1.

Equation of line 3x + 2y – 5 = 0 can be written in intercept form as js


a

x533y52=1frac{frac{x}{5}}{frac{3}{3}}-frac{y}{frac{5}{2}}=1

b

x5+y3=1frac{x}{5}+frac{y}{3}=1

c

x2+y5=1frac{x}{2}+frac{y}{5}=1

d

x53+y52=1frac{x}{frac{5}{3}}+frac{y}{frac{5}{2}}=1


2.

Two pipes A and B can fill a tank in 60 minutes and 75 minutes respectively. There is also an outlet C. If A, B and C are opened together, the tank is full in 50 minutes. How much time will be taken by C to empty the full tank?


a

120 minutes

b

100 minutes

c

125 minutes

d

110 minutes


3.

Three friends divide Rs. 624 among themselves in the ratio 12:13:14frac{1}{2}: frac{1}{3}: frac{1}{4} the share of the third friend is


a

Rs. 192

b

Rs. 288

c

Rs. 148

d

Rs. 144


4.

Suppose ABC is a triangle with AB of unit length. D and E are the points lying on AB and AC respectively such that BC and DE are parallel. If the area of triangle ABC is twice the area of triangle ADE, then the length of AD is


a

12frac{1}{2} unit

b

12frac{1}{sqrt{2}} unit

c

13frac{1}{3} unit

d

13frac{1}{sqrt{3}} unit


5.

A man bought nine pens for a rupee. How many pens should he sell for a rupee to gain 50%?


a

3

b

6

c

8

d

7


6.

Two observers are stationed due north of a tower (of height x metre) at a distance y metre from each other. The angles of elevation of the tower observed by them are 30° and 45° respectively. Then xyfrac{x}{y} is equal to


a

312frac{sqrt{3}-1}{2}

b

1

c

212frac{sqrt{2}-1}{2}

d

3+12frac{sqrt{3}+1}{2}


7.

What is the average of first 29 even numbers?


a

33

b

32

c

30

d

31


8.

Rs. 64,000 will amount to Rs. 68,921 at 5% per annum and interest payable half yearly in


a

2122 frac{1}{2} years

b

2 years

c

3123 frac{1}{2} years

d

1121 frac{1}{2} years


9.

A truck moves along a circular path and describes 100 m when it has traced out 36° at the centre. The radius of the circle is equal to


a

250πfrac{250}{pi} metre

b

100πfrac{100}{pi} metre

c

500πfrac{500}{pi} metre

d

600πfrac{600}{pi} metre


10.

(sin35cos55)2(cos55sin35)2+2sin30left(frac{sin 35^{circ}}{cos 55^{circ}} ight)^{2}-left(frac{cos 55^{circ}}{sin 35^{circ}} ight)^{2}+2 sin 30^{circ} is equal to


a

1

b

0

c

2

d

–1


11.

On an article the profit is 210% of the cost price. If the cost price increases by 40% but the selling price remains constant, approximately what per cent of selling price will be the profit?


a

62

b

74

c

85

d

55


12.

A square is inscribed in a right-angled triangle with legs p and q, and has a common right angle with the triangle. The diagonal of the square is given by


a

pqp+2qfrac{p q}{p+2 q}

b

2pqp+qfrac{sqrt{2} p q}{p+q}

c

pq2p+qfrac{p q}{2 p+q}

d

2pqp+qfrac{2 p q}{p+q}


13.

If tanθ=xyx+y an heta=frac{x-y}{x+y}, the value of sinθsin heta is equal to [If 0θ900^{circ} leq heta leq 90^{circ} ]


a

xy2(x2y2)frac{x-y}{sqrt{2left(x^{2}-y^{2} ight)}}

b

x+y2(x2y2)frac{x+y}{sqrt{2left(x^{2}-y^{2} ight)}}

c

x+y2(x2+y2)frac{x+y}{sqrt{2left(x^{2}+y^{2} ight)}}

d

xy2(x2+y2)frac{x-y}{sqrt{2left(x^{2}+y^{2} ight)}}


14.

The value of k, for which the system of equations 3x – ky – 20 = 0 and 6x – 10y + 40 = 0 has no solution,


a

3

b

5

c

6

d

10


15.

The average of five consecutive odd numbers is 27. What is the product of the first and the last number?


a

725

b

667

c

713

d

621


16.

If 3A=5B3 A=5 B, what is the value of (A+B)B?frac{(A+B)}{B} ?


a

83frac{8}{3}

b

53frac{5}{3}

c

58frac{5}{8}

d

85frac{8}{5}


17.

If xaybtanθ=1frac{x}{a}-frac{y}{b} an heta=1 and xatanθ+yb=1frac{x}{a} an heta+frac{y}{b}=1, then the value of x2a2+y2b2frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{2}} is


a

2 sec2θ

b

2 cos2θ

c

cos2θ

d

sec2θ


18.

A clock strikes once at 1 o’clock, twice at 2 o’clock and thrice at 3 o’clock and so on. If it takes 8 seconds to strike at 5 o’clock, the time taken by it to strike at 10 o’clock is


a

None of the above

b

18 seconds

c

14 seconds

d

16 seconds


19.

If a sum of money at a certain rate of simple interest per year doubles in 5 years and at a different rate of simple interest per year becomes three times in 12 years, then the difference in the two rates of simple interest per year is


a

3%3 \%

b

413%4 frac{1}{3} \%

c

2%2 \%

d

313%3 frac{1}{3} \%


20.

The following pie-chart shows the expenditure (in percentage) of five companies P, Q, R, S and T in the year 2016. Total Expenditure = Rs. 48 crores


What is the respective ratio between the total expenditure of company P, Q and S together to the total expenditure?


a

50 : 31

b

31 : 60

c

31 : 50

d

60 : 31


21.

Total amount spent by company S is what percent of total amount spent by companies T and R?


a

41

b

42.1

c

39.68

d

43


22.

The profit earned by company R is equal to the 14frac{1}{4} th of the expenditure of company Q. What is the profit (in Rs. crores) of company R?


a

4.84

b

3.24

c

2.64

d

5.66


23.

By how much per cent expenditure of company Q and R together is greater than that of company P?


a

60%

b

66.67%

c

75%

d

33.33%


24.

What was the total expenditure (in Rs. crores) of the company Q, R and T together?


a

31.4

b

24.3

c

28.8

d

19.2


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