1. ABC is a right angled triangle in which ∠A=90 and AB=AC. Find ∠B and ∠C ?
A. 65
B. 45
C. 75
D. 55
(As AB=AC ….so, ∠B=∠C
Also, ∠A+∠B+∠C=180
90 + 2∠B=180….∠B=90/2
∠C=∠B=45 )
2. The angles of quadrilateral are in the ratio of 3:5:9:13. Find all the angles of the quadrilateral.
A. 36, 60, 108, 156
B. 56, 67, 89, 160
C. 78, 56, 134, 45
D. 69, 120, 54, 90
(Let the angles be 3x, 5x, 9x and 13x.
Then, 3x + 5x + 9x + 13x = 360
X = 12
36, 60, 108 and 156 ans)
3. ABCD is a parallelogram, AE ⊥DC and CF⊥AD.If AB= 16 cm, AE=8 cm and CF=10 cm, find AD?
A. 11.6 cm
B. 13 cm
C. 12.8 cm
D. 10.9 cm
(Ar. of llgram = b x h
∴ Ar. of llgram ABCD = AB x AE = (16 x 8) = 128 cm^2
Also, Ar. of llgram ABCD = AD x CF = (AD x 10)
∴ AD = 128/10 = 12.8 cm)
4. In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.
A. 4.4 m^2
B. 6.5 m^2
C. 7.8 m^2
D. 4.3 m^2
(Total radiating surface in the system = C.S.A of the pipe = 2πrh
2 x 22/7 x 0.025 x 28 = 4.4 m^2)
5. Find the radius of a sphere whose area is 154 cm square.
A. 8.9 cm
B. 3.5 cm
C. 5.6m
D. 5.4 cm
(Surface area = 4πr^2
154 = 4 x 22/7 x r^2
R^2 = 12.25 cm
R = 3.5 cm)
6. How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?
A. 408.78 litre
B. 303.18 litre
C. 209.76 litre
D. 756.64 litre
(Diameter = 10.5/2 = 5.25 cm
Vol. of the bowl = 2/3 πr^3
2/3 x 22/7 x (5.25)^3
= 303.1875 cm^3 = approx. 303 litre )
7. Find the cost of digging a cuboidal pit 8 m long, 6m broad and 3 m deep at the rate of Rs 30 per m cube.
A. 5467 Rs
B. 6686 Rs
C. 7684 Rs
D. 4320 Rs
(Volume of the pit = lbh = 8 x 6 x 3 = 144 m cube
Rate of digging = 144 x 30 = 4320 Rs )
8. A match box measures (4 x 2.5 x 1.5) cm. What will be the volume of a packet containing 12 such boxes?
A. 120
B. 239
C. 180
D. 160
(Volume of 1 match box = 4 x 2.5 x 1.5 =15 cm cube
Volume of 12 such boxes = 15 x 12 = 180 cm cube)
9. Find the total surface area of a hemisphere of radius 10 cm.
A. 942 cm square
B. 547 cm square
C. 833 cm square
D. 978 cm square
(T.S.A of hemisphere = 3πr^2 = 3 x 22/7 x 10 x 10
= 942 cm square)
10. Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.
A. 134 cm square
B. 126 cm square
C. 198 cm square
D. 165 cm square
(C.S.A of the cone = πrl = 22/7 x 5.25 x 10
= 165 cm square)
