Directions (1-5): In each of these questions, one term in the given number series is wrong. Find out the wrong term.
Q1. 142 119 100 83 65 59 52
(a) 65
(b) 100
(c) 59
(d) 119
(e) None of these
Q2. 8 12 24 46 72 108 152
(a) 12
(b) 24
(c) 46
(d) 72
(e) None of these
Q3. 13 25 40 57 79 103 130
(a) 25
(b) 40
(c) 57
(d) 79
(e) None of these
Q4. 2 10 18 54 162 486 1458
(a) 18
(b) 54
(c) 162
(d) 10
(e) None of these
Q5. 850 600 550 500 475 462.4 456.25
(a) 600
(b) 550
(c) 500
(d) 462.5
(e) None of these
Q6. A hemispherical bowl of thickness 1 cm and external diameter 10 cm is to be painted all over. What is the cost of painting at the rate of Rs. 0.70 per cm^2?
(a) Rs. 200
(b) Rs. 400
(c) Rs. 800
(d) Rs. 100
(e) Rs. 500
Q7. A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. The fraction of water that overflows is:
(a) 1 : 4
(b) 1 : 2
(c) 3 : 8
(d) 5 : 8
(e) None of these
Q8. If the longer side of a rectangle is doubled and the other is reduced to half, then the area of the new rectangle goes up by:
(a) 50%
(b) 100%
(c) 0%
(d) 150%
(e) None of these
Q9. The front wheels of a wagon are 2π feet in circumference and the back wheel are 3π feet in circumference. When the front wheels have made 10 more revolutions than back wheels, how many feet has the wagon travelled?
(a) 30π
(b) 90π
(c) 60π
(d) 150π
(e) None of these
Q10. MoonStar Life Insurance Company issues standard, preferred and ultra-preferred policies. Among the company’s policy holders of a certain age, 50% are standard with a probability of 0.01 of dying in the next year, 30% are preferred with a probability of 0.008 of dying in the next year and 20% are ultra-preferred with a probability of 0.007 of dying the next year. If a policy holder of that age dies in the next year, what is the probability of the decreased being a preferred policy holder?
(a) 0.1591
(b) 0.2727
(c) 0.375
(d) 0.265
(e) None of these
Q11. A management institute has six senior professors and four junior professors. Three professors are selected at random for a Government project. The probability that at least one of the junior professors would get selected is:
(a) 5/6
(b) 2/3
(c) 1/5
(d) 1/6
(e) None of these
Q12. Rajat draws a 10 × 10 grid on the ground such that there are 100 identical squares numbered from 1 to 100. If he has to place two identical stones on any two separate squares in the grid, how many distinct ways are possible?
(a) 2475
(b) 4950
(c) 9900
(d) 1000
(e) None of these
Q13. A man borrows a certain sum and pays it back in 2 years in two equal instalments. If the compound interest is reckoned at 4% and if he pays back annually Rs. 676 the sum borrowed is:
(a) Rs. 1275
(b) Rs. 1078
(c) Rs. 1870
(d) Rs. 1256
(e) None of these
Q14. Sushant took a loan from the bank at 8% per annum and was supposed to pay a sum of Rs. 2240 at the end of 4 years. If the same sum is cleared off in four equal annual installments at the same rate, the amount of annual installments will be:
(a) Rs. 500
(b) Rs. 550
(c) Rs. 600
(d) Rs. 1000
(e) None of these
Q15. The simple interest on a certain sum at 5% for 9 months is Rs. 10 greater than the simple interest on the same sum at the rate of 3% for 14 months. What is the sum of interest in both the cases (i.e. total sum of interest)?
(a) Rs. 130
(b) Rs. 290
(c) Rs. 120
(d) Rs. 330
(e) None of these
Solutions
S1. Ans.(a)
Sol.
So, wrong number = 65
Correct number = 83 - 13 = 70
S2. Ans.(c)
Sol.
So, wrong number = 46
Correct number = 24 × 1.5 = 36
S3. Ans.(c)
Sol.
So, wrong number = 57
Correct number = 40 + 18 = 58
S4. Ans.(d)
Sol.
So, wrong number = 10
Correct number = 2 × 3 = 6
S5. Ans.(a)
Sol.
So, wrong number = 600
Correct number = 850 - 200 = 650
In ∆ACD and ∆EOC
∠ADC = ∠OEC = 90°
∠ACD = ∠OCE (common angle)
∠CAD = ∠EOC (remaining angle)
∴ ∆ACD ~ ∆EOC
Also, AD = AE = 6 cm
(∴ the length of two tangents drawn from an external point to circle are equal)
∴ EC = AC - AE = 10 - 6 = 4 cm
In similar ∆ACD and ∆EOC
S9. Ans.(c)
Sol. Suppose the back wheel has made x revolutions.
∴ Front wheel has made (10 + x) revolutions
⇒ 3πx = 2π(10 + x)
⇒ πx = 2π × 10 ⇒ x = 20
∴ The wagon has travelled 3πx = 60π
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