1.
what will the di,erence between the upper limit of modal class and lower
limit of median class?
2. Find the radius of a quadrant of a circle whose circumference is 22 cm.
3. Assertion : If the length of shadow of a vertical pole is equal to its height,
then the angle of elevation of the sun is 450.
Reason : According to Pythagoras theorem, h2 = p2 + b2, where h =
hypotenuse, l = length and b = base.
4. the values of the trigonometric ratios of an angle do not vary with the
lengths of the sides of the triangle, if the angle remains the same.
True/false give reason for your answer.
5. A tower stands vertically on the ground. From a point on the ground,
which is 15 m away from the foot of the tower, the angle of elevation of
the top of the tower is found to be 60°. Find the height of the tower.
6. the hypotenuse is the longest side in a right triangle, the value of sin A or
cos A is always less than 1. Prove it by taking random values.
7. Do the points (3, 2), (–2, –3) and (2, 3) form a triangle? If so, name the type
of triangle formed.
8. Assertion: If a line is drawn parallel to one side of a triangle to intersect
the other two sides in distinct points, the other two sides are divided in
the same ratio.
Reason: The ratio of any two corresponding sides in two equiangular
triangles is always the same.
9. write the next two terms: ∛54, ∛128, ∛250, ∛432……
10. Find the dimensions of the prayer hall.
11. Assertion: 3x2 – 6x + 3 = 0 has repeated roots.
Reason: The quadratic equation ax2 + bx + c = 0 have repeated roots if
discriminant D > 0.
12. Akhila went to a fair in her village. She wanted to enjoy rides on the
Giant Wheel and play Hoopla (a game in which you throw a ring on the
items kept in a stall, and if the ring covers any object completely, you get
it). The number of times she played Hoopla is half the number of rides
she had on the Giant Wheel. If each ride costs ` 3, and a game of Hoopla
costs ` 4, how would you find out the number of rides she had and how
many times she played Hoopla, provided she spent ` 20. Form the
equations only.
13. Higher power of x in p(x) is called the degree of the polynomial p(x).
True/false show with an example.
14. Assertion: The prime factorisation of a natural number is unique,
except for the order of its factors.
Reason: Every composite number can be expressed (factorised) as a
product of primes, and this factorisation is unique, apart from the order in
which the prime factors occur.
15. the product and quotient of a non-zero rational and irrational
number is irrational. True/false give reason for your answer.
16. Find the type of polynomial shown in the given figure:
17. Find the zeroes of the polynomial x2 – 3 and verify the relationship
between the zeroes and the coe,icients.
18. The amount of air present in a cylinder when a vacuum pump
removes 1/4 of the air remaining in the cylinder at a time. Is it AP? Provide
reason for your answer.
19. The value of tan A is always less than 1. True/false give reason.
20. Two players, Sangeeta and Reshma, play a tennis match. It is known
that the probability of Sangeeta winning the match is 0.62. What is the
probability of Reshma winning the match?
Section B
21. Find a relation between x and y such that the point (x , y) is
equidistant from the points (7, 1) and (3, 5).
22. A box contains 12 balls out of which x are black. If one ball is drawn
at random from the box, what is the probability that it will be a black ball?
If 6 more black balls are put in the box, the probability of drawing a black
ball is now double of what it was before. Find x.
23. A fraction becomes 9/11 , if 2 is added to both the numerator and
the denominator. If, 3 is added to both the numerator and the
denominator it becomes 5/6 . Find the fraction.
24. (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A.
25. A car has two wipers which do not overlap. Each wiper has a blade
of length 25 cm sweeping through an angle of 115°. Find the total area
cleaned at each sweep of the blades.
Section C
26. In what ratio does the point (– 4, 6) divide the line segment joining
the points A(– 6, 10) and B(3, – 8)?
27. A girl of height 90 cm is walking away from the base of a lamp-post
at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the
length of her shadow after 4 seconds.
28. Shakila put ` 100 into her daughter’s money box when she was one
year old, ` 150 on her second birthday, ` 200 on her third birthday and
will continue in the same way. How much money will be collected in the
money box by the time her daughter is 21 years old?
29. A cottage industry produces a certain number of pottery articles in a
day. It was observed on a particular day that the cost of production of
each article (in rupees) was 3 more than twice the number of articles
produced on that day. If the total cost of production on that day was ` 90,
find the number of articles produced and the cost of each article.
30. Mayank made a bird-bath for his garden in the shape of a cylinder
with a hemispherical depression at one end (see Fig. 12.9). The height of
the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area
of the bird-bath.
31. Two dice, one blue and one grey, are thrown at the same time. Write
down all the possible outcomes. What is the probability that the sum of
the two numbers appearing on the top of the dice is (i) 8? (ii) 13? (iii) less
than or equal to 12?
Section D
32. The angles of depression of the top and the bottom of an 8 m tall
building from the top of a multi-storeyed building are 30° and 45°,
respectively. Find the height of the multistoreyed building and the
distance between the two buildings.
33. Sides AB and AC and median AD of a triangle ABC are respectively
proportional to sides PQ and PR and median PM of another triangle PQR.
Show that D ABC ~ D PQR.
34. The median of the following data is 525. Find the values of x and y, if
the total frequency is 100.
35. A gulab jamun, contains sugar syrup up to about 30% of its volume.
Find approximately how much syrup would be found in 45 gulab jamuns,
each shaped like a cylinder with two hemispherical ends with length 5
cm and diameter 2.8 cm.
OR
A vessel is in the form of an inverted cone. Its height is 8 cm and the
radius of its top, which is open, is 5 cm. It is filled with water up to the
brim. When lead shots, each of which is a sphere of radius 0.5 cm are
dropped into the vessel, one-fourth of the water flows out. Find the
number of lead shots dropped in the vessel.
Section E
36. To conduct Sports Day activities, in your rectangular shaped school
ground ABCD, lines have been drawn with chalk powder at a distance of
1m each. 100 flower pots have been placed at a distance of 1m from
each other along AD, Niharika runs 1/4 th the distance AD on the 2nd line
and posts a green flag. Preet runs 1/5 th the distance AD on the eighth
line and posts a red flag.
i. What is the distance between both the flags?
ii. If Rashmi has to post a blue flag exactly halfway between the line
segment joining the two flags, where should she post her flag?
iii. If Rashmi moves one line towards preet. What will be the ratio
between Niharika and preet.
37. Vijay is trying to find the average height of a tower near his house.
He is using the properties of similar triangles. The height of Vijay’s house
if 20 m when Vijay’s house casts a shadow 10 m long on the ground. At
the same time, the tower casts a shadow 50 m long on the ground and
the house of Ajay casts 20 m shadow on the ground.
(a) What is the height of the tower? (1)
(b) What is the height of Ajay’s house? (1)
(c) What will be the length of the shadow of the tower when Vijay’s house
casts a shadow of 12 m? (2)
38. In a potato race, a bucket is placed at the starting point, which is 5
m from the first potato, and the other potatoes are placed 3 m apart in a
straight line. There are ten potatoes in the line (see Fig. 5.6) A competitor
starts from the bucket, picks up the nearest potato, runs back with it,
drops it in the bucket, runs back to pick up the next potato, runs to the
bucket to drop it in, and she continues in the same way until all the
potatoes are in the bucket.
i. What is the total distance the competitor has to run?(2)
ii. Distance she covers upto collect 5 patatoes is equal to the distance
she covers to pick the potatoes after five? (2)
