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# Maths Quiz for CTET Exam 2016

1. Rs. 1500 were divided into two parts. One part was put at 6% and the other at 5% interest. If the whole annual interest from both investments was Rs. 85, then the investment at 6% was:
A. Rs. 1200
B. Rs. 1000
C. Rs. 1300
D. Rs. 1150
(Suppose, one part of sum = Rs. x
∴ Other part of the sum = Rs. (1500 – x)
According to question,
(x×6×1)/100+((1500-x)×5×1)/100=85
6x + 7500 – 5x = 8500 or, x = 1000)

2. 800 becomes Rs. 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what amount will Rs. 800 become in 3 years?
A. Rs. 1020.80
B. Rs. 1025
C. Rs. 1052
D. Rs. 1050
(SI = 956 – 800 = Rs. 156
Therefore, rate of interest
=(SI × 100)/(Principal × Time )
=(156 × 100)/(800 × 3)=6.5% per annum.
Thus, new rate = 10.5%
So,
S.I. =(Principal × Time × Rate )/100
=(800 × 3 × 105)/100 = Rs. 252
Hence, Amount = 800 + 252 = Rs. 1052.)

3. Prakash lends a part of Rs. 20,000 at 8% simple interest and remaining at 4/3% simple interest. His total income after a year was Rs. 800. Find the sum lent at 8%.
A. Rs. 8000
B. Rs. 12000
C. Rs. 6000
D. Rs. 10000
(Let the amount lent at 8% rate of interest be =Rs. x
∴ Amount lent at 4/3% rate of interest = Rs. (20,000 – x)
∴ SI =(Principal × Rate× Time   )/100
∴(x × 8 × 1)/100+((20000-x)  ×4/3  × 1)/100=800
⇒ 2x/25+(20000 – x)/75=800
⇒ (6x + 20000 – x)/75=800
⇒ 5x + 20000 = 75 × 800 = 60000
⇒ 5x = 60000 – 20,000 = 40000
⇒ x=40000/5 = Rs. 8000)

4. A man invested 1/3 of his capital at 7%, 1/4 at 8% and the remaining at 10% rate of simple interest. If his annual income from interests is Rs. 561, then the capital invested was:
A. Rs. 6000
B. Rs. 5600
C. Rs. 6600
D. Rs. 7200
(Let the total capital invested be Rs. x
∴ Total interest
=(1/3 x × 7 × 1)/100+(1/4 x × 8 × 1)/100+((1-1/3-1/4)x × 10x × 1)/100
=7x/300+8x/400+5x/120
=(28x + 24x + 50x )/1200=102x/1200
Now, according to the question,
561=102x/1200
∴ x=(561 × 1200)/102 = Rs. 6600)

5. Mohan can finish a job in 60 days whereas Ram can finish the same job in 20 days. If they work together, the job will be over in-
A. 7.5 days
B. 15 days
C. 25 days
D. 55 days
(1/t=1/60+1/20=1/15
Time =15 days)

6. A shopkeeper loses the S.P of 4 pencils on selling 36 pencils. His loss% –
A. 12.5%
B. 10%
C. 15%
D. 25%
(Let S.P of 1 pencil= 1 Rs , S.P of 36 pencils= 36 Rs
S.P<C.P (as loss) , C.P= 36+4= 40 Rs.
L%= (4/40) ×100= 10% )

7. If a, b, c are respectively the number of faces, edges and vertices of a pentagonal pyramid, then the value of (a-b+c/2)^2 – 2 is-
A. 2
B. 1.75
C. -1
D. -1.5
(Euler’s rule: F+V-E=2, a+c–b = 2
By putting it in question: (2/2)^2 – 2 = -1 ans)

8. An amount of Rs. 15,000 is distributed among A, B and C in the ratio 4:5:6. What is the share of B?
A. 5000
B. 6000
C. 4000
D. 7000
(let share of A=4x, B=5x, C=6x
Total amount = A+B+C ; 4x+5x+6x= 15000
15x= 15000, x= 1000
B’s share(5x) = 5000 Rs)

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)