Mathematics Sample paper 7, Part - B for class 10th

 Mathematics Sample paper

19. Case Study III

Telecasting Tower

A straight highway leads to the foot of a national communication and telecasting tower. A watchman standing at the top of the tower observes a car at an angle of depression of 30° which is approaching the foot of the tower with a uniform speed. Two minutes later, the angle depression was found to be 60°. The watchman suspects that some terrorist are approaching the tower. It needs half a minute for the watchman to inform the security staff so that it may alert.

a) The angle of depression from object  to the point on the ground and the angle of elevation of the same point on the ground to the same object is

i. Equal

ii. Double

iii. Triple

iv. None of these

b) The angle of .......... of an object viewed, is the angle formed by the line of sight with the horizontal.

i. Depression 

ii. Elevation

iii. Don't say anything

iv. None of these

c) How much time the car will take to reach the foot of the tower?

i. 1 min

ii. 2 min

iii. 3 min

iv. 4 min

d) Suppose a distance between the ball and tree is 10√3m and one person is sitting at the top surface of a tree. Find the angle in which the observer see the ball.

i. 30°

ii. 60°

iii. 45°

iv. 55°

e) If the angle of elevation of Sun above the tower decrease, then length of shadow of a tower

i. Increase

ii. Decrease

iii. Remain Same

iv. none of these

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20. Case Study IV

Play Cards

There are three friends and they want to play some interesting game. Firstly, they consider some cards and marked with the numbers 2 to 101 are placed in a box and mixed through. One card is drawn from this box.

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

i. 1/2

ii. 1/4

iii. 3/4

iv. 1/3

b) Find the probability that the drawn on the card is number less than 14.

i. 4/25

ii. 3/25

iii. 3/5

iv. 7/25

c) Find the probability that the drawn on the card is a number which is perfect square.

i. 3/100

ii. 7/10

iii. 7/100

iv. 9/100

d) Find the probability that the drawn on the card is a prime number and it is less than 20.

i. 2/25

ii. 3/25

iii. 7/25

iv. 11/25

e) Find the probability that drawn card is anyone of the number from 2 to 101.

i. 1

ii. 2

iii. 3

iv. 4

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

21. Find the sum of the series

7+ 10 1/2 + 14+. . . . .  84.

Or

Poonam saved Rs 5 in the first week of the year and then increased her weekly savings by Rs 1.75 each week. In which week will her weekly savings be Rs 20.75?

22. In a right angled triangle ABC, right angled at B, if the ratio of AB to AC is 1:√2, then find the values of

i. 2 tanA / 1-tan² A

ii. 2 tan A/1+tan²A

23. Find the ratio in which the line segment joining A(1,-5) and  B(-4,5) is divided by the X-axis. Also, find the coordinates of the point of intersection.

Or

The line segment joining the points (3,-4) and (1,2) is trisected  at the points P and Q. If the coordinates of P and Q are (p,-2) and (5/3,q) respectively, find the values of p and q.

24. If the sum of the deviations of a set of values x1,x2,x3.........xn measured from 50 is (-10) and the sum of deviations of the values from 46 is 70, then find it's mean.

25. In an isosceles ∆ABC, if AB=AC and D is a point on BC, then prove that

AB² - AD² = BD . CD

26. Prove that √3 + √7 is irrational.

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

27. For which value of k, will the following pair of linear equations have no solution?

3x + y= 1, (2k-1)x + (k-1) y= 2k+ 1

Or

Represent the following system of linear equations graphically.

3x + y -5= 0, 2x - y -5= 0

From the graph, find the points where the lines intersect the Y- axis.

28. Find the points on the X- axis, which are at a distance of 2√5 from the point (7,-4).

How many such points are there?

29. Find the median in the following distribution.

30. A boy is cycling that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60cm, calculate the speed per hour with which the boy is cycling.

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31. Find the values of 

5sin²30° + cos²45° - 4tan²30°/ 2 sin 30° cos 30° + tan45°

Or

Given, cos∅=21/29, determine the value of 

sec∅/tan∅ - sin∅

32. Solve the following equation for x, 

9(x² + 1/x²) - 9(x+1/x) -52=0.

33. A man sold a chair and a table together for Rs 1520 there by making a profit of 25% on the chair and 10% on table. By selling them together for Rs 1535, he would have made a profit of 10% on the chair and 25% on the table. Find the cost price of each.

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

34. Draw a circle of radius 8cm. From a point 17cm away from it's centre, construct a pair of tangents to the circle and measure their lengths.

35. A right angled triangle whose sides are 15cm  and 20cm is made to revolve about it's hypotenuse. Find the volume and surface area of the double cone so formed.

(Take π= 3.14)

Or

A solid toy is in the form of a hemisphere surmounted by a right circular cone. Height of the cone is 4cm and the diameter of the base is 8cm. If a right circular cylinder circumscribes the solid. Find how much more space it will cover?

36. Find the sum of all natural numbers less than 1000 which are neither divisible by 5 nor by 2.

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Posted by:- Anuranjan Gadekar

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