BSF Head Constable Mock Test - 3 - CDS MCQ

The Orangutan is a type of monkey. These are  species of the great apes native to Indonesia and Malaysia. They are the most arboreal and spend most of the time in the trees. The Orangutans are currently found only in rainforests of Borneo and Sumatra.

Security Paper Mill was established in 1968 at Hoshangabad, Madhya Pradesh. It produces paper for bank notes and non-judicial stamps.

ISI and Agmark are the symbols of quality of goods. ISI is a certification for industrial products, Agmark is a certification for food articles.

Garba is a popular dance form of the state of Gujarat. It is derived from a Sanskrit word Garbha and Deep. The dancers dance around a centrally lit lamp and a picture or statue of Maa Shakti (Ambe Maa).

Mercury is the planet nearest to the sun. The planet orbits the sun faster than any other planet and completes the revolution in 88 days. It is named after the Roman deity 'Mercury'. 

The value of √8-2√15 can be calculated by using the formula,
(a-b)² = a² + b² - 2ab
Therefore,
√5+3-2√15
= √(√5)² + (√3)² - 2(√5) x √3
= √(5)-(√3)²
= √5 - √3

A prime number is a number that is divisible only by itself and 1.
31, 37 and 43 are prime numbers.
87 is not a prime number. It comes in the table of 3.
It is the product of 29 and 3.
Hence, option D is correct.

Divisibility rule for 4: Check the last two digits of the given number. If it is divisible by 4, then the whole number is divisible by 4.
From the given options, the last two digits which are divisible by 4 are 24, 52 and 44.
But 50 is not divisible by 4.
Therefore, 314250 is not divisible by 4.

Given that,
A can do a piece of work in 12 days.
B can do the work in 15 days.
C's one day work can be calculated as follows;
C's one-day work =(A+B+C)'s one-day work −A-'s one-day work −B-'s one-day work
= (1/4) - (1/12 + 1/15)
= (1/4) - (1/12 + 1/15)
= (1/4) - (9/60)
= (1/4) - (3/20)
= (1/10)
Therefore, C can alone do the same work in 10 days.

The area of a square in terms of its diagonal is as follows;
Area = (Diagonal)²/2
= (12)²/2
= 144/2
= 72 cm²
 

Let the price of the article be ₹100.
According to the question,
Marked price of the article =160%×100
= (160/100) x 100 = ₹160
Discount =20%
Selling price = (100− Discount)% of MP
= 80% x 160
= (160 x 80)/100 
= ₹128
P%  = (P/CP) x 100
= (128 - 100)100 x 100
= (28/100) x 100
= 28%
Thus, 28% is the correct answer.

5x+6y/5x−2y
Dividing numerator and denominator by y and putting the value of x/y from the question.
= (5(x/y) + 6)/(5(x/y)-2)
= (5 x (5/4) + 6)/(5x(5/4)-2)
= ((25/4)+6)/((25/4)-2)
⇒ 49/17 = 49 : 17

Let the cost price of the article be Rs. 100.
Using, SP=(100+Gain)%×CP
At 80% gain,
Selling price =180%×100= (180/100) x 100 = Rs. 180
If he sells it at half the price,
Selling price = 180/2  = Rs. 90
The loss percentage can be calculated as follows;
Loss % = (Loss/CP) x 100
= (10/100) x 100
= 10%

The required percentage can be calculated as follows;
% Increase = decreased %/100-decreased%
= (25/(100-25))x100
= (25/75) x 100 = 33.33%
Hence, option C is the correct one.

The expression for average speed is as follows;
Average speed = (2xy)/(x+y)
= (2 x 40 x 55)/(40 + 55)
=  (2 x 40 x 55)/(95)
= 46.31 km/hr

The expression for principal for two years is as follows;
Sum = Difference in interest × (100/Rate)²
= (1290 - 1200) x (100/15)²
= 90 x (100/15)²
= Rs. 4000
Hence, first option is the correct one.

Total sales of the company in the given period is
55+66+75+82.5+75+87.5+105
= 546 crore
The average sale of the company
= 546/7
= 78 crore.

The required percentage can be calculated as follows;
Required % = ((sales in 2104−sales in 2016))/sales in 2104) x 100
= (87.5 - 70)/87.5)x100
= (17.5/87.5) x 100
= 20%

Given:
CI @ 11% is 6,963
Formula:
A = P (1 + r/100)^t
CI = P (1 + r/100)^t - P
Calculation:
P (1 + 11/100)² - P = 6963
⇒ P × 1.11² - P = 6963
⇒ 1.2321P - P = 6963
⇒ 0.2321P = 6963
⇒ P = 6963/0.2321
⇒ P = 30,000
∴ The sum is ₹ 30,000.

Concept:
L.C.M.: L.C.M. of any two numbers is the value that is evenly divisible by the two given numbers.
H.C.F.: H.C.F. of two numbers is the highest possible number that divides both numbers completely.
Calculation:
Let the numbers be x and 4x
⇒ L.C.M. × H.C.F. = Product of two numbers
⇒ 84 × 21 = (x) × (4x)
⇒ 4x² = 84 × 21
⇒ x² = (84×21)/4
⇒ x² = 21 × 21
⇒ x = 21
The largest number is 4x = 4 × 21 = 84
∴ Therefore, the largest number is 84.

Given:
Speed of first train = 80 km/hr
Length of first train = 150m
Speed of Second train = 62 km/hr
Length of  Second train = 180m
Formula used:
Time taken by the two trains to cross each other = Sum of the lengths of the trains / Relative speed of the trains
Calculation:
Relative speed of train = 80 - 62 = 18 km/hr
Converting it into m/s = 18 × 5/18 =  5m/s
⇒ 150 + 180 / 5
⇒ 330 / 5 = 66
Hence, option 4 is correct answer.

Calculation:
150% of 15 + 75% of 75 

⇒ 78.75

Given:
The cost price of 91 books is equal to the selling price of 65 books.
Concept used:
Profit = SP - CP
Profit% = Profit/CP × 100 
Calculation:
Let the cost price of each book be Rs. 1
CP of 65 books = Rs. 65
SP of 65 books = CP of 91 books = Rs. 91
Profit = Rs. (91 - 65) = Rs. 26
Profit% = (26/65) x 100 = 40%
∴ The required profit% is 40%.

Given:
Gain = 400
Calculation:
Let the CP is 100
MP = 120% × 100 = 120
SP = MRP × (100 - Discount)%
SP = 120 × 90/100 = 108
Profit = 108 - 100 = 8
8 unit → 400, 1 unit → 50
so, CP will be 50 × 100 = 5000
∴ CP is 5000.

Formula Used:
X% = X/100
Calculation:
(120% of 675) + 92 = (? % of 1240) + 716
⇒ (120/100) × 675 + 92 = (?/100) × 1240 + 716
⇒ 810 + 92 = 12.4 × ? + 716
⇒ 902 - 716 = 12.4 × ?
⇒ 186/12.4 = ? = 15
∴ The correct answer is 15.

Given, 
Loss =10 %
Formula used:
((CP - SP ) / CP ) x 100 = 10
Calculation:
⇒ ( (CP−180) / CP ) x 100 = 10
⇒ CP−180 = 0.1CP
⇒ 0.9CP = 180
⇒ CP = 200
To make a profit of 15 %, he must sell it at 
⇒ SP = CP + 15 % of CP = 200 + 30 = Rs. 230
Hence, option 2 is correct answer.  

Given :
The slant height of a frustum of cone is 10 cm and the height of the frustum is 8 cm.

Calculation:
We know, the relationship between slant height, height and radius
l² = h²+(R−r)²
Let R and r be the radius of two circular ends.
Slant height is l = 10 cm
Height is h = 8 cm
l² = h²+(R−r)²
10² = 8²+(R−r)²
100 = 64+(R−r)²
R−r = √36
R−r = 6
Therefore, The difference of radii of its two circular ends is 6 cm.

Given:
Percentage of poor products = 13%
Number of correct products = 4698
Concept used:
Number of products = Percentage x Total number of products
Total percentage = 100%
Calculation:
We know that,
Percentage of correct products = 100 - Percentage of poor products = 100 - 13 = 87%
Number of correct products = Percentage x Total number of products
4698  = 87% × total number of products
4698 = (87 × total number of products) / 100
Total number of products = (4698 x 100) / 87 = 5400
Number of poor products = Total number of products - number of correct products = 5400 - 4698 = 702
Therefore, the correct answer is option 1.

Given:
A person spends average Rs. 1800 per month in first 4 months.
In next 8 months he spends average Rs. 2000 per month.
In the end of the year he saves Rs. ​5600.
Concept used: 
Average = Sum of observation / Number of observations
Calculation:
Money spent in first 4 months = 1800 x 4
⇒ Rs. 7,200
Money spent in last 8 months = 2000 x 8
⇒ Rs. 16,000
Money saved = Rs. 5,600
Total money earned in year = 7,200 + 16,000 + 5,600
⇒ Rs. 28,800
⇒ Monthly income = 28800/12 = Rs. 2,400
∴ His monthly income is Rs. 2,400.

Given: 
√2 = 1.4142,
Calculation:    

By rationalization

1.4142 - 1
0.4142 
∴ The correct answer is "0.4142".