Chapter -3 , Pair of linear equations in two variables
①. Aruna has only ₹ 1 and ₹ 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is ₹ 75, then the number of ₹ 1 and ₹ 2 coins are, respectively. [Ans. 25, 25]
②. The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages (in year) of the son and the father are, respectively [Ans.6, 36]
③. Draw the graphs of the equations x = 3, x = 5 and 2x – y – 4 = 0. Also find the area of the quadrilateral formed by the lines and the X-axis. [Ans.8sq. m]
④. In a competitive examination, 1 mark is awarded for each correct answer while 1/2 mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly? [Ans.100]
⑤. There are some students in the two examination halls A and B. To make the number of students equal in each hall, 10 students are sent from A to B but, if 20 students are sent from B to A, the number of students in A becomes double the number of students in B,then find the number of students in the both halls. [Ans.100 , 80]
⑥. A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days and an additional charge for each day thereafter. Latika paid ₹ 22 for a book kept for six days, while Anand paid ₹ 16 for the book kept for four days. Find the fixed charges and the charge for each extra day. [Ans.₹10, ₹3]
⑦.For which value (s) of k will the pair of equations
kx+3y = k – 3, 12 x + ky =k ,has no solution? [Ans.-6]
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Chapter-4, Quadratic Equations
①. A natural number, when increased by 12, equals 160 times its reciprocal.Find the number. [Ans.8]
②. A train, travelling at a uniform speed for 360 km, would have taken 48 min less to travel the same distance, if its speed were 5 km/h more. Find the original speed of the train. [Ans.45km/h]
③. If Zeba were younger by 5 yr than what she really is, then the square of, her age (in years) would have been 11, more than five times her actual age, what is her age now? [Ans.14 years]
④. At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age. Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha. [Ans.27yrs, 5yrs]
⑤. In the centre of a rectangular lawn of dimensions 50m x 40m, a rectangular pond has to be constructed, so that the area of the grass surrounding the pond would be 1184 m2. Find the 'l' and 'b'of the pond. [Ans.34m, 24m]
⑥. At t min past 2 pm, the time needed by the minute hand of a clock to show 3 pm was found to be 3 min less than (t^2)/4 min. Find t. [Ans. 14min]
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Chapter-5 , Airthmetic Progressions
①. Yasmeen saves ₹ 32 during the first month, ₹ 36 in the second month and ₹ 40 in the third month. If she continues to save in this manner, in how many months will she save ₹ 2000 ? [Ans. 25 months]
②. If sn denotes the sum of first n terms of an AP, then prove that s12 =3(s8-s4)
③. Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to
④. Jaspal Singh repays his total loan of ₹ 118000 by paying every month starting with the first installment of ₹ 1000. If he increases the installment by ₹ 100 every month, what amount will be paid by him in the 30th installment? What amount of loan does he still have to pay after the 30th installment?
⑤. The students of a school decided to beautify the school on the annual day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags.Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance she did cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag? [Ans.26m]
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Chapter - 7 , Co-ordinate Geometry
①. Find the values of k, if the points A(k + 1, 2k), B(3k, 2k + 3) and C (5k – 1, 5k) are colli near. [Ans. 2, 1/2]
②. Find the ratio in which the line 2x+ 3y – 5 = 0 divides the line segment joining the points (8, – 9) and (2,1). Also, find the coordinates of the point of division.
③. If the point A(2, – 4) is equidistant from P(3, 8) and Q(- 10, y), then find the value of y. Also, find distance PQ.
④. If P(9a -2, – b) divides line segment joining A(3a + 1,-3) and B(8a, 5) in the ratio 3 : 1, then find the values of a and b.
⑤. If the centre of a circle is (2a, a – 7), then Find the values of a, if the circle passes through the point (11, – 9) and has diameter 10√2 units.
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Chapter 8 , Trigonometry and it's applications
①. If sinθ + 2 cosθ = 1, then prove that 2 sinθ – cosθ = 2.
②.A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag staff are α and β respectively. Prove that the height of the tower is
③. If tan θ + sec θ = l, then prove that secθ =
④. The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60° and the angle of elevation of the top of the second tower from the foot of the first tower is 30°. Find the distance between the two towers and also the height of the tower.
[Ans. 10√3 m and 10 m]
⑤. A ladder against a vertical wall at an inclination a to the horizontal. Sts foot is pulled away from the wall through a distance p, so that its upper end slides a distance q down the wall and then the ladder makes an angle B to the horizontal. Show that
⑥. A window of a house is h m above the ground. Form the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be a and p, respectively. Prove that the height of the other house is h(1+tanα cot β)m.
⑦. If sinθ + cosθ = p and sec θ + cosec θ = q, then prove that q(p2-1) = 2p.
⑧. Simplify (1 + tan2 θ) (1 – sinθ) (1 + sinθ)
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Chapter 12 , Surface, Area and Volume of Solids
1. The rain water from a roof of dimensions 22 m x 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall (in cm). [Ans. 2.5cm]
2. A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap. [Ans. 36cm , 43. 267cm]
3. A solid iron cuboidal block of dimensions 4.4 m x 2.6m x lm is recast into a hollow cylindrical pipe of
internal radius 30 cm and thickness 5 cm. Find the length of the pipe. [Ans. 112m]
4. Water is flowing at the rate of 15 kmh-1 through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm? [Ans. 2 hours]
5. A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover heap? [Ans. 80.61 sq. m]
6. A wall 24 m long, 0.4 m thick and 6 m high is constructed with the bricks each of dimensions 25 cm x 16 cm x 10 cm. If the mortar occupies
th of the volume of the wall, then find the number of bricks used in constructing the wall. [Ans. 12960]
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