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Test: Unitary Method- 2 - CLAT MCQ

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25 Questions MCQ Test - Test: Unitary Method- 2

Test: Unitary Method- 2 for CLAT 2024 is part of CLAT preparation. The Test: Unitary Method- 2 questions and answers have been prepared according to the CLAT exam syllabus.The Test: Unitary Method- 2 MCQs are made for CLAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Unitary Method- 2 below.

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Test: Unitary Method- 2 - Question 1

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(16)^3/4 is equal to

A.
4√2
B.
8
C.
2√2
D.
16
E.
None of these

Detailed Solution for Test: Unitary Method- 2 - Question 1

(16)^3/4 can be written as ( 2 ) ⁴^{x 3/4}

( 2 ) ³ = 8

So option B is the correct answer.

Test: Unitary Method- 2 - Question 2

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A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is

A.
220030
B.
22030
C.
1220
D.
1250
E.
None of these

Detailed Solution for Test: Unitary Method- 2 - Question 2

Let the number be N

the quotient, in this case, would be = 2(555-445)= 2 x 110 = 220

The Divisor would be = 555+445 = 1000

Remainder = 30

therefore number N would be = Divisor x Quotient + Remainder

which would be = 1000 x 220 + 30 = 220030

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Test: Unitary Method- 2 - Question 3

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A number divided by 68 gives the quotient 269 and remainder zero. If the same number is divided by 67, the remainder is

A.
0
B.
1
C.
2
D.
3
E.
None of these

Test: Unitary Method- 2 - Question 4

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Given that the number of factors of 12 are 6. The number of factors of 24 must be

A.
7
B.
8
C.
9
D.
12
E.
None of these

Test: Unitary Method- 2 - Question 5

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The difference of two numbers is 3 and the difference of their squares is 39, then the larger number is

A.
8
B.
9
C.
12
D.
13
E.
None of these

Test: Unitary Method- 2 - Question 6

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If (12ⁿ + 1) is divisible by 13 then n is

A.
Any even integer
B.
1 only
C.
Any odd integer
D.
12 only
E.
None of these

Detailed Solution for Test: Unitary Method- 2 - Question 6

(xⁿ + aⁿ) is divisible by (x + a) when n is odd.
∴ (12ⁿ + 1) is divisible by (12 + 1) i.e., 13 when n is odd.

Test: Unitary Method- 2 - Question 7

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is equal to

A.
4/7
B.
7/4
C.
4/3
D.
3/4
E.
None of these

Test: Unitary Method- 2 - Question 8

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A man is paid Rs. 20 for each day he works and forfeits Rs. 3 for each day he is idle. At the end of 60 days he gets Rs. 280. Then he was idle for

A.
20 days
B.
25 days
C.
30 days
D.
40 days
E.
None of these

Detailed Solution for Test: Unitary Method- 2 - Question 8

D is the correct option. Suppose the worker remained idle for x days. Then,
He worked for (60 – x) days.
Bindu 20 (60 – x) – 3x = 280
a
1200 – 23x = 280
==> 23x = 920 ==> x = 40
So, the worker remained idle for 40 days.

Test: Unitary Method- 2 - Question 9

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The product of two fractions is 14/15 and their quotient is 35/24, the greater fraction is

A.
7/4
B.
7/6
C.
7/3
D.
4/5
E.
None of these

Detailed Solution for Test: Unitary Method- 2 - Question 9

B is the correct option. Solution-
Let the no. be x and y.
xy= 14/15
x/y= 35/24
xy×x/y= (14/15)×(35/24)
x^2= 490/360= 49/36
x= 7/6
xy= 14/15
7y/6=14/15
y= 4/5
therefore, 7/6 is the greater fraction.

Test: Unitary Method- 2 - Question 10

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The sum of squares of two positive numbers is 100 and difference of their squares is 28. The sum of the numbers is

A.
12
B.
13
C.
14
D.
15
E.
None of these

Test: Unitary Method- 2 - Question 11

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Three fourth of two third of a number is 782. What is three fourth of one fourth of the same number

A.
293.25
B.
432.6
C.
342.6
D.
243
E.
None of these

Detailed Solution for Test: Unitary Method- 2 - Question 11

Acc to given data,
let the no. be y,
3/4×2/3y = 782
y = 1564
3/4×1/4×1564 = 293.25

Test: Unitary Method- 2 - Question 12

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A number is 25 more than its two – fifths. Find the number

A.
145/3
B.
125/3
C.
145
D.
125
E.
None of these

Test: Unitary Method- 2 - Question 13

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The sum and product of two numbers is 12 and 35 respectively. What is the sum of their reciprocals?

A.
12
B.
35
C.
12/35
D.
35/12
E.
None of these

Test: Unitary Method- 2 - Question 14

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A number consists of two digits whose sum is 8. If 18 is subtracted from the number, the digits inter change their places. What is the number.

A.
62
B.
26
C.
35
D.
53
E.
None of these

Detailed Solution for Test: Unitary Method- 2 - Question 14

The correct option is D as
62-18=44Which is not equal to 26, Which is the interchange of its digit.
And we can easily see that we will never get 62 or 53 by substracting18 from 26 or 35 respectively.
Also 53-18=35 which have interchanged digits of 53.
So the answer is option D 53.

Test: Unitary Method- 2 - Question 15

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One fourth of a number exceeds its one – seventh by 24. What is the number

A.
422
B.
112
C.
242
D.
224
E.
None of these

Test: Unitary Method- 2 - Question 16

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The sum of the digits of a two digit number is 10. The number formed by reversing the digit is 18 less than the original number. Find the original number.

A.
82
B.
64
C.
73
D.
91
E.
None of these

Test: Unitary Method- 2 - Question 17

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The product of two numbers is 24 times the difference of these numbers. If the sum of these numbers is 14, find the larger number.

A.
8
B.
56
C.
18
D.
6
E.
None of these

Test: Unitary Method- 2 - Question 18

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Find the smallest positive integer which must be subtracted from both the terms of ratio 6 : 7. So that the result gives a ratio, less than 16 : 21

A.
2
B.
4
C.
3
D.
5
E.
None of these

Detailed Solution for Test: Unitary Method- 2 - Question 18

C is the correct option. Let the whole number is X.
Now, according to question,
(6 -X) /(7 -X) < 16/21.
21 *(6 -X) < 16 *(7 -X)
126 - 21X < 112 - 16X
126 - 112 < - 16X + 21X
14 < 5X
5X > 14
X > 2.8
So, Least such a whole number would be 3.

Test: Unitary Method- 2 - Question 19

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The numerator of a certain fraction is increased by 100% and the denominator is increased by 200%. The new fraction thus farmed is 4/21. What is the original fraction?

A.
2/7
B.
3/7
C.
2/5
D.
4/7
E.
None of these

Test: Unitary Method- 2 - Question 20

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The sum of 18 % of a number and 6% of the same number is 492. What is 12% of that number?

A.
234
B.
242
C.
256
D.
264
E.
None of these

Test: Unitary Method- 2 - Question 21

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The difference between two numbers is 18. If 4 times the second number is less than three times the first number by 18, what is the sum of these two numbers.

A.
100
B.
80
C.
86
D.
92
E.
None of these

Test: Unitary Method- 2 - Question 22

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Five ninth of a number is equal to 2790 what is the number

A.
8100
B.
7200
C.
6300
D.
8500
E.
None of these

Test: Unitary Method- 2 - Question 23

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What is the value of two fifth of three-fourth of one – fourth of 26000.

A.
1900
B.
1950
C.
1980
D.
1930
E.
None of these

Test: Unitary Method- 2 - Question 24

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If a number is multiplied by three – fourth of itself, value so obtained is 1728. What is the number.

A.
38
B.
44
C.
46
D.
58
E.
None of these

Test: Unitary Method- 2 - Question 25

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What is the value of two – fifth of 60 % of 320?

A.
37.4
B.
38.4
C.
78.6
D.
76.6
E.
None of these

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