Q1. If a hemisphere is melted and four spheres of equal volume are made, the radius of each sphere will be equal to
(a) 1/4th of the hemisphere
(b) radius of the hemisphere
(c) 1/2 of the radius of the hemisphere
(d) 1/6th of the radius of the hemisphere
Q2. A boat takes half time in moving a certain distance downstream than upstream. The ratio of the speed of the boat in still water that of the current is
(a) 2 : 1
(b) 4 : 3
(c) 1 : 2
(d) 3 : 1
Q3. The compound interest on Rs. 5,000 for 3 years at 10% p.a. will amount to:
(a) Rs. 1,654
(b) Rs. 1,655
(c) Rs. 1,600
(d) Rs. 1,565
Q5. BL and CM are medians of ∆ABC, right angled at A and BC = 5 cm. If BL =(3√5)/2 cm, then the length of CM is
(a) 2√5 cm
(b) 5√2 cm
(c) 10√2 cm
(d) 2√10 cm
Q6. In a circle of radius 17 cm, two parallel chords of length 30 cm and 16 cm are drawn. If both chords are on the same side of the centre. Then the distance between the chords is
(a) 9 cm
(b) 7 cm
(c) 23 cm
(d) 11 cm
Q7. If x sin 45° = y cosec 30°, then x^4/y^4 is equal to
(a) 4^3
(b) 6^3
(c) 2^3
(d) 8^3
Q9. Three years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average of the family remains the same today. The age of the baby today is
(a) 2.5 years
(b) 2 years
(c) 1 year
(d) 1.5 years
Q10. In the given figure, BC = AC = AD, ∠EAD = 81°, find the value of x:
(a) 45°
(b) 54°
(c) 63°
(d) 36°
Solutions
S7. Ans.(a)
Sol. x sin 45° = y cosec 30°
⇒ x/y=(cosec 30°)/(sin 45°) ⇒x/y=2/(1/√2)⇒x/y=2√2
x^4/y^4 =(2√2)^4=16×4=64=4^3
S9. Ans.(b)
Sol. Sum of age of family 5 year ago was = 17 × 5 = 85
Sum of present age of family = 17 × 6 = 102
Age of boys = 102 – (85 + 5 × 3)
= 102 – 100 = 2 years
S10. Ans.(b)
Sol.
∠DAE is the exterior angle of ∆ABD
x+(x/2)=81
3x/2=81
x=(81 × 2)/3=54°
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