Mathematics Sample paper Part-B for class 10th

 Mathematics Sample paper

Part-B

19. Case Study III.

During the Lock down period

During the lockdown period, people were very puzzled and they decided to play some game. Firstly, they collect the 17cards and write the numbers 1 to 17 and put them in a box.

People make a bet for the chances of drawing the number either the prime, odd, or even number etc.

a) Find the probability that the number on the card is an odd number.

i. 9/17

ii. 8/17

iii. 6/17

iv. 7/17

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b) Find the probability that the number on the card is a prime number.

i. 7/17

ii. 9/17

iii. 8/17

iv. 5/17

c) Find the probability that the number on the card is divisible by 2 and 3 both.

i. 2/17

ii. 3/17

iii. 4/17

iv. 5/17

d) Find the probability that the number on the card is a multiple of 3 or 5.

i. 7/17

ii. 5/17

iii. 9/17

iv. 2/17

e) An event happening only one outcome of the random experiment is called

i. Elementary event

ii. Compund event

iii. Equilikely

iv. None of the above

20. Case study IV

Storm in Kolkata

Few months ago, heavily storm comes out in Kolkata. Due to this storm thousands of trees breaks and electric pole bent out (or break). Some of the electric poles bent into the shape of parabolic which is shown in figure.

a) Suppose the quadratic polynomial for given curve is ax²+bx+c, then always a is

i. >0

ii.<0

iii. ≤0

iv. ≥0

b) Find the zeroes of the given curve.

i. 2 and -1

ii. -2 and 1

iii. -2, -1

iv. None of the above

c) The polynomial expression of given curve is 

i. x²-x+2

ii. x²+x-2

iii. x²+x+2

iv. None of the above

d) If x=2, then find the value of polynomial.

i. 4

ii. 3

iii. 2

iv. -4

e) If we move the parabola right side of one unit, then find it's polynomial expression.

i. x²-3x+2

ii. x²+x+2

iii. x²-x-2

iv. x²+x-2

Part-B

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

21. Which term of the Arithmetic progression 5,15, 25,..... will be 140 more than 31st term?

22. Check whether (5,-2), (6,4) and (7,-2) are the vertices of an isosceles triangle.

23. Explain why 7×11×13+13 and 7×6×5×4×3×2×1+5 are composite numbers.

If HCF (28,35 and 343)=7, find the LCM (28,35 and 343).

24. A bag contains 20 balls out of which x balls are white. If one ball is drawn at random, the probability of drawing a white ball is y. Now, place this ball and 10 more white balls in the bag. Now, if a ball is drawn from the bag, the probability of drawing the white ball is 2y, Find x.

Or

Cards marked with numbers 3,4,5....,50 are placed in a box and mixed thoroughly. Once card is drawn at random from the box. Find the probability that number on the drawn card is 

i. Divisible by 7

ii. A number which a perfect square.

25. In ∆ABC, right angled at B, if tanA =1/√3,then find the value of 

i. sin Acos C +cosAsinC

ii. cosAcosC - sinA sinC.

26. In the given figure, ABCD is a square of side 14cm. With centres A, B,C and D,four circles are drawn,such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.

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Directions (Q.nos. 27-33 are of 3 marks each)

27. Solve the following system of equations.

1/2(2x+3y) +12/7(3x-2y)= 1/2

and 

7/2x+3y +4/3x-2y=2

Or

Solve the pair of equations for x and y, 2/√x +3/√y =2 and 4/√x-9√y=1; x≠0, y≠0.

28. Three sets of English, Hindi and Mathematics book have to be stacked in such a way that all the books are stored topicwise and the height of each stack is the same. The number of English book is 96, the number of Hindi books is 240 and the number of Mathematics books is 336. Assuming that the books are of the same thickness, determine the number of stacks of English, Hindi and Mathematics books.

29. AD is a median of ∆ABCand bisectors of angle ADB and angle ADC are DE and DF, which meet AB at E and AC at F. Prove that EF\\BC.

Or

A girl of height 120cm is walking away from the base of a lamp post at a speed of 1.2m/s. If the lamp is 4.8m above the ground, then find the length of her shadow after 6s.

30. The following table shows the age distribution of cases of a certain disease admitted during a year in a particular hospital.

Find the modal age.

31. If alpha and beeta are zeroes of x²- p(x+1)-c, then find the value of (alpha+1) (beeta+1)=1-c and also show that alpha + 2alpha +1/alpha²+2alpha+c +beeta²+2beeta +1/beeta²+2beeta+c=1.

32. Find the ratio in which line 2x+y=4 divides the join of A (2,-2) and B (3,7). Also, find the coordinates of the point of intersection.

33. Find the volume and curved surface area of largest right circular cone that can be cut out of a cube whose edge is 10cm.

Directions (Q.nos. 34-36 are of 5 marks each)

34. The sums of n terms of three Arithmetic progression are S1,S2 and S3. The first term of each is unity and the common difference are 1,2,3 respectively. Prove that S1 +S3= 2S2

35. Construct a tangent to a circle of radius 1.8cm from a point on the concentric circle of radius 2.8cm and measure it's length. Also, verify the measurement by actual calculation.

36. Draw the graphs of the equations x-y+1=0 and 3x+2y -12=0. Determine the coordinates of the vertices of the triangle formed by these lines and the X-axis and shade the triangular region.

Or

A boat covers 32km upstream and 36 km downstream in 7h. Also, it covers 40km upstream and 48 km downstream in 9h. Find the speed of the boat in still water and that of the stream.

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Posted by:- Anuranjan Gadekar

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