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All questions of Simplification & Approximation for Delhi Police Constable Exam
7.8 + 5.4 x 8.2 = ?- a)52.08
- b)108.24
- c)48.05
- d)102.05
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
7.8 + 5.4 x 8.2 = ?
a)
52.08
b)
108.24
c)
48.05
d)
102.05
e)
None of these
|
Knowledge Center answered |
Solution for 7.8 + 5.4 × 8.2
We solve using the order of operations (BODMAS):
- First, perform the multiplication:
5.4 × 8.2 = 44.28 - Next, add the result to 7.8:
7.8 + 44.28 = 52.08
Correct Answer: A: 52.08
- a)2 - √3
- b)2 + √3
- c)16 - √3
- d)14 - √3
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
a)
2 - √3
b)
2 + √3
c)
16 - √3
d)
14 - √3
e)
None of these
|
|
Knowledge Center answered |
Given expression:
[(2 + √3) / (2 - √3)] + [(2 - √3) / (2 + √3)] + [(√3 - 1) / (√3 + 1)]
- Simplify the first two terms:
- The denominator simplifies to 1.
- The numerator becomes 14.
- Result: 14.
- Simplify the third term:
- Rationalize the denominator to get 2 - √3.
- Add the results:
- 14 + (2 - √3) = 14 - √3.
Correct Answer: C: 14 - √3
(?)3 x (55) ÷ 225 = 3000- a)6
- b)8
- c)5
- d)9
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
(?)3 x (55) ÷ 225 = 3000
a)
6
b)
8
c)
5
d)
9
e)
None of these
|
|
Knowledge Center answered |
To solve (?)³ × (5⁵) ÷ 225 = 3000, follow these steps:
- Rearrange the equation:
(?)³ = (3000 × 225) ÷ 5⁵ - Calculate 5⁵:
5⁵ = 3125 - Simplify the numerator:
3000 × 225 = 675000 - Divide:
675000 ÷ 3125 = 216 - Find the cube root of 216:
√³(216) = 6
Correct Answer: A: 6
- a)51
- b)59
- c)57
- d)53
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
a)
51
b)
59
c)
57
d)
53
e)
None of these
|
|
Knowledge Center answered |
Solution for ∛185193
To solve ∛185193, we find the cube root:
- The cube root of 185193 is 57, since 57³ = 185193.
Correct Answer: C: 57
[(5√6 + √6) x (16√6 + 9√6)] – 96 = ?- a)704
- b)804
- c)606
- d)806
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
[(5√6 + √6) x (16√6 + 9√6)] – 96 = ?
a)
704
b)
804
c)
606
d)
806
e)
None of these
|
Preeti Khanna answered |
[(5√6 + √6) x (16√6 + 9√6)] – 96
[√6(5 + 1) x √6(16 + 9)] – 96
900 – 96 = 804
[√6(5 + 1) x √6(16 + 9)] – 96
900 – 96 = 804
- a)62/3
- b)6
- c)31/3
- d)3
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
a)
62/3
b)
6
c)
31/3
d)
3
e)
None of these
|
Faizan Khan answered |
On solving, we will get x = 3 or x = -2
Ignoring the negative value answer is 3.
Ignoring the negative value answer is 3.
If the sum of a number and its square is 156, what is the number?- a)16
- b)14
- c)12
- d)13
- e)None
Correct answer is option 'C'. Can you explain this answer?
If the sum of a number and its square is 156, what is the number?
a)
16
b)
14
c)
12
d)
13
e)
None
|
|
Knowledge Center answered |
Let the number be x.
x+x2=156
x2+x−156=0
(x−12)(x+13)=0
x+x2=156
x2+x−156=0
(x−12)(x+13)=0
x+13=0
x=−13 (Since x is a natural number)
x−12=0
x=12
x=−13 (Since x is a natural number)
x−12=0
x=12
12.5 * 14 ÷ 8.75 + 12 = 20 + ? - a)14
- b)11
- c)12
- d)18
- e)15
Correct answer is option 'C'. Can you explain this answer?
12.5 * 14 ÷ 8.75 + 12 = 20 + ?
a)
14
b)
11
c)
12
d)
18
e)
15
|
Sankar Rane answered |
12.5 * 1.6 = 20 ; 20 + 12 – 20 = 12
5616 ÷ 18 ÷ 8 = ?- a)34
- b)39
- c)38
- d)37
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
5616 ÷ 18 ÷ 8 = ?
a)
34
b)
39
c)
38
d)
37
e)
None of these
|
Kavya Saxena answered |
5616 ÷ 18 = 312
312 / 8 = 39
312 / 8 = 39
- a)2 - √2
- b)√2 - 2
- c)2
- d)-2
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
a)
2 - √2
b)
√2 - 2
c)
2
d)
-2
e)
None of these
|
|
Prakhya Shrivastava answered |
√8 - √4 - √2
= 2√2 - 2 - √2
= √2-2
Hence option (b) is correct
= 2√2 - 2 - √2
= √2-2
Hence option (b) is correct
(85410 + 36885 + 24705) ÷ 1600 = ?- a)92.875
- b)91.875
- c)93.675
- d)92.675
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
(85410 + 36885 + 24705) ÷ 1600 = ?
a)
92.875
b)
91.875
c)
93.675
d)
92.675
e)
None of these
|
Aisha Gupta answered |
(85410 + 36885 + 24705) = 147000; 147000/1600 = 91.875
5610 ÷ 35.0625 * 25 = ?- a) 3000
- b) 2000
- c)5000
- d) 4000
- e) 6000
Correct answer is option 'D'. Can you explain this answer?
5610 ÷ 35.0625 * 25 = ?
a)
3000
b)
2000
c)
5000
d)
4000
e)
6000
|
Yash Patel answered |
5610 ÷ 35.0625 = 160; 160 * 25 = 4000
47.932 + 56 + 97.168 – 67 – 78.3 – 22.7- a)33
- b)32.1
- c)33.1
- d)34.1
- e)None
Correct answer is option 'C'. Can you explain this answer?
47.932 + 56 + 97.168 – 67 – 78.3 – 22.7
a)
33
b)
32.1
c)
33.1
d)
34.1
e)
None
|
|
Knowledge Center answered |
Expression:
( 47.932 + 56 + 97.168 - 67 - 78.3 - 22.7 )
Step 1: Add the positive terms:
( 47.932 + 56 + 97.168 = 201.1 )
Step 2: Add the negative terms:
( 67 + 78.3 + 22.7 = 168 )
Step 3: Subtract the sum of negative terms from the sum of positive terms:
( 201.1 - 168 = 33.1 )
Final Answer: The result of the expression is 33.1.
456 ÷ 24 * 38 – 958 + 364 = ?- a)167
- b) 146
- c)136
- d)128
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
456 ÷ 24 * 38 – 958 + 364 = ?
a)
167
b)
146
c)
136
d)
128
e)
None of these
|
|
Faizan Khan answered |
456 ÷ 24 = 19; 19 * 38 = 722; 722 + 364 – 958 = 128
468 ÷ 39*15 + 166 = (?)³ + 130- a)5
- b)6
- c)4
- d)7
- e)2
Correct answer is option 'B'. Can you explain this answer?
468 ÷ 39*15 + 166 = (?)³ + 130
a)
5
b)
6
c)
4
d)
7
e)
2
|
Nikita Singh answered |
12 * 15 + 166 = (?)³ + 130
(?)³ = 216
(?)³ = 216
? * (523.5 + 687.5) = 24220- a)24
- b)20
- c)28
- d) 27
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
? * (523.5 + 687.5) = 24220
a)
24
b)
20
c)
28
d)
27
e)
None of these
|
|
Anaya Patel answered |
x * 1211 = 24220; x = 20
? % of 1400 – 18% of 750 = 159- a)27
- b)29
- c)17
- d)21
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
? % of 1400 – 18% of 750 = 159
a)
27
b)
29
c)
17
d)
21
e)
None of these
|
All Film Mistakes answered |
21% of 1400 is 294 18 % of 750 is 135 294-135 is 159
x * (523.5 + 687.5) = 24220
- a)10
- b)15
- c)17
- d)20
- e)30
Correct answer is option 'D'. Can you explain this answer?
x * (523.5 + 687.5) = 24220
a)
10
b)
15
c)
17
d)
20
e)
30
|
Nasir Shaik answered |
523.5 + 687.5 =1211
Now in RHS unit digit is '0' so it should be multiple by 0. tTen' digit is 2 .So it should be multiple by 2.
so ans is 20
Now in RHS unit digit is '0' so it should be multiple by 0. tTen' digit is 2 .So it should be multiple by 2.
so ans is 20
(169 – 144)½ ÷ (64 + 36)½ = ?
- a)0.5
- b)0.25
- c)2.5
- d)5
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
(169 – 144)½ ÷ (64 + 36)½ = ?
a)
0.5
b)
0.25
c)
2.5
d)
5
e)
None of these
|
|
Knowledge Center answered |
To solve the given expression:
1. Calculate the values inside the parentheses first: √(169 - 144 = 25) and √(64 + 36 = 100).
2. Now simplify the expression further: √25/√100 .
3. Calculate the square roots: 5/10
4. Finally, divide the two results: 0.5
Therefore, the correct answer is A: 0.5.
1. Calculate the values inside the parentheses first: √(169 - 144 = 25) and √(64 + 36 = 100).
2. Now simplify the expression further: √25/√100 .
3. Calculate the square roots: 5/10
4. Finally, divide the two results: 0.5
Therefore, the correct answer is A: 0.5.
–224 + (–314) x (–9) = ?- a)2602
- b)547
- c)– 547
- d)–2602
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
–224 + (–314) x (–9) = ?
a)
2602
b)
547
c)
– 547
d)
–2602
e)
None of these
|
|
Nishtha Pandey answered |
So here v hav to follow BODMAS rule i.e
bracket open divide multiply add sub
-224+(-314)×(-9)
-224+(2826) [ -×-=+ ]
+2602
bracket open divide multiply add sub
-224+(-314)×(-9)
-224+(2826) [ -×-=+ ]
+2602
(656 ÷ 164)² = √?- a)4
- b)16
- c)256
- d)400
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
(656 ÷ 164)² = √?
a)
4
b)
16
c)
256
d)
400
e)
None of these
|
|
Alok Verma answered |
656 ÷ 164 = 4; √? = 16 ; ? = 256
69.69 – 51.54 + 73.65 = ? + 32.42- a)26.38
- b)32.38
- c)43.38
- d)57.38
- e)59.38
Correct answer is option 'E'. Can you explain this answer?
69.69 – 51.54 + 73.65 = ? + 32.42
a)
26.38
b)
32.38
c)
43.38
d)
57.38
e)
59.38
|
|
Kavya Saxena answered |
69.69 – 51.54 = 18.15
18.15 + 73.65 = 91.80
91.80 – 32.42 = 59.38
18.15 + 73.65 = 91.80
91.80 – 32.42 = 59.38
5.8 * 2.5 + 0.6 * 6.75 + 139.25 = ?- a)139.80
- b) 157.80
- c) 156.70
- d)170.70
- e)176.60
Correct answer is option 'B'. Can you explain this answer?
5.8 * 2.5 + 0.6 * 6.75 + 139.25 = ?
a)
139.80
b)
157.80
c)
156.70
d)
170.70
e)
176.60
|
|
Kavya Saxena answered |
5.8 * 2.5 + 0.6 * 6.75 + 139.25 = 157.80
- a)
- b)
- c)4
- d)
- e)None of these
Correct answer is 'C'. Can you explain this answer?
a)
b)
c)
4
d)
e)
None of these
|
Dils George answered |
8 can be written as 2 cube , cube can be cut down and will remain with 2 square so answer is 4
[(272-32)(124+176)]/(17*15-15) = ?- a)240
- b)320
- c)400
- d)380
- e)300
Correct answer is option 'E'. Can you explain this answer?
[(272-32)(124+176)]/(17*15-15) = ?
a)
240
b)
320
c)
400
d)
380
e)
300
|
|
Aarav Sharma answered |
Given expression: [(272-32)(124 176)]/(17*15-15)
Simplifying the expression step by step:
1. [(272-32)(124 176)] = 24000
2. (17*15-15) = 240
3. [(272-32)(124 176)]/(17*15-15) = 24000/240
4. [(272-32)(124 176)]/(17*15-15) = 100
Therefore, the correct answer is option 'E': 300.
Simplifying the expression step by step:
1. [(272-32)(124 176)] = 24000
2. (17*15-15) = 240
3. [(272-32)(124 176)]/(17*15-15) = 24000/240
4. [(272-32)(124 176)]/(17*15-15) = 100
Therefore, the correct answer is option 'E': 300.
(786*74) ÷ x = 1211.75- a)62
- b)55
- c)52
- d)48
- e)46
Correct answer is option 'D'. Can you explain this answer?
(786*74) ÷ x = 1211.75
a)
62
b)
55
c)
52
d)
48
e)
46
|
|
Faizan Khan answered |
(786*74) ÷ x = 1211.75
x = 48
x = 48
- a)88
- b)74
- c)77
- d)84
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
a)
88
b)
74
c)
77
d)
84
e)
None of these
|
|
Kavya Saxena answered |
8/21 * x = 1008
x = 21168 / 8
x = 2646
8% of 800 x ? = 224- a)4.5
- b)3.5
- c)4
- d)3
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
8% of 800 x ? = 224
a)
4.5
b)
3.5
c)
4
d)
3
e)
None of these
|
|
Aishwaryasingla123 answered |
8/100 (x*800)=22464*x=224x=7/2 x=3.5
12.5% of 350 * 8.4% of 250 = ?- a)912.75
- b)915.75
- c)913.75
- d)918.75
- e)916.75
Correct answer is option 'D'. Can you explain this answer?
12.5% of 350 * 8.4% of 250 = ?
a)
912.75
b)
915.75
c)
913.75
d)
918.75
e)
916.75
|
|
Faizan Khan answered |
12.5% of 350 * 8.4% of 250 = 6.25 * 7 * 21 = 918.75
(?)1/4/ 8 = 48/(?)3/4- a)324
- b)364
- c)384
- d)374
- e)314
Correct answer is option 'C'. Can you explain this answer?
(?)1/4/ 8 = 48/(?)3/4
a)
324
b)
364
c)
384
d)
374
e)
314
|
Devansh Tomar answered |
Let? =x
A/q
Croos multiple then
X=8×48
X= 384
A/q
Croos multiple then
X=8×48
X= 384
- a)6241
- b)6889
- c)6561
- d)5929
- e)None of thes
Correct answer is option 'C'. Can you explain this answer?
a)
6241
b)
6889
c)
6561
d)
5929
e)
None of thes
|
|
Anaya Patel answered |
C is the correct option. Solution-
4028÷53=76
6156÷76=81
So the value needed is a square of 81 which is 6561.
4028÷53=76
6156÷76=81
So the value needed is a square of 81 which is 6561.
- a)
- b)
- c)
- d)
- e)
Correct answer is option 'C'. Can you explain this answer?
a)
b)
c)
d)
e)
|
|
Knowledge Center answered |
= we know,
(4-3+13-8)+(1/2 - 1/7 + 2/7 -1/4)
= 6 + 11/28
= option C
(4-3+13-8)+(1/2 - 1/7 + 2/7 -1/4)
= 6 + 11/28
= option C
√676 * 12 – 864÷36 = ? + 61- a)234
- b)227
- c)232
- d)244
- e)256
Correct answer is option 'B'. Can you explain this answer?
√676 * 12 – 864÷36 = ? + 61
a)
234
b)
227
c)
232
d)
244
e)
256
|
|
Preeti Khanna answered |
√676 * 12 – 864÷36 = ? + 61
x = 227
x = 227
4.5 + 23.50 + 14.58 – 17.68 * 0.5 = ?- a)23.74
- b)33.74
- c)34.74
- d)36.74
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
4.5 + 23.50 + 14.58 – 17.68 * 0.5 = ?
a)
23.74
b)
33.74
c)
34.74
d)
36.74
e)
None of these
|
|
Faizan Khan answered |
17.68 * 0.5 = 8.84
42.58 – 8.84 = 33.74
42.58 – 8.84 = 33.74
Which one of the following fractions is the greatest?- a)1/7
- b)2/9
- c)4/11
- d)3/10
- e)None
Correct answer is option 'C'. Can you explain this answer?
Which one of the following fractions is the greatest?
a)
1/7
b)
2/9
c)
4/11
d)
3/10
e)
None
|
|
Knowledge Center answered |
1/7 = 0.1429
2/9 = 0.2222
4/11 = 0.3636
3/10 = 0.3
So, the greatest fraction is 4/11
2/9 = 0.2222
4/11 = 0.3636
3/10 = 0.3
So, the greatest fraction is 4/11
1(2/3) + 2(4/9) – 3(7/15) = ?
- a)0.14
- b)0.55
- c)0.72
- d)0.58
- e)0.46
Correct answer is option 'A'. Can you explain this answer?
1(2/3) + 2(4/9) – 3(7/15) = ?
a)
0.14
b)
0.55
c)
0.72
d)
0.58
e)
0.46
|
Rohan Sengupta answered |
2/3 + 8/9 - 21/15
28/18 - 21/15
140-126/90
7/45 = 0.15
So option A is correct
69 ÷ 3 * 0.85+ 14.5 – 3 = ?- a)36.15
- b)32.15
- c)33.05
- d)32.05
- e)None of these
Correct answer is option 'E'. Can you explain this answer?
69 ÷ 3 * 0.85+ 14.5 – 3 = ?
a)
36.15
b)
32.15
c)
33.05
d)
32.05
e)
None of these
|
|
Aisha Gupta answered |
69 ÷ 3 * 0.85 = 23 * 0.85 = 19.55
19.55 + 14.5 – 3 = 31.05
19.55 + 14.5 – 3 = 31.05
If a – b = 7 and a2 + b2 = 53, find the value of ab.- a)5
- b)3
- c)0.5
- d)1
- e)2
Correct answer is option 'E'. Can you explain this answer?
If a – b = 7 and a2 + b2 = 53, find the value of ab.
a)
5
b)
3
c)
0.5
d)
1
e)
2
|
|
Anaya Patel answered |
2ab = (a2 + b2) – (a – b)2
2ab = 53-49 =4
ab =4/2 = 2
2ab = 53-49 =4
ab =4/2 = 2
(32.4 * 8 * 5 + 4) ÷ 26 + 14 = (?)² - a)8
- b)2
- c)18
- d)12
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
(32.4 * 8 * 5 + 4) ÷ 26 + 14 = (?)²
a)
8
b)
2
c)
18
d)
12
e)
None of these
|
Sagar Sharma answered |
The expression (32.4 * 8 * 5 4) can be simplified as follows:
(32.4 * 8 * 5 4) = (259.2 * 5 4) = (1296 + 4) = 1300
(32.4 * 8 * 5 4) = (259.2 * 5 4) = (1296 + 4) = 1300
Find the number in the unit place in (321)321 x (325)326.- a)1
- b)5
- c)6
- d)8
- e)None
Correct answer is option 'B'. Can you explain this answer?
Find the number in the unit place in (321)321 x (325)326.
a)
1
b)
5
c)
6
d)
8
e)
None
|
|
Faizan Khan answered |
321 raised to 321=1 in unit digit and any number ending in 5 raised to any number has always 5 as unit digit, so 1×5=5
(331 + 19)*(15 – 11)*(37 + 13) = ?- a)67600
- b)70000
- c)69850
- d)72000
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
(331 + 19)*(15 – 11)*(37 + 13) = ?
a)
67600
b)
70000
c)
69850
d)
72000
e)
None of these
|
|
Aisha Gupta answered |
(331 + 19)*(15 – 11)*(37 + 13) = 350 * 4 * 50 = 70000
? / 529 = 324 / ? - a)325
- b)414
- c)456
- d)448
- e)352
Correct answer is option 'B'. Can you explain this answer?
? / 529 = 324 / ?
a)
325
b)
414
c)
456
d)
448
e)
352
|
|
Preeti Khanna answered |
x² = 529 * 324 ⇒ x = 23 * 18 = 414
What is the number in the unit place in (5427)641?- a)1
- b)7
- c)9
- d)3
- e)None
Correct answer is option 'B'. Can you explain this answer?
What is the number in the unit place in (5427)641?
a)
1
b)
7
c)
9
d)
3
e)
None
|
Deepali singhania answered |
The correct answer is B as the unit place will be 7 only .
The sum of the digits of a two-digit number is 8. If the digits are reversed, the number is decreased by 54. Find the number.- a)42
- b)53
- c)17
- d)71
- e)None
Correct answer is option 'D'. Can you explain this answer?
The sum of the digits of a two-digit number is 8. If the digits are reversed, the number is decreased by 54. Find the number.
a)
42
b)
53
c)
17
d)
71
e)
None
|
|
Aarav Sharma answered |
Problem Solving:
Let us assume that the tens and units digits of the number are x and y respectively. Therefore, the number can be expressed as 10x + y. According to the given information,
x + y = 8 ... (1)
10y + x = 10x + y – 54
=> 9y – 9x = –54
=> y – x = –6
=> x – y = 6 … (2)
Adding equations (1) and (2), we get
2x = 2
=> x = 1
Substituting x = 1 in equation (1), we get
y = 7
Therefore, the required two-digit number is 10x + y = 10(1) + 7 = 17.
Answer: Option (c) 17.
Let us assume that the tens and units digits of the number are x and y respectively. Therefore, the number can be expressed as 10x + y. According to the given information,
x + y = 8 ... (1)
10y + x = 10x + y – 54
=> 9y – 9x = –54
=> y – x = –6
=> x – y = 6 … (2)
Adding equations (1) and (2), we get
2x = 2
=> x = 1
Substituting x = 1 in equation (1), we get
y = 7
Therefore, the required two-digit number is 10x + y = 10(1) + 7 = 17.
Answer: Option (c) 17.
(√3 + 1)² = ? + √12- a)2
- b)6
- c)3
- d)4
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
(√3 + 1)² = ? + √12
a)
2
b)
6
c)
3
d)
4
e)
None of these
|
|
Nikita Singh answered |
(√3 + 1)² = ? + √12
3 + 2√3 + 1 = ? + 2√3 = 4
3 + 2√3 + 1 = ? + 2√3 = 4
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