Q1. When 73^2 is subtracted from the square of a number, the answer that is obtained is 5280. What is the number?
(a) 97
(b) 103
(c) 99
(d) 101
Sol.
x^2-73^2=5280
⇒ x^2=5280+5329=10609
Or x=√10609=103
Q2. Find the value of
(a) 11/2
(b) (√29 +1)/2
(c) (√13 +1)/2
(d) (√29 +5)/2
Sol.
Q3. If x^2+1/x^2 =34, then find the value of x+1/x
(a) 4
(b) 6
(c) 8
(d) 17
Sol.
x^2+1/x^2 =34
⇒ (x+1/x)^2-2×1/x=34
[a^2+b^2=(a+b)^2=2ab]
⇒ (x+1/x)^2=36
⇒ x+1/x=6
Q4. The ratio of the length to the breadth of a rectangle is 2 : 1. Its perimeter is 60 cm, find its area.
(a) 250 sq cm
(b) 200 sq cm
(c) 300 sq cm
(d) 205 sq cm
Sol.
2(2x + x) = 60 cm
⇒ x = 10 cm
∴ Area = 2x
x = 2(100) = 200 cm2
Q5. What value should come in place of question mark (?)
(1.06+0.04)^2- ? 4×1.06×0.04
(a) 1.0404
(b) 1.4
(c) 1.5
(d) 1.45
Sol.
(1.06+0.04)^2- ?=4×1.06×0.04
⇒ 1.06^2+0.04^2+2×1.06×0.04 – ?
= 4 × 1.06 × 0.06
⇒ ? =1.06^2+0.04^2-2×1.06×0.04
=(1.06-0.04)^2=(1.02)^2
i.e. = 1.0404
Q6. Sum of first 20 terms of the Arithmetic Progression (A P) 11, 7, 3,….is
(a) 20
(b) –540
(c) 980
(d) –65
Sol.
n = 20
First term a = 11
Sum =n/2 (2a+n-1d)=20/2 [2(11)+19(-4)]
= 10(22 – 76) = – 540
Q7. On decreasing the radius of a sphere by 20%. By what per cent its volume will be decreased?
(a) 20
(b) 28.8
(c) 57.6
(d) 48.8
Sol.
Let original radius = 100 units
Let original radius = 100 units
Then, new radius = 80 units
Per cent decrease in volume
=(4/3 π(80)^(3 )- 4/3 π(100)^3)/(4/3 π(100)^3 )×100
=(10^3 (8^3-10^3 ))/(10^3.10^3 )×100
=((512-1000)/1000) ×100=-48.8
Q8. If a card is drawn from a pack of cards, what is the probability of getting a black coloured card?
(a) 1/3
(b) 1/2
(c) 3/4
(d) 3/8
Sol.
Required probability = number of black cards in
=(The pack )/(Total number of cards )
=26/52=1/2
Q9. A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. If one ball is drawn at random find the probability that it is not green.
(a) 1/6
(b) 5/6
(c) 5/8
(d) 1/2
Sol.
Required probability = 1 – probability
(drawing a green ball)
=1-4/24=5/6
Q10. A number when tripled and decreased by 15 we get the result as 120. Find the number.
(a) 45
(b) 40
(c) 42
(d) 50
Sol.
3x – 15 = 120 ⇒ x = 45
