Question

The area of triangle formed by the points (−5,0) , (0,−5) and (5,0) is

(A) 0 sq.units (B) 25 sq.units (C) 5 sq.units (D) none of these

2. If slope of the line PQ is

1

3

then slope of the perpendicular bisector of PQ is

(A)

3

(B) - 3

(C)

1

3

(D) 0

3. A straight line has equation 8y = 4x +21. Which of the following is true

(A) The slope is 0.5 and the y intercept is 2.6 (B) The slope is 5 and the y intercept is 1.6

(C) The slope is 0.5 and the y intercept is 1.6 (D) The slope is 5 and the y intercept is 2.6

4. The slope of the line joining (12, 3) , (4,a) is

1

8

. The value of ‘a’ is

(A) 1 (B) 4 (C) -5 (D) 2

5. (2, 1) is the point of intersection of two lines.

(A) x −y −3 = 0; 3x −y −7 = 0 (B) x +y = 3; 3x +y = 7

(C) 3x +y = 3; x +y = 7 (D) x + 3y −3 = 0; x −y −7 = 0

6. The value of

2

2

1

sin

1 tan









is equal to

(A) tan2

 (B) 1 (C) cot2



(D) 0

7. If x =a tan  and y =b sec  then

(A)

2 2

2 2 1

y x

b a

 

(B)

2 2

2 2 1

x y

a b

 

(C)

2 2

2 2 1

x y

a b

 

(D)

2 2

2 2 0

x y

a b

 

8. If 5x = sec  and

5

x

= tan  , then

2

2

1

x

x

 is equal to

(A) 25 (B)

1

25

(C) 5 (D) 1

9. The electric pole subtends an angle of 30° at a point on the same level as its foot. At a second point ‘b’

metres above the first, the depression of the foot of the pole is 60° . The height of the pole (in metres) is

equal to

(A)

3 b

(B)

3

b

(C)

2

b

(D)

3

b

10. The angle of depression of the top and bottom of 20 m tall building from the top of a multistoried building

are 30° and 60° respectively. The height of the multistoried building and the distance between two

buildings (in metres) is

(A) 20, 10

3

(B) 30, 5

3

(C) 20, 10 (D) 30, 10

3

11. If two solid hemispheres of same base radius r units are joined together along their bases, then curved

surface area of this new solid is

(A)

2

4 . r sq units

(B)

2

6 . r sq units

(C)

2

3 . r sq units

(D)

2

8 . r sq units

12. The total surface area of a cylinder whose radius is

1

3

of its height is

(A) 2

9

.

8

h

sq units 

(B) 2

24 . h sq units (C) 2

8

.

9

h

sq units 

(D) 2

56

.

9

h

sq units​

Answer 1

Answer:

Keys:-

Red line- Multi-storage building

Blue line-20m tall building

Green Line- Distance between two buildings

Angle made between small black line and up green line is 30°

Angle made between big black line and down green line is 60°

In ΔABC,

1/√3 =h/x

x=√3*h

In ΔADE,

√3=(20+h)/√3*h

√3 * √3 h =20+h

3h=20+h

3h-h=20

2h=20

h=10 meters.

∴Length of multi-storage building

= h+20

=10+20

=30 meters.

Now,

Distance x (or) Length of DE=√3*h

=√3*10

Hence, Option D is your required answer..