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1.

Train A of length 180m and speed 72 km/hour crosses train B of length 120 m and speed 108 km/hour moving in the opposite direction in :

a

30 seconds

b

24 seconds

c

12 seconds

d

6 seconds

2.

If (a – 7) (b – 10) (c – 12) = 1000, the least possible value of (a + b + c) is

a

30

b

59

c

14

d

16

3.

If a = 12, b = 13, c = 15, then the value of a^{^³} + b^{^³} + c^{^³} – 3abc is ;

a

280

b

270

c

250

d

290

4.

Three equal circles each of radius 1 cm are circumscribed by a larger circle. Find the perimeter of the circumscribing circle.

a

$\frac{\sqrt{3}}{2}(2-\sqrt{3}) \pi \mathrm{cm}$ .

b

$\frac{2}{\sqrt{3}}(2+\sqrt{3}) \pi \mathrm{cm}$ .

c

$\frac{2+5 \sqrt{3}}{3} \mathrm{~cm} .

d

None of these

5.

A vessel contains 100 litres of milk. From this, 10 litres of milk was taken out and replaced by water. The process was repeated further two times. How much milk is now contained in the vessel ?

a

72.9 litres

b

60.4 litres

c

71.6 litres

d

81 litres

6.

A man on the top of a rock rising on a seashore observed a boat coming towards it. If it takes 10 minutes for the angle of depression to change from 30° to 60°, how soon will the boat reach the shore?

a

4 minutes

b

5 minutes

c

7 minutes

d

10 minutes

7.

Three sides of triangle ABC are a, b and c. a = 4700 cm, b = 4935 cm and c = 6815 cm. The internal bisector of ∠A meets BC at P and the bisector passes through incentre O. PO : OA = ?

a

2 : 5

b

2 : 3

c

5 : 2

d

3 : 2

8.

If $x^{2}-2 \sqrt{10} x+1=0$ , what is the value of $\left(x-\frac{1}{x}\right) ?$

a

4

b

6

c

3

d

5

9.

What will be the equation of line for which p = 3 and D = 120° ?

a

$x-\sqrt{3} y=6$

b

$\sqrt{3} x+y=6$

c

$-x+\sqrt{3} y=6$

d

$x-\sqrt{3} y=5$

10.

The area of the triangle formed by the lines 2x + 3y = 12, x – y – 1 = 0 and y = 0 is

a

7 sq. units

b

5 sq. units

c

6.5 sq. units

d

6 sq. units