17
Explanation :
32: Solve the system of equations by using cross multiplication method:
4x + 7y = 10;
Explanation :
33: A person can row downstream 20 km in 2 hours and upstream 4 km in 2 hours. Find man's speed of rowing in still water and the
speed of the current.
Explanation :
6 km/hour, 4 km/hour
34: Umesh travels 600 km to his home partly by train and partly by car. He takes 8 hours if he travels 120 km by train and the rest by
car. He takes 20 minutes longer if he travels 200 km by train and the rest by car. Find the speed of the train and car.
Explanation :
60 km/hour, 80 km/hour