Haryana CET Exam, 05.11.2022 (Shift-I)

Total Questions: 100

31. The closest approximation of the following product 0.3333 × 0.25 × 0.499 × 0.125 × 24 is :

Correct Answer: (1) 1/8
Solution:

32. If x is a 3-digit number and y is a number obtained by permuting the digits of x in any manner, then (x – y) is always divisible by :

Correct Answer: (3) 9
Solution:

Let the three digit number
X = pqr
X = (100 × p) + q(10) + r
  = 100p + 10q + r ______(i)
All possible Value of ‘Y’ after permuting the digits
Y = prq, qpr, qrp, rpq, rqp
We consider first ‘prq’
Y = prq = 100p + 10r + q _____(ii)
eqⁿ(i) – eqⁿ(ii)
X – Y = (100p + 10q + r) – (100p + 10r + q)
  = 9q – 9r = 9 (q – r)
∴ ‘X – Y’ will be divisible by ‘9’
Similarly for number y= qpr, qrp, rpq, rqp, the term (X – Y), will always divisible by ‘9’.

33. The sum of two numbers is 45 and their difference is one-ninth of the sum. Then their LCM is :

Correct Answer: (1) 100
Solution:

Let the numbers are x and y.
According to the question,
x + y = 45

x - y = 5—(ii)
After adding eqn (i) & (ii)
2x = 50      ∴ x = 25
From eqⁿ (i)
∴ y = 45 – 25 = 20
For LCM
25 = 5 × 5
20 = 5 × 4
∴ LCM = 5 × 5 × 4 = 100

34. The traffic lights at three different signal points change after every 45 seconds, 75 seconds and 90 seconds respectively. If all change simultaneously at 7 : 20 : 15 hours, then they will next change again simultaneously at :

Correct Answer: (2) 7 : 27 : 45 hours
Solution:

LCM of 45, 75, 90

LCM = 3 × 3 × 5 × 5 × 2
= 450 second
450 second = (60 × 7) + 30 = 7 minutes 30 second
Required time when all three Signal points next change again Simultaneously
= 7 hours + 20 minutes + 15 second) + (7 minute + 30 second)
= 7 : 27 : 45 hours

35. If the income of A is 10% more than that of B and the income of B is 20% less than that of C, then the incomes of A, B and C, respectively, are in the ratio :

Correct Answer: (2) 22 : 20 : 25
Solution:

Let income of B = 100

∴ Required ratio of income of A, B & C
 A : B : C = 110 : 100 : 125
         = 22 : 20 : 25

36. Mr. X has some money with him. He has to distribute this money among five labourers in the ratio 1/2 : 1/3 : 1/4 : 1/5 : 1/7. What is the minimum amount he should have, so that each labourer gets an exact number or rupees ?

Correct Answer: (2) Rs. 420
Solution:

Given ratio

The minimum amount should ‘x’ have, that each labour gets an exact number of rupees :
LCM of 2, 3, 4, 5, 7

LCM = 2 × 3 × 2 × 5 × 7 = 420

37. There are three positive numbers. One-third of the average of all the three numbers is 8 less than the greatest number. The average of the smallest and the second smallest number is 8. What is the greatest number ?

Correct Answer: (3) 11
Solution:

Let three positive numbers are x, y, z, where x > y > z
According to question,
Again,

From eqⁿ (i)

38. (∛1331 × ∛216 + ∛729 + ∛64) is equal to :

Correct Answer: (2) 79
Solution:

39. When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must the plot be sold in order to gain 15% ?

Correct Answer: (3) Rs. 25,300
Solution:

 Cost Price of Plot
= S.P. × 100/(100 – loss%)

For 15 % profit

40. If an article is sold at 20 percent profit, then which of the following is the ratio of its cost price to its selling price ?

Correct Answer: (2) 5 : 6
Solution:

Let cost Price of a article = Rs. 100