Mathematics Previous year sample paper, Part- A for class 10th

 Mathematics Sample paper

Part- A

Section-A

Directions (Q.nos. 1 to 20 are of 1 marks each)

1. The value of k for which the System of equation x+y-4=0 and 2x+ky=3 has no solution, is

a) -2

b) ≠2

c) 3

d) 2

2. The HCF and the LCM of 12, 21, 15 are respectively are

a) 3, 140

b) 12, 420

c) 3, 420

d) 420, 3

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3. The value of x for which 2x, (x+10) and (3x+2) are the three consecutive terms of an AP, is

a) 6

b) -6

c) 18

d) -18

4. The first term of an AP is p and the common difference is q, then it's 10th term is

a) q+9p

b) p-9q

c) p+9q

d) 2p+9q

5. If one of the zeroes of the quadratic polynomial x²+3x+k is 2, then the value of k is

a) 10

b) -10

c) -7

d) -2

6. The total number of factors of a prime number is 

a) 1

b) 0

c) 2

d) 3

7. The quadratic polynomial, the sum of whose zeroes is -5 and their product is 6, is 

a) x² +5x+6

b) x²-5x+6

c) x²-5x-6

d) -x² +5x+6

8. The value of p, for which the points A(3,1), B(5,p) and C(7,-5) are collinear, is 

a) -2

b) 2

c) -1

d) 1

9. The distance between the points (a cos∅ +b sin∅, 0) and (0, a sin∅-bcos∅), is

a) a²+b²

b) a²-b²

c) √a² + √b²

d) √a² - √b²

10. If the point P(k,0) divides the line segment joining the points A(2,-2) and B(-7,4) in the ratio 1:2 then the value of k is

a) 1

b) 2

c) -2

d) -1

11. Given ∆ABC~∆PQR, if AB/PQ =1/3,then 

ar (∆ABC)/are (∆PQR) =..........

12. In the figure, ∆ABC is circumscribing a circle, the length of BC is ........ cm

13. The value of (sin²∅ + 1/1+tan²∅)=.......

Or

The value of 

(1+tan²∅) (1-sin∅) (1+sin∅)=.........

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14. A ladder 10 m long reaches a window 8 m above the ground. The distance of the foot of the ladder from the base of the wall is ......m

15. 2cos67°/sin23° - tan40°/cot 50° - cos0° =.......

16. If the mean of the first n natural number is 15, then find n.

17. A die is thrown once, what is the probability of getting a number less than 3?

Or

If the probability of winning a game is 0.7,what is the probability of losing it?

18. The ratio of the length of a vertical rod and the length of it's shadow is 1:√3. 

Find the angle of elevation of the sun at that moment?

19. Two cones have their heights in the ratio 1:3 and radii in the ratio 3:1. What is the ratio of their volumes?

20. A pair of dice is thrown once. What is the probability of getting doublet?

Section - B

Directions (Q.nos. 21-26 are of 2 marks each)

21. In the figure, DE\\AC and DC\\AP. Prove that BE/EC=BC/CP.

Or

In the given figure, two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that 

Angle PTQ=2Angle OPQ.

22. The rod AC of a TV disc antenna is fixed at right angles to the wall AB and a rod CD is supporting the disc as shown in the figure, if AC=1.5m long and CD=3m, find 

i. tan∅

ii. sec∅+ cosec∅,.

23. If a number x is chosen at random from the numbers -3 -2, -1, 0, 1, 2, 3. What is the probability that x²≤4?

24. Find the mean of the following distribution:

Or

Find the mode of the following data:

25. The minute hand of a clock is 12m long. Find the area of the face of the clock described by the minute hand in 35min.

26. The sum of the first 7 term of an AP is 63 and that of it's next 7 terms is 161. Find the AP.

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Posted by:- Anuranjan Gadekar

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