Section A
(i) Section A carries 40 marks.
(ii) This section contains four questions. All the questions are compulsory.
Find the compound interest paid when a sum of Rs 15000 is invested for 1 year and 4 months at 
per annum compounded annually.
Using property of proportion, prove that if
, then 
(i) If
, then find the values of x and y.
(ii) A real number x is greater than or equal to 2 more than one-third of the number itself and is less than or equal to 3 more than half the number itself. How this situation can be represented in form of an inequality?
The distance between two points P and Q is 6 units. The coordinates of point P are (4, −6). Find the coordinates of point Q, if the ordinate of Q is thrice its abscissa.
In the given figure, a cyclic quadrilateral PQRS is shown and an isosceles triangle PST with PT = TS is shown.
The line RST is a straight line. Also, PQ = QS
If ∠PQR = 72° and ∠PSQ = 56°, then find:
(i) ∠PST
(ii) ∠POS
(i) If tangents XY and YZ from a point Y to a circle with centre O are inclined to each other at an angle of 64°, then find ∠YOZ.
(ii) In the given figure, a cyclic quadrilateral WXYZ is shown. Find the values of x and y.
From a solid metallic cylinder of height 24 cm, a cone of same height and same base (as cylinder) is taken out. The density of the metal is 10 gm per cm3. If the mass of the remaining portion of the cylinder is 24.64 kg, then find the cost required to paint the remaining portion at a rate of Rs 3 per 440 cm2.
The minute hand of a clock swept an area of 115.5 cm2 while its tip travelled a distance of 22 cm. Find the radius of the minute hand and the time of rotation. 
A cylindrical glass vessel of base radius 14 cm and 40 cm height contains water up to 30 cm height. If 12 spherical metallic balls of radius 3.5 cm are dipped into it, then find the gap between the water level and the total height of the container.
If m = cosec θ − cot θ and n = sec θ, then prove that 
Convert the following more than type ogive into a less than type ogive.
(i) Prove that: 
(ii) Express cot 56° − sec 68° + cos 61° in terms of trigonometric ratios of angles between 0° and 35°.
Section B
(i) Section B also carries 40 marks.
(ii) This section contains seven questions. Answer any four questions.
Anju purchased a microwave for Rs 27,500. After two years, its value got depreciated by 4.5%. Find the value of the microwave after 2 years.
Jammy ordered dinner for his family from a restaurant. The bill for the lunch was Rs 428 including a VAT of 7%. Find the bill amount before VAT was added.
Mr. Ambani invests Rs 9000 in shares of a certain company. He buys Rs 50 shares at a premium of Rs 10 and earns an annual income of Rs 375.
(i) Find the rate of dividend on the shares.
(ii) If he wants to increase his annual income by Rs 100, then how many more shares should he buy?
The point X (4, 3 m − 4) divides the line segment joining the points P (2, −5) and Q (7, 5) in the ratio 2:3 internally. Find the value of m.
(i) What is the solution of the inequality
?
(ii) What are the coordinates of the foot of the perpendicular drawn from the point (3, 5) to the line, 2x + 3y + 7 = 0?
A retailer cuts three pieces from a single piece of cloth of length 93 cm. The length of the second piece is 5 cm longer than the shortest piece and the length of the third piece is twice that of the shortest piece. If the third piece is to be at least 5 cm longer than the second, then the length of the shortest piece can vary from
Draw the line(s) of symmetry of the following figures and state the number of lines of symmetry in each case.
(i)
(ii)
(iii)
Draw a circle of radius 5 cm. From a point 13 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. Also measure the angles between the tangents. Give the justification of the construction.
ΔABC is shown in the figure.
D and E are points on the sides AB and AC respectively such that DE||BC.
(i) Prove that ΔADE ∼ ΔABC
(ii) If DE = 2 cm and BC = 6 cm, find 
(iii) Find 
3 spheres of radii 6 cm, 8 cm, and 10 cm are melted to form a cone whose radius is twice its height. Find the surface area of this cone in terms of π.
A right-angled triangle ABC with AB = 8 cm, BC = 15 cm, and ∠B = 90° is rotated along its hypotenuse AC. What is the solid so obtained? Find the surface area and volume of the solid. [Use
]
From the top of a 10 m high building, the angle of elevation of the top of a tower is θand the angle of depression of its foot is 45°. Find the angleθ, if the height of the tower is 17 m more than the height of the building. (Take
)
A helicopter flying at an altitude of 1600 metres finds that two ships are sailing in the same direction towards it. The angles of depression of the ships as observed from the helicopter are 45° and 30° respectively. Find the distance between the two ships.
Arjun standing on a horizontal plane observes that a bird at a distance of 100 m from him is at an elevation of 60°. Aditi standing on a roof of a 30 m tall building observes that the same bird is making an angle of elevation of 45°. Both Arjun and Aditi are on the opposite sides of the bird. Find the distance of the girl from the bird.
The mean of the following frequency distribution is 31.4. If there are 100 observations in total, then find the value of f1 and f2.
Class interval | Frequency |
0 − 10 | 10 |
10 − 20 | f1 |
20 − 30 | 20 |
30 − 40 | f2 |
40 − 50 | 14 |
50 − 60 | 16 |
Total | 100 |
Draw the histogram for the following data. Hence calculate the mode.
Class interval | 0 − 100 | 100 − 200 | 200 − 300 | 300 − 400 | 400 − 500 |
Frequency | 6 | 10 | 9 | 18 | 7 |
State true or false and give reasons in support of your answer.
(i) Probability of an event can be 
.
(ii) Total number of outcomes for the experiment of tossing a coin and rolling a die together is 8.
(iii) The probability of drawing a red marble from a bag containing blue marbles only is 0.
A box contains 4 red balls, 8 white balls, and some blue balls. The probability of drawing a ball, which is neither blue nor red, is
.
(i) What is the number of blue balls in the box?
(ii) Find the probability of drawing a blue ball or a white ball.
From a well-shuffled deck of 52 cards, a card is drawn at random. Find the probability that the card drawn is
(i) neither a face card nor a red card
(ii) not a spade
(iii) black or club
(iv) black or red
Answer : Click here
No comments:
Post a Comment