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Question 161

MP Police ASI 2023• Test

If 1st January, 1601 is Monday, What day is 1st  January of 1701?

  1. AOption (a)

    Thursday

  2. BOption (b)

    Wednesday

  3. COption (c)

    Monday

  4. DOption (d)

    Saturday

View answer & explanation

Correct answer

Answer: (d)D.

Saturday

Why this answer is correct

Given: 1st January, 1601 is Monday

The 1701 year = 1601 + 100 

So, as we know that the number of odd days in 100 years is 5

So, in between 1601 to 1701 years the number of odd days is 5.

Now, 1st January 1701 is,

Monday + 5 = Saturday.

Hence, the correct answer is "Saturday".

Question 162

MP Police ASI 2023• Test

Read the following data and answer the questions that follow it.

Details about companies listed in Stock Exchange in different years. 

YearNumber of CompaniesBSE ∶ NSEPvt. Ltd ∶ Ltd.% of companies out of Pvt. Ltd. having net worth less than 100 cr
200124,00011 ∶ 97 ∶ 546%
200230,00019 ∶ 1117 ∶ 862%
200344,0007 ∶ 43 ∶ 172%
200438,00012 ∶ 723 ∶ 1563%
200556,0005 ∶ 219 ∶ 952%
200640,0005 ∶ 34 ∶ 150%

How many Pvt. Ltd. companies are listed in 2003 and 2005 having net worth less than 100 cr?

  1. AOption (a)

    43520

  2. BOption (b)

    48950

  3. COption (c)

    51260

  4. DOption (d)

    53340

View answer & explanation

Correct answer

Answer: (a)A.

43520

Why this answer is correct

Calculation:

In 2003 

4 unit = 44000

1 unit = 11000

3 unit = 33000

⇒ 33000 × 72/100 = 23760

In 2005

28 unit = 56000

1 unit = 2000

19 unit = 38000

⇒ 38000 × 52/100 = 19760

Companies having net worth less than 10 Cr = 23760 + 19760 = 43520

∴ The correct answer is 43520.

Question 163

MP Police ASI 2023• Test

Which of the following words cannot be formed using the letters of the given word.

TRANSFORMER

  1. AOption (a)

    FORTS

  2. BOption (b)

    STORM

  3. COption (c)

    SPORT

  4. DOption (d)

    REFORM

View answer & explanation

Correct answer

Answer: (c)C.

SPORT

Why this answer is correct

1) FORTS→ can be formed → TRANSFORMER

  1. STORM → can be formed → TRANSFORMER

3) SPORT → since there is no P in the word TRANSFORMER so it cannot be formed

4) REFORM → can be formed → TRANSFORMER

Hence, the correct answer is "SPORT".

Question 164

MP Police ASI 2023• Test

What value will come in place of question mark (?) in the following question?

28% of 145 + 36% of 150 - 22% of 65 = ?

  1. AOption (a)

    60.3

  2. BOption (b)

    80.3

  3. COption (c)

    70.3

  4. DOption (d)

    90.3 

View answer & explanation

Correct answer

Answer: (b)B.

80.3

Why this answer is correct

Calculation:

28% of 145 + 36% of 150 - 22% of 65 

⇒ 40.6 + 54 - 14.3

⇒ 80.3

∴ The correct answer is 80.3.

Question 165

MP Police ASI 2023• Test

Solve the given expression and find the value of '∠A-

\(\rm \frac{Sin \ A}{(Sec\ A +1)}+\frac{Sin \ A}{(Sec\ A -1)}=2\sqrt3 \)

  1. AOption (a)

    45° 

  2. BOption (b)

    30°

  3. COption (c)

    15°

  4. DOption (d)

    60°

View answer & explanation

Correct answer

Answer: (b)B.

30°

Why this answer is correct

Given:

\(\rm \frac{Sin \ A}{(Sec\ A +1)}+\frac{Sin \ A}{(Sec\ A -1)}=2\sqrt2\)

Calculation:

Checking option (1),

∠A = 30° 

R.H.S = \(\rm \frac{Sin \ 45}{(Sec\ 45 +1)}+\frac{Sin \ 45}{(Sec\ 45 -1)}\)

⇒ \(\dfrac{1}{\sqrt{2}}[\dfrac{1}{\sqrt{2}+1}+\dfrac{1}{\sqrt{2}-1}]\) 

⇒ \(\dfrac{1}{\sqrt{2}}[\dfrac{\sqrt{2}-1+\sqrt{2}+1}{2-1}]\) = \(2\sqrt{2}\)

⇒ R.H.S = \(\sqrt{2}\)

R.H.S ≠ L.H.S

Checking option (2),

R.H.S = \(\rm \frac{Sin \ 30}{(Sec\ 30 +1)}+\frac{Sin \ 30}{(Sec\ 30 -1)}\)

⇒ \(\dfrac{1}{2}[\dfrac{1}{\dfrac{2}{\sqrt{3}}+1}+\dfrac{1}{\dfrac{2}{\sqrt{3}}-1}]\)

\(\dfrac{\sqrt{3}}{2}[\dfrac{1}{2+{\sqrt{3}}}+\dfrac{1}{2-{\sqrt{3}}}]\)

\(\dfrac{\sqrt{3}}{2}[\dfrac{2-\sqrt{3}+2+\sqrt{3}}{4-3}]\)

\(\dfrac{\sqrt{3}}{2}\times4\) = 2\(\sqrt{3}\)

R.H.S = L.H.S 

∴ Option (2) is the correct answer.

Question 166

MP Police ASI 2023• Test

The angle of elevation of a point P with respect to the top of a tower is 30°. If the distance between the foot of the tower and P is 75 m, what is the height of the tower?

  1. AOption (a)

    75√3 m

  2. BOption (b)

    150 m

  3. COption (c)

    75 m

  4. DOption (d)

    25√3 m

View answer & explanation

Correct answer

Answer: (d)D.

25√3 m

Why this answer is correct

Calculation:

We know tanθ = P/B

tan30° = 1/√3

So,

⇒ 1/√3 = P/75

⇒ P = 75/√3

⇒ P = 75/3 × √3

⇒ P = 25√3

∴ The correct answer is 25√3.

Question 167

MP Police ASI 2023• Test

In the following diagram, the circle represents college Professors, the triangle stands for surgical Specialists, and medical Specialists are represented by the rectangle. Whom does C represents ?

  1. AOption (a)

    College Professors

  2. BOption (b)

    Medical Specialists

  3. COption (c)

    Surgical Specialists

  4. DOption (d)

    Medical and surgical Specialists

View answer & explanation

Correct answer

Answer: (c)C.

Surgical Specialists

Why this answer is correct

From the given information,

As we can see that "C" represents the surgical Specialists.

Hence, the correct answer is "surgical Specialists".

Question 168

MP Police ASI 2023• Test

X alone can do a piece of work in 15 days and Y can do the same work in 10 days. Rs. 4800 were allocated to finish the work. If with the help of Z they were able to finish the work in 5 days, how much amount will Z get?

  1. AOption (a)

    Rs. 800

  2. BOption (b)

    Rs. 1600 

  3. COption (c)

    Rs. 1200

  4. DOption (d)

    Rs. 1800

View answer & explanation

Correct answer

Answer: (a)A.

Rs. 800

Why this answer is correct

Formula used:

Work done = time × Efficiency

Calculation:

Let total work is 30.

Efficiency of X = 30/15 = 2

Efficiency of Y = 30/10 = 3

Efficiency of (X + Y + Z) = 30/5 = 6 

Efficiency of Z = 6 - (3 + 2) = 1

Now the money will be divide in the ratio of their efficiency

⇒ 6 unit = 4800

⇒ 1 unit = 800

Amount Z will get is Rs.800

∴ The correct anwer is Rs.800.

Question 169

MP Police ASI 2023• Test

At 3 ∶ 20 in a clock, the angle between the minute and hour hands is.

  1. AOption (a)

    20°

  2. BOption (b)

    10°

  3. COption (c)

    40°

  4. DOption (d)

    30°

View answer & explanation

Correct answer

Answer: (a)A.

20°

Why this answer is correct

By applying the formula we can get the answer is:

Angle = |[11/2M ± 30H]|

Where M = 20 and H = 3

At 3: 20, the angle between the hour hand and the minute hand of a clock is

⇒  |[(11/2)× (20) ± 30 × (3)]|

⇒ |[110 ± 90]|

⇒ 20° or 200° 

Hence, the correct answer is "20°".

Question 170

MP Police ASI 2023• Test

From the given alternatives, select the word which can be formed using the letters of the given word.

QUINTESSENCE

  1. AOption (a)

    SCOT

  2. BOption (b)

    ESTEEM

  3. COption (c)

    QUITE

  4. DOption (d)

    QUOTE

View answer & explanation

Correct answer

Answer: (c)C.

QUITE

Why this answer is correct

Given word: QUINTESSENCE

Let’s check all the options:

(1) SCOT ⇒ It can’t be formed as it requires O.

(2) ESTEEM⇒ It can’t be formed as it requires M.

(3) QUITE ⇒  It can be formed.

(4) QUOTE ⇒ It can’t be formed as it requires O.

Hence, the correct answer is "QUITE"