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QUESTION: 1

Solution:
Mother's age when Ayesha's brother was born = 36 years.

Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.

∴ Required difference = (42 - 36) years = 6 years.

Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.

∴ Required difference = (42 - 36) years = 6 years.

QUESTION: 2

Find x and y x^{2} - xy = 4 and y^{2} - xy = -3

Solution:

x^{2} - xy = y .....(1)

y^{2} - xy = -3 .....(2)

Subtracting equation (2) from equation (1) we

Putting the value of x - y in equation (1) we get

Putting value of x in equation (2) we get,

putting value of y in equation (2) we get

y^{2} - xy = -3

⇒ 9 - 3x = -3

⇒-3x - -3 -9 = - 12

⇒ x = 4

So, (x, y) = (4, 3) or (-4, -3)

QUESTION: 3

An expression, which when divided by(x+1) gives (x^{2}-x+1) as quotient and 3 as remainder, is equal to

Solution:

QUESTION: 4

Of the following quardratic equation, which is the one whose roots are 2 and -15?

Solution:
Sum of roots = - 13

Product of roots = - 30

∴ Equation = x^{2} - x (sum of roots) + product of roots = 0

x^{2} + 13x - 30 = 0

Product of roots = - 30

∴ Equation = x

x

QUESTION: 5

Factorise a²-b²:

Solution:

QUESTION: 6

A square is inscribed in a circle of radius 10 units. The area of the circle not included in the square......(use π = 3.14)

Solution:

Let the side of square be x unit.

sider the right triangle ABD

have x^{2} + x^{2} = (10 + 10)^{2}

⇒ 2x^{2} = 400

x^{2} = 200

Area of square = 200 sq units

One of circle = πr^{2} = 22/7 x (10)^{2} = 314 sq units

One of shaded region not included in square

= 314 sq unit - 200 sq unit

= 114 sq unit.

QUESTION: 7

Size of a tile is 9 inches by 9 inches. The number of tiles needed to cover a floor of 12 feet by 12 feet is

Solution:

Length of floor = 12 feet

Breath of floor = 12 feet

So Area of floor = 12 x 12 = 144 feet

Area of tile = 9/12 x 9/12 = 9/16 feet

So the number of tile = = 256 tiles

QUESTION: 8

An equilateral triangle has a side of 18 cm. Find the perimeter of triangle (in cm):

Solution:

QUESTION: 9

In a certain yr, the average monthly income of a person is Rs 3400 and that for the first 8 months is Rs 3160 and for the last 5 months is Rs 4120. The income in the eight month of the year is

Solution:

x_{1} + x_{2} + ..... + x_{12} = 3400 x 12 .....(i)

x_{1} + ..... + x_{8} = 3160 x 8 .....(ii)

x_{8} + ..... + x_{12} = 4120 x 5 .....(iii)

from (i) and (ii)

x_{9} + ..... + x_{12} = 40800 - 25280 = 15520 .....(iv)

from (iii) and (iv) the income in the eight month of the year

x_{8} = 20600 - 15520 = Rs. 5080

QUESTION: 10

Visitors to a show were charged Rs 15 each on the first day;Rs 7.50 on the second ;Rs 2.50 on the third and total attendence of three days were in the ratio 2:5:13 respectively. Find the average per person for the whole show.

Solution:

QUESTION: 11

if the pair of lines ax² + 2hxy + by² + 2gx + 2fy + c = 0

Solution:

QUESTION: 12

What will be the compound interest acquired on a sum of Rs 12000 for 3 years at the rate of 10% p.a?

Solution:

QUESTION: 13

A shopkeeper allows a discount of 10% on the marked price of an item but charges a sales tax of 8% on the discounted price. If the customer pays Rs 680.40 as the price including the sales tax, what is the marked price of the item?

Solution:

QUESTION: 14

The cube root of 1.061208 is

Solution:

QUESTION: 15

What is the difference between the niggest and the smallest fraction among 2/3, 3/4, 4/5 and 5/6?

Solution:

QUESTION: 16

Determine the value of ∠AOE

Solution:

QUESTION: 17

A rectangular box is open on one side. The number of pairs of parallel planes of such a box is :

Solution:

QUESTION: 18

Two numbers,both greater than 29, have HCF 29 and LCM 4147. The sum of the numbers is

Solution:

Product of numbers = 29 × 4147

Let the numbers be 29a and 29b

Then, 29a × 29b = (24 × 4147)

⇒ ab = 143

Now, co-primes with product 143 are (1, 143) and (11, 13)

So,the numbers are (29 × 1, 29 × 143) and (29 × 11, 29 × 13)

Since both numbers are greater than 29, the suitable pair is (29 × 11, 29 × 13)

i.e., (319, 377)

∴ Required sum = (319 + 377) = 696

QUESTION: 19

AB and CD are two diameters of circles which are perpendicular to each other. The length of the chord BD is

Solution:

QUESTION: 20

A light house is 60 metres high with its base being at the sea level.If the angle of depression of a boat in the sea from the top of the light house is 15º,then the distance of the boat from the foot of the light house is equal to

Solution:

QUESTION: 21

The correct statement out of the following is

Solution:
∠A = ∠F; ∠B = ∠E and ∠C = ∠D

Hence, ∆ABC$\sim $∆FED.

Hence, ∆ABC$\sim $∆FED.

QUESTION: 22

How many digits in all are required to write numbers from 1 to 50?

Solution:

1 to 9 = 9 (1 digit number)

10 to 50 = 41(2 digit number) = 41 x 2 = 82

total digits = 82 + 9 = 91

QUESTION: 23

Suresh's monthly income is 30% more than that of Vinod. Vinod's monthly income is 20% less than that of Vinay.If the difference between the monthly incomes of Suresh and Vinay is Rs 800.What is the monthly income of Vinod?

Solution:

Suresh = Vinod + 30% of Vinod

= 1.3 Vinod

Vinod = Vinay - 20% of Vinay

= 80% of Vinay

= 0.8 Vinay

∴ Suresh = 1.3 x 0.8 Vinay

= 1.04 Vinay

Now, Suresh - Vinay = 1.04 Vinay - Vinay

= 0.04 Vinay

= Rs 800 (given)

∴ Vinay = Rs 20000

∴ Vinod = 0.8 x 20000 = Rs 16000

QUESTION: 24

Two-fifths of 30% of one-fourth of a number is 15. What is 20% of that number?

Solution:

QUESTION: 25

Two taps can fill a tank in 4 hours and 6 hours, respectively. A third tap can empty the tank in 3 hours. If all the three taps are opened how much time will it take to fill the tank?

Solution:

QUESTION: 26

A man sold two watches for Rs. 240 each on one he gained 20% and on the other he lost 20%. The gain or loss percent in the transaction is

Solution:

S.P. of both the watches = Rs. 480

S.P. of each watch = Rs. 240

Gain = 20%

QUESTION: 27

If cost price is Rs 80,overhead is Rs 20 and selling price is Rs 120,then the profit percent is

Solution:

QUESTION: 28

Two sides of a triangle are 2√2cm and 2√3 cm and the angle opposite to the shorter side of the two is π/4. The largest possible length of the third side is

Solution:

QUESTION: 29

One year ago the ratio of Karan's and Ankit's ages was 6:7, respectively. Four years hence this ratio would become 7:8. How old is Ankit?

Solution:

QUESTION: 30

If m is proportional to n and m=5 when n=4,then what is the value of m when n=18?

Solution:

QUESTION: 31

1³ - 2³ + 3³ - 4³ + ... + 9³ =

Solution:

QUESTION: 32

A sum of money doubles itself in 12 yrs if invested at simple interest. What is the rate of interest allowed on the investment?

Solution:

QUESTION: 33

(√72 − √18)÷√12 is equal to

Solution:

QUESTION: 34

The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?

Solution:

The two trains meet x hrs after 8 a.m.

Distance covered by 1st train in x hrs + Distance covered by 2nd train in (x - 1) hrs = 330 km

60x + 75 (x - 1) = 330

60x + 75x - 75 = 330

x = 405/135 = 3

So, they will meet 3 hrs past 8 a.m. i.e., 11 a.m.

QUESTION: 35

A alone can complete a work in 16 days and B alone in 12 days. Starting with A, they work on alternate days. The total work will be completed in :

Solution:

QUESTION: 36

If A+C=B, then tanA tanB tanC=

Solution:

QUESTION: 37

Solution:

QUESTION: 38

The value of cos 12°+cos 84°+cos 156°+cos 132° is

Solution:

QUESTION: 39

A cubical vessel can hold 1331l of water. The length of side of the vessel in m is

Solution:

QUESTION: 40

A milk tanker cylindrical is shape having diameter 2 m and length 4.2 m supplies milk to two booths A and B in the ratio 3:2. Milk booth A is a rectangular vessel having base area as 3.96m^{2} and milk booth B is a cylindrical vessel having diameter 2m. The level of milk in vessels in booths A and B respectively are

Solution:

QUESTION: 41

Find the minimum number of cubes required to construct a cuboid of dimension 20cm × 16cm × 12cm ?

Solution:

Volume of cuboid = 20 x 16 x 12 = 3840 cm^{3}

Since minimum no. of cubes required

So length of cube = HCF of 20, 16, 12 cm = 4

QUESTION: 42

**The following line-graph gives the percent profit earned by two companies X and Y during the period 1996-2001. Study the line-graph and answer the questions that are based on it.**

**Q. **If the expenditure of Company Y in 1997 was Rs. 220 crores, what would its income in 1997 ?

Solution:

Profit perecent of Company Y in 1997 = 35

Let the income of Company Y in 1997 be Rs x crores

⇒ x = 297

∴ Income of Company Y in 1997 = Rs 297 crores

QUESTION: 43

**The following line-graph gives the percent profit earned by two companies X and Y during the period 1996-2001. Study the line-graph and answer the questions that are based on it.**

**Q. **If the incomes of the two companies were equal in 1999, then what was the ratio of expenditure of Comapany X to that of Company Y in 1999 ?

Solution:

Let the incomes of each of the two Companies X and Y in 1999 be Rs. x.

And let the expenditures of Companies X and Y in 1999 be E1 and E2 respectively.

Then, for Company X we have:

QUESTION: 44

**The following line-graph gives the percent profit earned by two companies X and Y during the period 1996-2001. Study the line-graph and answer the questions that are based on it.**

**Q. **If the expenditure of companies X and Y in 1996 were equal and the total income of the two companies in 1996 was Rs. 342 crores, what was the total profit of the two companies together in 1996 ?

Solution:

Let the expenditures of each companies X and Y in 1996 be Rs x crores

And let the income of Company X in 1996 be Rs z crores

So that the income of Company Y in 1996 = Rs (342 - z) crores

Then, for Company X we have:

Substituting z = 168 in (i), we get : x = 120

∴ Total expenditure of Companies X and Y is 1996 = 2x = Rs 240 crores

Total income of Companies X and Y in 1996 = Rs 342 crores

∴ Total profit = Rs (342 - 240) crores = Rs 120 crores

QUESTION: 45

**The pie charts show estimated revenue and expenditure budgets for 2004-2005 for country X.
Notes: 1. Corporate tax revenues increased by Rs.2545 crore in the budget estimates for 2004-2005 over the estimates for 2003-2004.
2. Service tax brings in Rs.3990crore according to the budget for 2004-2005.
3. Total expenditure on defence increased by a whopping 28 percent from Rs.6030crore in 2003-2004 to Rs.7700crore in 2004-2005.**

**Q. **The revenue generated by Custom duty, Income tax and Corporate tax according to the budget for 2004-2005 is.

Solution:

QUESTION: 46

Notes: 1. Corporate tax revenues increased by Rs.2545 crore in the budget estimates for 2004-2005 over the estimates for 2003-2004.

2. Service tax brings in Rs.3990crore according to the budget for 2004-2005.

3. Total expenditure on defence increased by a whopping 28 percent from Rs.6030crore in 2003-2004 to Rs.7700crore in 2004-2005.

**Q. **What is the percentage increase in the revenue generated by corporate tax is 2004-2005 over 2003-2004 according to the budgets?

Solution:

QUESTION: 47

Notes: 1. Corporate tax revenues increased by Rs.2545 crore in the budget estimates for 2004-2005 over the estimates for 2003-2004.

2. Service tax brings in Rs.3990crore according to the budget for 2004-2005.

3. Total expenditure on defence increased by a whopping 28 percent from Rs.6030crore in 2003-2004 to Rs.7700crore in 2004-2005.

**Q. **If the percentage distribution for the sectors from he Expenditure graph remain the same for the 2003-2004 and 2004-2005 budgets, then what is the difference in budgeted expenditures in 2003-2004 and 2004-2005?

Solution:

QUESTION: 48

Notes: 1. Corporate tax revenues increased by Rs.2545 crore in the budget estimates for 2004-2005 over the estimates for 2003-2004.

2. Service tax brings in Rs.3990crore according to the budget for 2004-2005.

3. Total expenditure on defence increased by a whopping 28 percent from Rs.6030crore in 2003-2004 to Rs.7700crore in 2004-2005.

**Q. **According to the budget for 2004-2005, the revenue generated by non-debt capital receipts is what percent of expenditure on subsides?

Solution:

QUESTION: 49

**In the chart given below, A, B,C,D and E represents the costs of paper , printing , binding , miscellaneous and the royalty respectively in publishing a book.**

**Q. **What is the angle of the pie chart showing the expenditure incurred on royalty ?

Solution:

% of Royalty = 15%

∴ Angle made by Royalty = 360/100 × 15 = 54°

QUESTION: 50

**Q. **The income of the companies X and Y in 2000 were in the ratio of 3 : 4 respectively. What was the respective ratio of their expenditures in 2000 ?

Solution:

Let the incomes in 2000 of Companies X and Y be 3x and 4x respectively.

And let the expenditures in 2000 of Companies X and Y be E1 and E2 respectively.

Then, for Company X we have:

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