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Important Questions For You!

Chapters 1: GST [Goods and Services Tax]

Q 1. M/s Ram Traders, Delhi, provided the following services to M/s Geeta Trading Company in Agra (UP). Find the amount of bill.                [3M]

Number of services

8

12

10

16

Cost of each service (in Rs.)

680

320

260

420

GST %

5

12

18

12


Q 2.
 National Trading Company, Meerut (UP) made the supply of the following goods/services to Samarth Traders, Noida (UP). Find the total amount of bill if the rate of GST = 12%                                                                                                      [4M]

Quantity (no. of pieces)

20

30

12

40

MRP (in Rs. per piece)

225

320

300

250

Discount %

40

30

50

40


Q 3.
Mr. Malik went on a tour to Goa. He took a room in a hotel for two days at the rate of Rs. 5000 per day. On the same day, his friend John also joined him. Hotel provided an extra bed charging Rs. 1000 per day for the bed. How much GST, at the rate of 28% is charged by the hotel in the bill to Mr. Malik for both the days?                                                                              [3M]


Q 4.
A is a dealer in Meerut (U.P.). He supplies goods/services, worth Rs. 15,000 to a dealer B in Ratlam (M.P.). Dealer B, in turn, supplies the same goods/services to dealer C in Jabalpur (M.P.) at a profit of Rs. 3000. If rate of tax (under GST system) is 18%, find                                                                                                                                                                           [4M]

  1. The cost of goods/services to the dealer C in Jabalpur.
  2. Net tax payable by dealer B.

Q 5.
For a dealer A, the list price of an article is Rs. 9000, which he sells to dealer B at some lower price. Further, dealer B sells the same article to a customer at its list price. If the rate of GST is 18% and dealer B paid a tax, under GST, equal to Rs. 324 to the government, find the amount (inclusive of GST) paid by dealer B.                                                                    [4M]


Q 6.
A is a manufacturer of T.V. sets in Delhi. He manufacturers a particular brand of T.V. set and marks it at Rs. 75,000. He then sells this T.V. set to a wholesaler B in Punjab at a discount of 30%. The wholesaler B raises the marked price of the T.V. set bought by 30% and then sells it to dealer C in Delhi. If the rate of GST = 5% find tax (under GST) paid by wholesaler B to the government.    [4M]  


Chapter 2: Banking (Recurring Deposit Account)

Q 1. Renu deposited Rs. 500 per month in a bank for 15 months under a recurring deposit account scheme. What will be the maturity value of her deposits, if the rate of interest is 6% per annum and the interest is calculated at the end of every month? [3M]


Q 2.
Mr A opened a recurring deposit account in a certain bank and deposited Rs. 2520 per month for 5 years. Find the maturity value of this account if the bank pays interest at the rate of 9% per year.                                                                [3M]   


Q 3.
Arun has a recurring deposit account for 2 years at 5% p.a. He receives Rs. 1250 as interest on maturity.           [4M]

  1. Find the monthly instalment amount
  2. Find the maturity amount


Q 4. 
Mrs Singh deposits Rs. 1750 per month in her recurring bank account for a period of 2 years. At the time of maturity, she would get Rs. 47250. Find the                                                                                                                       [4M] 

  1. Rate of interest p.a.
  2. Total interest earned by Mrs Singh


Chapter 3: Linear Inequations (in one variable)

Q 1. Solve the given inequation and graph the solution on the number line.              [3M]

6y – 2 < y + 8 ≤ 3y + 6; y ε  R                                                                                                                         


Q 2.
If A = {x : 9x – 3 > 2x + 4, x ε R} and B = {x : 12x – 7 ≥ 5 + 6x, x ε R}, find the range of set A ∩ B and represent it on the number line.                                                                                                                                                     [4M] 


Q 3.
Solve the inequation and represent the solution set on the number line.                                                            [4M]

begin mathsize 12px style 7 plus straight x less or equal than fraction numerator 5 straight x over denominator 2 end fraction minus 2 less or equal than 9 over 2 2 straight x comma space straight x element of straight I end style

Chapter 4: Quadratic Equations

Q 1. Without solving the quadratic equation, find the value of ‘m’ for which the given equation has real and equal roots.    [3M] 

x2 + 2(m – 3)x + (m + 3) = 0


Q 2.
 Solve: begin mathsize 12px style fraction numerator x over denominator x minus 2 end fraction minus fraction numerator x minus 2 over denominator x end fraction equals 1 1 half end style                                                                                                                           [3M]


Q 3.
 begin mathsize 12px style open parentheses 1 plus fraction numerator 1 over denominator straight x minus 1 end fraction close parentheses fraction numerator 1 over denominator straight x minus 1 end fraction equals 7 over 8. end style Give your answer correct to two significant decimal places.                                            [3M]


Q 4.
Solve for x: begin mathsize 12px style 4 open parentheses straight x minus 1 over straight x close parentheses squared minus 8 open parentheses straight x plus 1 over straight x close parentheses equals 29 semicolon space straight x not equal to 0 end style                                                                                               [4M]


Q 5.
The sum of a square of a certain whole number and 45 times it is 900. Find the number.                                         [3M]


Q 6. The product of a boy’s age two years ago with his age 5 years later is 60. Find his present age.                               [3M]


Q 7. By increasing the speed of a car by 15 km/hr, the time of the journey for a distance of 60 km is reduced by 20 minutes. Find the original speed of the car.                                                                                                                                       [4M]


Q 8. The area of a big room is 375 m2. If the length is decreased by 10 m and the breadth is increased by 10 m, then the area would remain unaltered. Find the length of the room.                                                                                      [4M]


Q 9. A motor boat, whose speed is 6 km/h in still water, goes 8 km downstream and returns in a total time of 3 hours. Find the speed of the stream.                                                                                                                                [3M]


Q 10. Rs. 600 is divided equally among ‘x’ children. If the number of children were 10 more, then each would have got Rs. 10 less. Find ‘x’.                                                                                                                                                                [3M]

 

Chapter 5: Ratio and Proportion

Q 1. If begin mathsize 12px style fraction numerator square root of straight a plus square root of straight b over denominator square root of straight a minus square root of straight b end fraction equals 5 over 2 end style, find the value of  begin mathsize 12px style fraction numerator straight a squared plus straight b squared over denominator straight a squared minus straight b squared end fraction end style.                                                                                                    [3M]


Q 2. 
If a, b, c and d are in proportion, prove that  begin mathsize 12px style fraction numerator ma squared plus nb squared over denominator mc squared plus nd squared end fraction equals fraction numerator ma squared minus nb squared over denominator mc squared minus nd squared end fraction end style .                                                             [4M]


Q 3.
If begin mathsize 12px style fraction numerator straight x cubed plus 3 xy squared over denominator straight y cubed plus 3 straight x squared straight y end fraction equals 63 over 62 end style, then find x:y.                                                                                                                     [4M]


Q 4.
Find the numbers such that their mean proportion is 14 and third proportion is 112.                                                 [3M] 

 

Chapter 6:  Factorisation of Polynomials

Q 1. x – 2 is a factor of the expression x3 + ax2 + bx + 6. When this expression is divided by x – 3, the remainder is 3. Find the values of a and b.                                                                                                                                          [3M]


Q 2.
Show that 2x + 7 is a factor of 2x3 + 5x2 – 11x – 14. Hence, factorise the given expression completely using the factor theorem.           [3M]


Q 3.
The polynomials 3x3 – 9x2 + 5x – 13 and (a + 1)x2 – 7x + 5 leaves the same remainder when divided by x – 3. Find the value of a.                                                                                                                                                [3M]

   

Chapter 7: Matrices

Q 1. Find the value of x given that A2 = B                                                                                                                    [3M]

begin mathsize 12px style straight A equals open square brackets table row cell negative 4 end cell 2 row 3 1 end table close square brackets comma space straight B equals open square brackets table row 22 cell negative 6 end cell row straight x 7 end table close square brackets end style


Q 2.
If begin mathsize 12px style straight A equals open square brackets table row 2 3 row cell negative 2 end cell cell negative 1 end cell end table close square brackets end style and begin mathsize 12px style straight B equals open square brackets table row 1 4 row cell negative 3 end cell 0 end table close square brackets end style; find the matrix X such that AX = B.                                                              [4M]


Q 3.
Given begin mathsize 12px style straight A equals open square brackets table row 2 cell negative 1 end cell row 2 0 end table close square brackets end style, begin mathsize 12px style straight B equals open square brackets table row cell negative 3 end cell 2 row 4 0 end table close square brackets end style and begin mathsize 12px style straight C equals open square brackets table row 1 0 row 0 2 end table close square brackets end style, find the matrix X such that  A + X = 2B + C.                           [3M]


Q 4.
Given begin mathsize 12px style straight A equals open square brackets table row 2 0 row cell negative 1 end cell 7 end table close square brackets end style and  begin mathsize 12px style straight I equals open square brackets table row 1 0 row 0 1 end table close square brackets end style,  and A2 = 9A + mI. Find m.                                                                          [4M]


Q 5.
Solve for x and y : begin mathsize 12px style open square brackets table row cell straight x minus straight y space space end cell cell straight x plus straight y end cell end table close square brackets open square brackets table row 3 cell negative 4 end cell row 5 cell negative 1 end cell end table close square brackets equals open square brackets table row 24 2 end table close square brackets end style                                                                                         [3M]


Q 6.
Evaluate: begin mathsize 12px style open square brackets table row cell 4 space sin space 30 degree end cell cell 2 space cos space 60 degree end cell row cell sin space 90 degree end cell cell 2 space cos space 0 degree end cell end table close square brackets open square brackets table row 4 5 row 5 4 end table close square brackets end style                                                                                                             [3M]

 

Chapters 8: Arithmetic Progression

Q 1. The 11th  term of an AP is 80 and the 16th term is 110. Find the 31st term.                                                                [3M]


Q 2.
If the third term of an AP is 18 and the seventh term is 30, then find the series.                                                         [3M]


Q 3.
If the 3rd and the 9th terms of an Arithmetic Progression are 4 and –8 respectively, then find:  S20                              [4M]


Q 4.
Split 180 into three parts such that these parts are in AP and the product of the two extreme terms is 3500.                [4M]

 

Chapters 9: Coordinate Geometry

Q 1. Using a graph paper, plot the points A(3, 5) and (0, 5).                                                                                            [4M]

  1. Reflect A and B in the origin to get the images A’ and B’.
  2. Write the co-ordinates of A’ and B’.
  3. State the geometrical name for the figure ABA’B’.
  4. Find its perimeter.


Q 2.
Use a graph paper for this question. A(1, 1), B(5, 1), C(4, 2) and D(2, 2) are the vertices of a quadrilateral. Name the quadrilateral ABCD. A, B, C and D are reflected in the origin A’, B’, C’ and D’, respectively. Locate them on the graph sheet and write their co-ordinates.                                                                                                                                  [4M]


Q 3.
Use a graph paper for this question:                                                                                                                     [6M]

(Take 2cm = 1 unit on both x and y axes)

i.  Plot the following points:
A(0,4), B(2,3), C(1,1) and D(2,0).
ii. Reflect points B, C, D about the y-axis and write down their coordinates. Name the images as B’, C’, D’ respectively.
iii. Join the points A, B, C, D, D’, C’, B’ and A in order, so as to form a closed figure. Write down the equation to the line about which if this closed figure obtained is folded, the two parts of the figure exactly coincide.


Q 4.
The mid-point of the line segment joining (2a, 4) and (−2, 2b) is (1, 2a + 1). Find the values of a and b.                  [3M]


Q 5.
In the given figure, line ACB meets the y-axis at point B and the x-axis at point A. C is the point (−6, 6) and AC:CB = 2:3. Find the coordinates of A and B.                                                                          [3M]


Q 6.
Show that P(2, m – 2) is a point of trisection of the line segment joining the points A(4, −2) and B(1, 4). Hence, find the value of m.                                                                                                                                                       [3M]


Q 7.
The equation of the line is 4x – 5y = 9. Find the                                                                                                        [4M]

  1. Slope of the line
  2. Equation of the passing through the intersection of the lines x + y = 1 and 2x + y = 2 with slope begin mathsize 12px style fraction numerator negative 5 over denominator 4 end fraction end style.


Q 8.
Find the equation of a line                                                                                                                      [3M]

  1. Whose inclination is 30˚ and y-intercept is −2
  2. With inclination 60˚ and passing through (−4, 2)
  3. Passing through the points (3, −4) and (7, 1)


Q 9.
Write the equation of the line whose gradient is begin mathsize 12px style 3 over 2 end style and which passes through P, where P divides the line segment joining A(−2, 6) and B(3, −4) in the ratio 2:3.                                                                                                                   [3M]


Q 10.
If the slope of a line joining P(6, k) and Q(1 – 3k, 3) is ½, find                                                                                [3M]

  1. k
  2. the mid-point of PQ using the value of k found in (i)


Chapter 10: Similarity

Q 1. In ΔABC, DE is drawn parallel to BC. If AB = 16 cm, AD = 4 cm, and AC = 24 cm, find                                             [4M]

  1. EC
  2. begin mathsize 12px style fraction numerator ar open parentheses DADE close parentheses over denominator ar open parentheses DABC close parentheses end fraction end style
  3. begin mathsize 12px style fraction numerator ar open parentheses DADE close parentheses over denominator ar open parentheses trapezium space BCED close parentheses end fraction end style

Q 2.
The scale of the map is 1:200000. A plot of land of area 20 km2 is to be represented on the map. Find the                  [3M]
  1. Number of kilometres on the ground which is represented by 1 cm on the map
  2. Area in sq km which can be represented by 1 cm2
  3. Area of the map which represents the plot of land


Q 3.
A model of a ship is made to a scale 1: 300.                                                                                                           [3M]

  1. The length of the model of the ship is 2 m. Calculate the length of the ship.
  2. The area of the deck of the ship is 180,000 m2. Calculate the area of the deck of the model.
  3. The volume of the model is 6.5 m3. Calculate the volume of the ship.

 

Chapters 11: Circles

Q 1. In the figure, AD = BC and AB || DC, begin mathsize 12px style angle end styleBAC = 40˚ and begin mathsize 12px style angle end styleCBD = 60˚. Find                                                              [4M]

  1. begin mathsize 12px style angle end styleBCD
  2. begin mathsize 12px style angle end styleBCA
  3. begin mathsize 12px style angle end styleABC
  4. begin mathsize 12px style angle end styleADB


Q 2.
AB and CD are two chords on the same side. AB = 12 cm and CD = 24 cm. Distance between two parallel chords is 4 cm. Find the radius of the circle.                                                                [4M]


Q 3.
 In the given figure, ABCD is a cyclic quadrilateral. Find the values of x and y.                                                            [3M]


Q 4. 
In the given figure, O is the centre of the circle. AB is a tangent to it at point B. begin mathsize 12px style angle end styleBDC = 60˚. Find begin mathsize 12px style angle end styleBAO.          [4M]


Q 5. 
In the given figure, O is the centre of the circle. Tangents at A and B meet at C. If begin mathsize 12px style angle end styleACO = 25˚, find                   [3M]

  1. begin mathsize 12px style angle end styleBCO
  2. begin mathsize 12px style angle end styleAOB
  3. begin mathsize 12px style angle end styleAPB


Q 6. 
AB is a line segment and M is its mid-point. Semi-circles are drawn with AM, MB and AB as diameters on the same side of the line AB. A circle C(O, r) is drawn so that it touches all the three semi-circles. Prove that begin mathsize 12px style straight r equals 1 over 6 AB end style                           [4M] 

 

Chapter 12: Area and Volume of Solids

Q 1. A conical tent is to accommodate 11 people. Each person must have 4 sq. metres of the space on the ground and 20 cubic metres of air to breathe. Find the height of the cone.                                                                                                        [4M]


Q 2. 
A steel wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the mass of the wire, assuming the density of steel to be 8.88 g per cm3.                      [3M]


Q 3. 
The area of the base of a right circular cone is 28.26 sq. cm. If its height is 4 cm, find its volume and the curved surface area. (use π = 3.14)                                                                                                                                                   [3M]


Q 4.
The volume of a right circular cone is 660 cm3 and the diameter of its base is 12 cm. Calculate                              [4M]

  1. the height of the cone,
  2. the slant height of the cone,
  3. the total surface area of the cone. 

 

Chapters 13: Trigonometrical Identities

Q 1. Prove that: begin mathsize 12px style fraction numerator cosA over denominator 1 plus sinA end fraction plus tanA equals secA end style                                                                                                                [3M]


Q 2.
 Evaluate: begin mathsize 12px style 2 open parentheses fraction numerator tan 38 degree over denominator cot 52 degree end fraction close parentheses squared plus open parentheses fraction numerator cot 67 degree over denominator tan 23 degree end fraction close parentheses minus 3 open parentheses fraction numerator sec 83 degree over denominator cosec 7 degree end fraction close parentheses end style                                                                                      [3M]


Q 3.
If sin A + tan A = p and tan A - sin A = q, prove that begin mathsize 12px style straight p squared minus straight q squared equals 4 square root of pq end style.                                                              [4M]


Q 4.
Prove that: sin4A - cos4A = 1 - 2cos4A                                                                                                                [3M]


Q 5.
If x = a sinθ and y = b tanθ, show that begin mathsize 12px style straight a squared over straight x squared minus straight b squared over straight y squared equals 1 end style.                                                                                         [3M]

Chapters 14: Heights and Distances

Q 1. A guard observes a boat from a tower at a height of 150 m above sea level to be at an angle of depression of 25° (Take tan25° = 0.4663).                                                                                                         [4M]                   

  1. Calculate the distance of the boat from the foot of the tower to the nearest metre.
  2. After some time, it is observed that the boat is 180 m from the foot of the tower. Calculate the new angle of depression.


Q 2.
A vertical pole and a vertical tower are at the same ground level. From the top of the pole, the angle of elevation at the top of the tower is 30° and the angle of depression of the foot of the tower is 60°. Find the height of the pole if the height of the tower is 100 m.                                                                                                          [4M]

 

Chapters 15: Graphical representation

Q 1. Draw a histogram for the following discontinuous distribution:                                         [6M]

Class interval

11–20

21–30

31–40

41–50

51–60

Frequency

25

10

27

18

20

 

Q 2. Draw a frequency polygon for the following distribution (continuous data):                 [4M]

Age group

0-8

8-16

16-24

24-32

32-40

40-48

48-56

No. of girls

5

16

9

29

7

10

2


Q 3. Draw a frequency polygon for the following distribution (discontinuous data):           [6M]

Marks

11–20

21–30

31–40

41–50

51–60

61–70

No. of boys

10

18

36

58

72

80

 

Chapters 16: Measures of Central Tendency

Q 1. The weight of 40 children in a class was recorded in kg as follows:                                   [4M]

Weight (in kg)

45

47

49

51

53

55

No. of children

8

6

7

12

5

2

Calculate the following for the given distribution:

  1. Median
  2. Mode


Q 2. 
The height of 25 students of a class is given in the following table:                                    [4M]

Height (in cm)

140

150

160

170

180

No. of students

6

8

4

5

2

Find the mean height using the short-cut method.


Q 3.
From the given frequency distribution table, find the following using a graph:             [6M]

  1. Lower quartile  
  2. Upper quartile
  3. Inter – quartile range

Class interval

5–10

10–15

15–20

20–25

25–30

30–35

Frequency

4

8

5

13

11

9

 

Q 4. The following numbers are written in the descending order of their values:                    [3M]

70, 62, 50, a – 2, a – 6, a – 8, 28, 22, 16 and 10

If their median is 35, find the value of ‘a’.                                                                                  


Q 5.
Calculate the mean marks of the following distribution using the step-deviation method.               [4M]

Class interval

25–30

30–35

35–40

40–45

45–50

50–55

Frequency

8

15

25

17

14

11


Q 6.
Using a graph, draw an ogive for the following distribution which shows the marks obtained in the Mathematics paper by 150 students.                                                                                                                                        [6M]

Marks

0–10

10–20

20–30

30–40

40–50

50–60

60–70

70–80

No. of students

5

8

20

34

26

31

12

14

Use the ogive to estimate

i.  Median    ii. Number of students who score more than 55

 

Chapter 17: Probability

Q 1. Twenty identical cards are numbered from 1 to 20. A card is drawn randomly from those 20 cards. Find the probability that the number on the card drawn is                                                                                                                          [4M]

  1. divisible by both 2 and 5
  2. greater than 20


Q 2. A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting.                                          [3M]

  1. an ace
  2. a queen
  3. not a jack.

Q 3. 
A single letter is selected at random from the word ‘STATISTICS’. Find the probability that it is a                         [3M]
  1. vowel  
  2. consonant


Q 4.
A face of a die is marked with a number 1, 2, 3, -1, -2 and -3, respectively. The die is thrown once. Find the probability of getting                                                                                                  [4M]

  1. a negative integer
  2. the smallest positive integer


Q 5.
Three identical coins are tossed together. Find the probability of getting                       [4M]

  1. exactly two tails        
  2. at least one tail