Subject: Mathematics
Grade: X
Marks: 40
Time: 90 mins
General Instructions:
- All questions are compulsory
- Question paper is divided into four sections: Section A contains 10 Objective type questions each carry 1 mark. Section B contains 3 questions each carry 2 marks, Section C contain 4 questions each carry 3 marks and Section D contain 3 questions each carry 4 marks.
Section A (1 marks each)
1. The HCF of 52 and 130 is
a) 52
b) 130
c) 26
d) 13
2. The decimal expansion of 63/(72 x 175) is
a) terminating
b) non-terminating
c) non termination and repeating
d) an irrational number
3. Which are the zeroes of p(x) = x2 + 3x – 10:
a) 5, -2
b) -5, 2
c) -5, -2
d) None of these
4. A quadratic polynomial whose sum and product of zeroes are -5 and 6 is
a) x2 – 5x – 6
b) x2 + 5x – 6
c) x2 + 5x + 6
d) None of the above
5. If the pair of equations 2x + 3y = 7 and kx + 9y/2 = 12 have no solution, then the value of k is:
a) 2/3
b) -3
c) 3
d) 3/2
6. The pair of equations 3x + 4y = 18 and 4x + 16y/3 = 24 has
a) infinite number of solutions
b) unique solution
c) no solution
d) cannot say anything
7. Which of the following is a rational number
a) π
b) 0.202002000…
c) 0.73737373….
d) √7
8. The sum of a number and its reciprocal is 10/3. Find the number.
a) 3
b) 1/3
c) Both (a) and (c)
d) None of these
9. Given that HCF (306, 657) = 9. Find LCM (306, 657)
a) 22365
b) 22338
c) 33822
d) 23328
10. What is the value of D when roots are real and equal
a) D < 0
b) D > 0
c) D = 0
d) None of the above
Section B (2 marks each)
11. Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and coefficients.
12. If the sum of the zeroes of the quadratic polynomial ky2 + 2y – 3k is equal to twice the product, find the value of k.
13. A motor boat whose speed is 18 Km/hr in still water take 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
Section C (3 marks each)
14. Prove that √7 is an irrational.
15. A number consists of two digits. Where the number is divided by the sum of its digit’s quotient is 7. If 27 is subtracted from the number, the digits interchange their places, find the number.
16. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively √2 and 1/3.
17. Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
Section D (4 marks each)
18. In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
19. 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 the time taken by 1 man alone.
20. Case Study Based Question
The below picture are few structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
1. The shape of the architecture shown is
a) Spiral
b) Ellipse
c) Linear
d) Parabola
2. In the standard form of quadratic polynomial, ax2 + bx + c, a, b and c are
a) All are Polynomials
b) All are rational numbers
c) ‘a’ is a non-zero real number and b and c are any Polynomials
d) All are integers.
3. If α and β are zeroes of x2 + x – 2, then 1/ α + 1/ β =
a) ½
b) 1/3
c) ¼
d) 1/5
4. If sum of zeroes of q(x) = kx2 + 2x +3k is equal to their product, then k =
a) 2/3
b) 1/3
c) -2/3
d) -1/3