1. A person crosses a 600 metre long street in 5 minutes. What is his speed in km/hr?

• 3.6

• 7.2

• 8.4

• 10

Answer

Speed = 600/(5*60) m/sec = 2m/sec.

Converting m/sec to km/hr = 2*18/5 km/hr.

= 7.2 km/hr.

So, Option B.

 

2. An airplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 ⅔ hours, it must travel at a speed of:

• 300 kmph

• 360 kmph

• 600 kmph

• 720 kmph

Answer

Distance = 240*5 = 1200 km.

Speed = Distance/Time.

= 1200/(1 ⅔) = 1200/(5/3) = 720 kmph

So, Option D.

 

3. If a person walks at 14 kmph instead of 10 kmph, he would have walked 20 km more. The actual distance traveled by him is:

• 50 km

• 56km

• 70 km

• 80 km

Answer

Let the actual distance by x km.

Then, x/10 = (x + 20)/14.

Or, 14x = 10x + 200.

Or, 4x = 200.

Or, x = 50 km.

So, Option A.

 

4. A train can travel 50% faster than a car. Both start from point A at the same time and reach point B, 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:

• 100 kmph

• 110 kmph

• 120 kmph

• 130 kmph

Answer

Let the speed of the car be x kmph.

Then, speed of the train = 150x/100 = 3x/2 kmph.

So, 75/x – 75/(3x/2) = 125/(10*60).

Or, x = 120 kmph.

So, Option C.

 

5. Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

• 9

• 10

• 12

• 20

Answer

Due to stoppages, it covers 9 kms less.

Time taken to cover 9 kms = 9*60/54 min = 10 min.

So, Option B.

1. A bank offers 5% C.I. calculated on a half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:

• Rs.120

• Rs.121

• Rs.122

• Rs.123

Answer

Amount = Rs. (1600 * (1 + 5/200)^2 + 1600 * (1 + 5/200))

= Rs. (1600*41*81)/(40*40)

= Rs. 3321

So, C.I. = Rs. (3321 – 3200) = Rs. 121

So, Option B.

 

2. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% p.a. is Re. 1. The sum (in Rs.) is:

• 625

• 630

• 640

• 650

Answer

Let the sum be Rs. X.

Then, C.I. = (x * (1 + 4/100)^2 – x) = 676x/625 – x = 51x/625.

S.I. = (4*2*x)/100 = 2x/25

So, 51x/625 – 2x/25 = 1.

Or, x = 625.

So, Option A.

 

3.There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12000 after 3 years at the same time?

• Rs. 2160

• Rs. 3972

• Rs. 6240

• None of these

Answer

Let P = Rs. 100. Then, S.I. = Rs. 60 and T = 6 years.

So, R = (100*60)/(100*6) = 10% p.a.

Now, P = Rs. 12000. T = 3 years and R = 10% p.a.

So, C.I. = Rs. 12000 * ((1 + 10/100)^3 – 1)

= Rs. 3972

So, Option B.

 

4.What is the difference between compound interests on Rs. 5000 for 1.5 years at 4% p.a. Compounded yearly and half-yearly?

• Rs. 2.04

• Rs. 3.06

• Rs. 4.80

• Rs. 8.30

Answer

C.I. when interest is compounded yearly = Rs. 5000 * (1 + 4/100) * (1 + 0.5*4/100) = Rs. 5304.

C.I. when interest is compounded half-yearly = Rs. 5000 * (1 + 2/100)^3 = Rs. 5306.04.

So, Difference = Rs. (5306.04 – 5304) = Rs. 2.04.

So, Option A.

 

5.The C.I. on Rs. 30000 at 7% p.a. is Rs. 4347. The period (in years) is:

• 2

• 2.5

• 3

• 4

Answer

Amount = Rs. (30000 + 4347) = Rs. 34347.

Let time be n years.

Then, 30000 * (1 + 7/100)^n = 34347.

Or, n = 2 years.

So, Option A.

1.An accurate clock shows 8 o’ clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o’ clock in the afternoon?

• 144 degrees.

• 150 degrees.

• 168 degrees.

• 180 degrees.

Answer

Angle traced by the hour hand in 6 hours = 360/12 * 6 = 180 degrees.

So, Option D.

 

2. The reflex angle between the hands of a clock at 10.25 is:

• 180 degrees.

• 192.5 degrees.

• 195 degrees.

• 197.5 degrees.

Answer

Angle traced by hour hand in 125/12 hours = 360/12 * 125/12 = 312.5 degrees.

Angle traced by minutes hand in 25 minutes = 360/60 * 25 = 150 degrees.

So, Reflex angle = 360 degrees – (312.5 – 150) degrees = 197.5 degrees.

So, Option D.

 

3.A clock starts at noon. By 10 minutes past 5, the hour hand has turned through:

• 145 degrees.

• 150 degrees.

• 155 degrees.

• 160 degrees.

Answer

Angle traced by hour hand in 12 hours = 360 degrees.

Angle traced by hour hand in 5 hours 10 mins or 31/6 hours = 360/12 * 31/6 = 155 degrees.

So, Option C.

 

4. A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o’ clock, the true time is:

• 59 7/12 minutes past 3.

• 4 p.m.

• 58 7/11 minutes past 3.

• 2 3/11 minutes past 4.

Answer

Time from 7 a.m. to 4.15 p.m. = 9 hours 15 minutes = 37/4 hours.

3 minutes 5 seconds of this clock = 3 minutes of the correct clock.

Or, 37/720 hours of this clock = 1/20 hours of the correct clock.

Or, 37/4 hours of this clock = 1/20 * 720/37 * 37/4 hours of the correct clock = 9 hours of the correct clock.

So, the correct time is 9 hours after 7 a.m. = 4 p.m.

So, Option B.

 

5. How much does a watch lose per day, if its hands coincide every 64 minutes?

• 32 8/11 minutes.

• 36 5/11 minutes.

• 90 minutes.

• 96 minutes.

Answer

55 minutes spaces are covered in 60 minutes.

60 minutes  spaces are covered in 60/55 * 60 minutes = 65 5/11 minutes.

Loss in 64 minutes = 65 5/11 – 64 = 16/11 minutes.

Loss in 24 hours = 16/11 * 1/64 * 24 * 60 = 32 8/11 minutes.

So, Option A.

1. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many days can it be done?

• 564

• 645

• 756

• None of these.

Answer

We may have (3 women and 2 women) or (4 men and 1 woman) or (5 men) only.

So, Required no. of ways = (7C3 * 6C2) + (7C4 * 6C1) + 7C5

= 525 + 210 + 21 = 756

So, Option C.

 

2. In how many ways can letters of the word ‘CORPORATION’ be arranged so that the vowels always come together?

• 810

• 1440

• 2880

• 50400

Answer

In the word ‘CORPORATION’, we treat the vowels OOAIO as one letter.

Thus, we have CRPRTN(OOAIO).

This has 6 + 1 letters of which R occurs 2 times and the rest are different.

No. of ways in which these letters can be arranged = 7!/2! = 2520.

Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in 5!/3! = 20 ways.

So, required no. of ways = 2520 * 20 = 50400.

So, Option D.

 

3. In how many ways can letters of the word ‘LEADING’ be arranged so that the vowels always come together?

• 360

• 720

• 5040

• None of the above.

Answer

The word ‘LEADING’ has 7 letters.

When the vowels EAI are always together, they can be supposed to form 1 letter.

Then, we have to arrange the letters LNDG(EAI).

Now, 4 + 1 letters can be arranged in 5! ways = 120 ways.

The vowels EAI can be arranged among themselves in 3! ways = 6 ways.

So, required no. of ways = 120*6 = 720 ways.

So, Option B.

 

4. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

• 210

• 1050

• 25200

• 21400

Answer

No. of ways of selecting 3 out of 7 consonants and 2 out of 4 vowels = 7C3 * 4C2 = 210.

No. of groups, each having 3 consonants and 2 vowels = 210.

Each group contains 5 letters.

No. of ways of arranging 5 letters among themselves = 5! = 120

So, required no. of ways = 210*120 = 25200.

So, Option C.

 

5.In how many ways can the letters of the word ‘LEADER’ be arranged?

• 72

• 144

• 360

• 720

Answer

The word ‘LEADER’ contains 6 letters.

So, required no. of ways = 6!/2! = 360.

So, Option C.

1. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

• 45

• 47

• 48

• 50

Answer

Relative speed = (60 + 90) km/hr.

= (150 x 5/18) m/sec.

= 125/3 m/sec

Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.

Required Time = (2000 x 3/125) sec = 48 sec.

So, Option C.

 

2.Two trains of equal length 140 meters are running in opposite directions on parallel tracks at the same speed. If the trains cross each other 14 seconds, find the speed of each train.

• 30 km/hr

• 32 km/hr

• 34 km/hr

• 36 km/hr

Answer

Let the speed of each train be x km/hr

Relative speed = x + x = 2x …………….. (1)

Also, Relative speed = (Total distance covered (sum of length of trains))/(Time taken by  trains to cross each other).

Relative speed = (140 + 140)/14 = 280/14 = 20 m/s

From equation (1) and (2),

2x = 20

x = 10 m/s

We need the answer to be in km/hr.

So, x = 10 * 18/5 = 36km/hr.

So, Option D.

 

3. A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

• 230 m

• 240 m

• 260 m

• 270 m

Answer

Speed = 72* 5/18 m/sec = 20 m/sec.

Time = 26 seconds.

Let the length of the train be x metres.

Then, (x + 250)/26 = 20.

Or, x = 270 m.

So, Option D.

 

4. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

• 65 seconds

• 89 seconds

• 100 seconds

• 150 seconds

Answer

Speed = 240/24 m/sec = 10 m/sec.

So, Required time = (240 + 650)/10 = 89 seconds.

So, Option B.

 

5. A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

• 3.6 seconds

• 18 seconds

• 36 seconds

• 72 seconds

Answer

Speed of train relative to jogger = (45 – 9) km/hr = 36 km/hr = 36 * 5/18 m/sec = 10 m/sec.

Distance to be covered = (240 + 120) m = 360 m.

So, Time taken = 360/10 seconds = 36 seconds.

So, Option C.

1.Today is Monday. After 61 days it will be:

• Wednesday

• Saturday

• Tuesday

• Thursday

Answer

Each day of the week is repeated after 7 days.

So, after 63 days, it will be Monday.

After 61 days, it will be Saturday.

So, Option B.

 

2. How many weekends are there in a year?

• 52

• 53

• 103

• 104

Answer

Weekend means Saturday & Sunday together. In total, we have 52 weeks in a year. So there are 52 weekends in a year.

Normally, we have 104 weekend days.

We know that each normal year has 365 days or 52 weeks plus one day, and each week has two weekend days, which means there are approximately 104 weekend days each year.

Whereas, in a leap year, we have 366 days; it adds one more day to the year. And what makes the change is the starting day of the year.

So, Option B.

3. How many days are there in x weeks x days?

1. 7x * x 
2. 8x
3. 14x
4. 7

Answer

No. of days in x weeks x days = (7x + x) days = 8x days.

So, Option B.

 

4. If 6th March, 2005 is Monday, what was the day on 6th March, 2004?

• Sunday

• Saturday

• Tuesday

• Wednesday

Answer

The year 2004 is a leap year. So, it has 2 odd days.

But, February 2004 is not included as we are calculating from March, 2004 to March, 2005 and so we have one odd day only.

So, the day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.

So, 6th March, 2004 is one day before Monday, ie., Sunday.

So, Option A.

 

5. Which of the following is not a leap year?

• 700

• 800

• 1200

• 2000

Answer

Centuries divisible by 400 are leap years.

So, 700 is not a leap year.

So, Option A.

 

1. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

• 1/2 

• 2/5 

• 8/15

• 9/20

Answer

Here, S = {1,2,3,4,……,20}.

Let E = Event of getting a multiple of 3 or 5 = {3,6,9,12,15,18,5,10,20}.

So, P(E) = n(E)/n(S) = 9/20.

So, Option D.

 

2. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

• 1/3

• 3/4

• 7/19

• 8/21

Answer

Total no. of balls = 8 + 7 + 6 = 21.

Let E = Event that the ball drawn is neither red nor green.

= Event that the ball drawn is blue.

So, n(E) = 7.

So, P(E) = n(E)/n(S) = 7/21 = 1/3.

So, Option A.

 

3. What is the probability of getting a sum 9 from two throws of a dice?

• 1/6 

• 1/8 

• 1/9

• 1/12

Answer

In two throws of a dice, n(S) = 6*6 = 36.

Let E = Event of getting a sum of 9 = { (3,6) , (4,5) , (5,4) , (6,3) }.

So, P(E) = n(E)/n(S) = 4/36 = 1/9.

So, Option C.

 

4. Three unbiased coins are tossed. What is the probability of getting at most 2 heads?

• 3/4

• 1/4

• 3/8

• 7/8

Answer

Here, S = {TTT, TTH, THT, HTT, HHT, HTH, THH, HHH}

Let E = Event of getting at most 2 heads.

Then E = {TTT, TTH, THT, HTT, HHT, HTH, THH}

So, P(E) = n(E)/n(S) = 7/8.

So, Option D.

 

5. In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected is:

• 21/46

• 25/117

• 1/50

• 3/25

Answer

Let S be the sample space and E be the event of selecting 1 girl and 2 boys.

Then, n(S) = no. of ways of selecting 3 students from 25 students = 25C3 = 2300.

And, n(E) = 10C1 * 15C2 = 10 * 105 = 1050.

So, P(E) = n(E)/n(S) = 1050/2300 = 21/46.

So, Option A.

1.A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

•  720

• 900

• 1200

• 1800

Answer

2 (15 + 12) * h = 2 (15 * 12).

h = 180/27 = 20/3 m.

Volume = (15 * 12 * 20/3) m cubic = 1200m^3.

So, Option C.

 

2. The dimensions of a hall are 40 m, 25 m and 20 m. If each person requires 200 cubic meters, find the number of persons who can be accommodated in the hall.

• 150

• 140

• 120

• 100

Answer

Length of the hall = 40 m.

Breadth of the hall = 25 m.

Height of the hall = 20 m.

Volume of the hall = l * b * h.

= 40 * 25 * 20 = 20,000 m^3.

Space occupied by each person = 200 m^3.

Number of persons that can be accommodated in the hall =

Volume of the hall/Space occupied by one person = 20000/200 = 100 persons.

So, Option D.

 

3. A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

• 12 pi cm^3

• 15 pi cm^3

• 16 pi cm^3

• 20 pi cm^3

Answer

We have r = 3 cm and h = 4 cm.

So, Volume = ⅓*pi*r^2*h = ⅓*pi*3^2*4 = 12 pi cm^3.

So, Option A.

 

4. In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

• 75 cu. m

• 750 cu. m

• 7500 cu. m

• 75000 cu. m 

Answer

1 hectare = 10000 m^2.

So, Area = 10000*1.5 = 15000 m^2.

Depth = 5/100 m = 1/20 m.

So, Volume = Area * Depth = 15000 * 1/20 = 750 m^3.

So, Option B.

 

5. 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m^3, then the rise in the water level in the tank will be:

• 20 cm

• 25 cm

• 35 cm

• 50 cm

Answer

Total volume of water displaced = 4*50 m^3 = 200 m^3.

So, Rise in water level = 200/(40 * 20) = 0.25 m = 25 cm.

So, Option B.

1.Two successive discounts of 10% and 5% are equivalent to a single discount of

• 18.5%
• 26.5%
• 14.5%
• None of these

 

Answer

Discount D₁ = 10%

Discount D₂ = 5%

equivalent discount = D₁  + D₂  – D₁.D₂/100

= 10 + 5 – 10*5/10 = 15 – 0.5 = 14.5%

So, Option C

 

2. P makes a profit of 12% on a transaction. Had he bought the article at 10% less and sold it for 4% less, by what percent his profit percentage would have increased?

• 65%
• 62.25%
• 4%
• None of these

 

Answer

Let the cost price of the article = ₹ 100

Selling price = 100 + 100 * 12/100 = ₹112

When cost price = 100 – 100 * 10/100 = ₹90

and selling price = 112 – 112 * 4/100 = ₹107.52

Profit % = ((107.52-90)/90) * 100 = 19.47%

Increase in profit percent

((17.47-12)/12) * 100 = 62.25%

So, Option B

 

3. A sum of INR 15000 is put on compound interest. This sum becomes 2 times in 5 years at this rate. What would the original sum become after 20 years?

• 60000
• 225000
• 140000
• None of these

Answer

Principal (P) = ₹ 15,000.

Time (T) = 5 years.

Amount (A) = 2 × 15000 = 2P.

So, 2P = P(1 + r/100)^5 => (1 + r/100)^5 = 2

Now, (1 + r/100)^20 = 2⁴ = 16 times

Hence, amount becomes = 16 × 15000 = ₹2,40,000

So, Option D

 

4. A sum of INR 27800 is invested for 2 years in 2 different schemes, both on simple interest. The rates of interest are 14% and 11% in the 1st and the 2nd schemes respectively. The total interest after 2 years is INR 7016. What sum was invested in the 2nd scheme?

• ₹ 12800
• ₹ 16200
• ₹ 14600
• None of these

Answer

Let amount invested in first and second schemes are x and (27800 – x) respectively.

ATQ,

x * 2 * 14/100 + (27800 – x) * 2 * 11/100 = 7016

6x/100 = 7016 – 6116

x = 900 * 100/6 = 15000

Hence, amount invested into second scheme = 27800 – 15000 = 12,800

So, Option A

 

5. A and B can finish a work in 10 days and 15 days respectively. They together work on it for 5 days and then the rest of the work is finished by C in 2 days.They get INR 450 for finishing this work. What should be the shares of A, B and C respectively?

• A = ₹ 180, B = ₹120, C = ₹ 150
• A = ₹ 225, B = ₹ 120,C = ₹ 105
• A = ₹ 225, B = ₹ 150, C = ₹75
• None of these

 

Answer

Work done by A and B in 5 days

= 5(1/10 + 1/15) = 5((3+2)/30) = 5/6

Rest work = 1 – 5/6 = 1/6

Amount of work finished by C in 2 day = 1/6

\C will finish whole work in 6 × 2 = 12 days.

Now, L.C.M. of 10, 15 and 12 = 60.

Unit of work done by them in one days are 60/10, 60/15 and 60/12 i.e. 6, 4 and 5 units respectively.

As A and B works for 5 days and C works for 2 days. Ratio of work done by them= 6 × 5 : 4 × 5 ; 5 × 2 = 3:2:1.

Now, 3x + 2x + x = 450

x = 75

Amount received by A = 3x = 3 × 75 = ₹ 225

Amount received by B = 2x = 2 × 75 = ₹150

Amount received by C = x = 75 = ₹ 75.

So, Option C

1.There are 10 people in a family: the average age of the 2 grandparents is 64 years; the average age of 2 uncles is 42 years; the average age of the 2 aunts is 38 years and the average age of 4 cousins is 16 years. What is the average age of the family members?

• 8
• 40
• 352
• None of these

Answer

Sum of the age of two grandparents

= 2 × 64= 128 years.

Sum of the age of two uncles

= 2 × 42 = 84 years.

Sum of the age of two Aunts

= 2 × 38 = 76years

Sum of the age of four cousins

= 4 × 16 = 64 years.

Average age of the family

= (125 + 84 + 76 +64)/10 = 35.2

So, Option C

2.The median salaries of 3 B-Schools A, B and C are in the ratio 7:6:5 in the year 2019. The median salaries of these 3 B-schools are in the ratio 3:3:4 in the year 2020. If the median salary of A increased by 20% from 2019 to 2020, by what percent did the median salary of B increase?

• 40%
• 38%
• 183%
• None of these

Answer

Let median salaries of A, Band C in 2019 are 7x, 6x and 5x respectively.

A’s salary in 2020 is 7x * 120/100 = 8.4x

Ratio of A and B salary in 2020 = 3 : 3.

Therefore, 3/3 = 8.4x/B’s salary

B’s salary in 2020 = 8.4x

% increase in B’s salary

= ((8.4x – 6x)/6x) * 100 = 40%

So, Option A

3.The combined age of a mother and daughter duo is 42 years. The product of their ages, 5 years back, was 60 years. What is the present age of the mother?

• 40 years
• 38 years
• 32 years
• None of these

Answer

Let present age of Mother and daughter are M and D respectively.

ATQ,

M + D = 42                                                 …(i)

(M – 5)(D – 5) = 60

MD –5(M + D) + 25 = 60.

MD – 5 (42) + 25 = 60.

MD – 210 + 25 = 60

MD = 245

Now, M – D = sqrt((M + D)^2 – 4MD)

= sqrt((42)^2 – 4 * 245)

therefore, M–D=28

From (i) and (ii), M = 35

Hence, Mother’s age = 35 years.

So, Option D

 

4.A is 2 times B and B is 2 times C. The average of the reciprocals of A, B and C is 7/12. What is the value of A?

• 2
• 4
• 1
• None of these

Answer

ATQ, A = 2B and B = 2C.

Average = (1/A + 1/B + 1/C)/3 = 7/12

Therefore, 1/A + 1/B + 1/C = 7/4        1/4C + 1/2C + 1/C = 7/4

C = 1, B = 2 and A = 4.

So, Option B

5.What is the value of log 8/log 64?

• 25
• 1/3
• 5
• None of these

Answer

log8/log64 = log8/log(8)^2 = 1/2 * log8/log8 = 0.5

So, Option C

1.Which of the following is a factor of?

• X² – 1
• X² + 3
• X² – 3
• None of these

Answer

f(x) = x⁴ + 4x² + 3

= x⁴ + 3x² + x²  + 3

= (x² + 3)(x² + 1)

Hence, factors are (x² + 3) and (x² + 1)

So, Option B

2. If one of the sides of a square is increased by 20% and the other side of decreased by 20% to get a rectangle, what percent of the area of the square will be the area of this rectangle?

• 96%
• 4%
• 60%
• None of these

Answer

Let side of the square is l.

then, area A = 1 * 1 = 1²

When one side increases by 20% and other decreases by 20%

New area A’ = (1 + 20*1/100) * (1 – 20*1/100)

= 1.2*1 * 0.8*1 = 0.96 * 1²

Required percent =

A’/A * 100 = (0.96*1²/1²) * 100 = 96%

So, Option A

3. There is a cube of edge 8 cm. This cube is immersed in a water-filled vessel with the dimension of its rectangular base (12cm × 20 cm). By how many cms will the level of water raise in the vessel?

• 75 cm
• 13 cm
• 03 cm
• None of these

Answer

Volume of water displaced = Volume of the cube = 12 × 20 × height (h) = 8 × 8 × 8.

Height (h) = 8*8*8/12*20 = 2.13cm

So, Option D

4. What is the value of sin + tan ?

• (sqrt(2) – 1)/sqrt(2)
• (2 – sqrt(2))/2
• (sqrt(2) + 1)/sqrt(2)
• None of these

Answer

sin 45^o + tan 45^o

= 1/sqrt(2) + 1 = (sqrt(2) + 1)/sqrt(2)

So, Option C

5. What is the value of sin / cos?

• 5
• 1
• (sqrt(2) – 1)/sqrt(2)
• None these

Answer

sin 42^o/cos 48^o = sin 42^o/cos(90^o – 42^o) = sin 42^o/sin 42^o = 1

So, Option B

1.What will be the missing term in the series:

11,88,……,6336, 57024, 456192?

• 704
• 862
• 764
• None of these

Answer

So, Option D

2. A bag has a total of 108 toys. These toys are of 3 different colours: black, green and white. If a toy is taken out randomly, the probabilities of getting a black and a green are 1/3 and 4/9 respectively. What is the number of white toys?

• 36
• 24
• 51
• None of these

Answer

Let number of black and green toys in the box are m and n respectively.

then, probability of getting a black toy

= ^mC₁/¹⁰⁸C₁ = m/108 = 1/3 (given)     therefore, m = 108/3 = 36

Probability of getting a green toy

= ⁿC₁/¹⁰⁸C₁ = n/108 = 4/9                   therefore, n = 108*4/9 = 12*4 = 48

Hence, number of white toy = 108 – 36 – 48 = 24.

So, Option B

3. The Average weight of three men A, B and C is 84 kg. D joins them and the average weight of the four becomes 80 kg. If E whose weight is 3 kg more then that of D replaces A, the average weight of B, C, D and E becomes 79 kg. The weight of A is.

• 65 kg
• 70kg
• 75 kg
• 80 kg

Answer

Total weight of A, B and C = 84 × 3 = 252 kg.

D’s weight = 80 × 4 – 84 × 3 = 68 kg.

E’s weight = 68 + 3 = 71 kg.

Total weight of B, C, D and E = 79 × 4 = 316 kg.

Then, total weight of B and C = 316 – 68 – 71 = 177kg.

Hence. A’s weight = 252 – 177 = 75 kg.

So, Option C

4. The sum of the digits of a number is 10. The difference between this number and a number formed with the same digits, but in the reverse order, is 18. What is the square of formed by reversing its digits.

• 2116
• 4096
• 1764
• None of these

Answer

Let two digits are x and y.

ATQ, x + y = 10 and, (10x + y) – (10y + x) = 18.

(x – y) = 2

From (i) and (ii), we get

x = 6 and y = 4.

Hence, number = 64

Hence, square of (46) = (46)² = 2116.

So, Option A

5. We have 60, 76 and 84 loaves of bread of companies A, B and C respectively. We have to supply these bread to retail stores so that a store has the bread of just one of the companies and tail the stores have the same number of loaves. What can be the minimum number of stores?

• 4
• 44
• 55
• None of these

Answer

H.C.E of 60,76 and 84 = 4.

Minimum number of stores

= 60/4 + 76/4 + 84/4 = 15 + 19 +21 = 55

So, Option C

1. There are 96 girls and 120 boys in s sports event. The sports teacher wants to arrange in rows in such a way that each row contains equal number of students and each row should have either girls or boys in it, not both. What is the greatest number of students that can be arranged in each row?
   • 20
   • 22
   • 24
   • 26
2. If x  = sqrt(12 + sqrt(140))/sqrt(12 – sqrt(140))  what is the value of(x + 1/x)² – (x – 1/x)²
   • 6
   • 4
   • 2
   • 1
3. If  ⁵√5  * 625 *  ⁴√5 = 5^{n +1/5} what will be the value of n?
   • 6.55
   • 4.55
   • 5.55
   • 7.55
4. Due to the pandemic, the sale of cricket balls in a sport shop decreased by 15%. If its price is also reduced by 15% what will be the effect on the total revenue collection?
   • 30% decrease
   • 75% decrease
   • 50% increase
   • 50% decrease
5. A person is able to buy 2kg more ₹ 198, due to a reduction of in the price of rice. What is the difference between the original and the reduced rate of rice per kg?
   • ₹ 0.50
   • ₹ 1.00
   • ₹ 0.25
   • ₹ 0.75

1. When a owner sells his house for ₹ 26,400, he loses 20%. At what price should he have sold the house in order to get profit of 12%?
   • ₹ 35,000
   • ₹ 36,000
   • ₹ 33,000
   • ₹ 36,960
2. A dry fruit seller sells his fruits at 5% loss on the price because of an urgent need of money. But due to some technical error in his weighing machine, it measures 19g instead of 20g. What is his profit or loss percentage?
   • 5% profit
   • 7.143% profit
   • 5% loss
   • No profit no loss
3. A certain sum of money invested at simple interest amounts to ₹ 990 in 3 years and to ₹ 1,125 in 1.25 years. What is the rate of interest per annum?
   • 13.5%
   • 13%
   • 12.5%
   • 12%
4. Raju lent out a certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. If the ratio between the difference of compound interest and simple interest of 2 years and that of 3 years is 10:31, what is the rate of interest per annum?
   • 10%
   • 12.5%
   • 15%
   • 7.5%
5. Two numbers A and B are respectively 30% and 60% less than the third number. By what per cent A is greater than B?
   • 35%
   • 45%
   • 75%
   • 85%

1. The number of 10 paisa, 20 paisa, 25 paisa and 50 paisa coins contained in a bag are in the ratio 1/5:1/4:1/3:1/2,  amounts to ₹ 240. The total value of 25 paisa and 50 paisa coins is:
   • ₹ 200
   • ₹ 180
   • ₹ 160
   • ₹ 150
2. The capacities of three container X, Y and Z are 1, 2 and 4 litres respectively. Initially X is empty, while Y and Z are full of water and milk respectively. X is filled from Y. Y is replenished from Z and X is emptied into Z. If this process is repeated once more, then what will be the ratio of milk in Y to water in Z?
   • 1:1
   • 3:5
   • 4:5
   • 4:3
3. Pipes A and B can empty a full tank in 12 hours and 18 hours respectively and C is filling pipe which can fill the empty tank in k hours. When all the three pipes are opened together, then 1/9 th part of the tank was emptied in 1 hour. What is the value of k?
   • 30
   • 32
   • 36
   • 40
4. Two engines having different speeds are to run on parallel tracks with the starting point of the slower being ahead of the faster by 5km and 6 km in two separate cases. What is the ratio between the distances that the faster train has to travel in these cases to catch up with the slower?
   • 2:3
   • 5:6
   • 5:12
   • 3:4
5. Rekha covers a certain distance by car. Had she moved 5km/h faster, she would have taken 30 minutes lesser time to cover the distance. If she had moved 2km/h slower, she would have taken 40 minutes more time to cover the distance. Find the distance on kms.
   • 20
   • 15
   • 10
   • 5

1.Five years ago, Rahul’s age was 5 years less than three times of the sum of the ages of his three children. After five years, his age will become 5 years more than the sum of the ages of his children. Then, what is the present age of Rahul?

• 40 years
• 45 years
• 50 years
• 55 years

2. The sum of the height and the radius of a solid right circular cylinder is 41 cm. if its total surface area is 2706 cm², then its volume (in cm³) is closest (Take pi = 22/7 )

• 9568
• 9584
• 10568
• 10584

3. If mean of 29 observations is 33 and on adding one more observation the new mean becomes 34 what is the value of the 30^th observation?

• 34
• 55
• 63
• 68

4. What is the Median time for the period, 1^st February to 20^th September of a leap year?

• Midnight between 26^th and 27^th May
• 12 Noon of 27^th May
• Midnight between 27^th and 28^th May
• 12 Noon of 28^th May

5. Four teams P, Q, R and S played Round Robin League (each playing against each other) matches, and the Points Table is as under:

Teams	Number of matches played	Number won	Number lost	Number drawn	Points Scored
P	3	2	0	1	7
Q	3	2	1	0	6
R	3	0	1	2	2
S	3	0	2	1	1

If A is the overall average points scored by four teams per match and B is the points scored by Q id the number of matches it had won, lost and drawn be the same, then what is the difference (correct to two decimal places) between A and B?

• 33
• 33
• 67
• 67

 

1.Find the missing term of the series:61,74, 89, 97,…., 121, 145

• 117
• 118
• 116
• None of these

Answer

So, Option A

2.Some As are Bs and some Bs arc Cs. Which of the following is necessarily true?

I. Some As are Cs                             II.  All Cs are As

• Only (I) follows
• Only(II) follows.
• Both (I) and (II) follows.
• Neither (I) nor (II) follow.

Answer

Hence, neither conclusion I nor II follow.

So, Option D

3. If H<G=J and J>K, then which of the following is necessarily true.

I. H>K             II.  G>K

• only (I) is true.
• only (II) is true.
• both (I) and (11) are true.
• Neither (I) nor (II) are true.

Answer

H < G = J > K

(I) H > K (Not sure) (II) G > K (True).

So, Option B

4.There are 40 people standing in a row. A is 12th from the left and B is 9th from the right. How many people are there in between A and B?

• 18
• 19
• 20
• None of these

Answer

Total number of people = 40.

A’s position from left = 12th.

B’s position from right = 9th.

Number of people between A and B = 40 – l2 – 9 = 19

So, Option B

5.Create meaningful words from the following and then find the odd one out.

• HIFS
• TBOA
• UOBY
• GATO

Answer

HIES — FISH

TBOA —BOAT

UOBY — BUOY

GATO—GOAT

Here, Fish, Boat and Buoy are somehow related to water, whereas Goat is not related to water.

So, Option D

1.Find the missing term in the series: A15, B10, D3.

• C6
• C7
• E3
• None of these

Answer

So, Option A

2. You are facing North. You take a right turn and walk for 5 Kms. You again take a right turn and walk for 3 Kms. You now take a left turn and walk for 2 Kms. You now take a 90-dcgree turn to your left. Which direction are you facing now?

• East
• West
• North
• South

Answer

Finally, you are facing towards North direction

So, Option C

3. Find the missing number that should come at the place of question mark (?).

17	13	19
272	156	342
306	?	380

• 182
• 184
• 187
• 191

Answer

17	13	19
272	156	342
272 + 2 × 17 = 306	156 + 2 × 13 = 182	342 + 2 × 19 = 380

So, Option A

4. The diagram below shows the number of people who attended seminars on Physics, Chemistry, Math and Biology. What is the number of people who attended exactly any two seminars?

• 21
• 36
• 38
• 42

Answer

Number of people, who attend exactly two seminars:

Physics and Math = 14.

Physics and Biology = 7.

Math and Biology = 5.

Chemistry and Math = 10.

Total number of people, who attend exactly any two seminars = 14 + 7 + 5 + 10 = 36.

So, Option B

5. If P means division, T means addition, M means subtraction and D means multiplication, then the value of: 8 D 1 6 P 3 2 T 1 6 D 3 2 P 6 4 is:

• 12
• 23
• 6
• 3

Answer

P -> ÷       T -> +        M -> –        P -> ×

8 D 16 P 32 T 16 D 32 P 64

=> 8 × 16 ÷ 32 + 16 × 32 ÷ 64

=> 4 + 8 = 12

So, Option A

1.Directions: In this question, a statement is followed by two courses of action numbered 1 and 11. Consider everything in the statement to be true and decide which of the suggested courses of action logically follow(s) for pursuing.

Statement: The government of state ‘Y’ has decided to remove hutments and buildings that have come up beside the roads to broaden them in city ‘A’.

Courses of action:

I. The government of state ‘Y’ should rehabilitate the affected residents of hutments/buildings.

II. The government should compensate the residents of targeted houses with a reasonable amount.

• Only I follows
• Only II follows
• Either I or II follow
• Neither I or II follow

Answer

Both courses of actions I and II follows. Either government should rehabilitate the affected residents of hutments/Buildings. Or, they should compensate the residents of targeted houses.

So, Option C

2. Some have suggested a correlation between not wearing polished shoes and being lethargic– that those who don’t polish their shoes are generally lethargic than those who do. This, however, is not the case. I work at the employment exchange and the majority of the applicants have polished shoes. Which of the following assumptions is made by the author of the argument?

• Lethargy and polished shoes are learned behaviours.
• People with polished shoes are never unemployed.
• Lethargy has its origins in an individual’s family background.
• People who apply for employment at the employment exchange are lethargic.

Answer

Assumption made by the Author of the argument is “Lethargy has its origins in an individual’s family background”.

So, Option C

3.

• 18
• 11
• 8
• 7

Answer

sqrt(20-4) = sqrt(16) = 4

sqrt(45 – 20) = sqrt(25) = 5

sqrt(120 – 20) = sqrt(100) = 10

sqrt(90 – 26) = sqrt(64) = 8

So, Option C

4. If DIP is coded as 172203, then what is the code for “TAKE”?

• 07152418
• 07142418
• 33142418
• 07142518

Answer

D	1	P
|	|	|
4	9	16
Letter’s position

=> Code = (4 + 13), (9 + 13), (16 + 13) = 172229

Similarly,

= 1722(29 – 26) = 172203

T	A	K	E
|	|	|	|
20	1	11	5
Letter’s position

 

=>  Code = (20 + 13), (1 + 13)(11 + 13),(5 + 13)

= 33 14 24 18 = (33 – 26) 14 24 18

= 07 14 24 18.

So, Option B

5. In the following figure, the Pentagon, the Rectangle, the Triangle and the Circle represent the number of students in a class who play cricket. Soccer, Hockey and Baseball respectively.

Which of the following is the highest?

• Number of students who play at least one of Hockey or Baseball.
• Number of students who play exactly two of the sports.
• Number of students who play exactly one of the four sports,
• Number of students who play at least one of Cricket or Soccer.

Answer

(a) Number of students who play at least one of Hockey or Baseball = 7 + 8 + 6 + 3+11 + 8 + 4 + 5 + 9 = 66

(b) Number of students who play exactly two of the sports =8+7+5+5= 25.

(c) Number of students who play exactly ones of the four sports =10 + 9 + 9+7 = 35.

(d) Number of students who play atleast ones of cricket or soccer = 10 + 8 + 6 + 7 + 9 + 3 + 11 + 8 + 4 + 5 = 71

So, Option D

1.Two adjacent faces of a cube are painted red and out of the remaining sides, two opposite faces are painted green. The cube is then cut into 125 equal smaller cubes. How many smaller cubes will have at most two sides painted?

• 121
• 123
• 117
• 113

Answer

Total number of smaller cubes = 125.

Number of smaller cubes have 3 painted faces = 2.

Hence, number of smaller cubes have at most two painted faces = 125 – 2 = 123.

So, Option B

2. Prashant forgot his five-digit ATM pin. However he remembers that the ATM PIN has a cube of a number in the 3rd place and prime numbers in the first and the last places. The even prime number is in the 1^st He also remembers that the digit in the 3^rd place is equal to the product of the digits in the first and the second places and the sum of the digits in the first and the second places is equal to the digit in the fourth place. The digit in the last place is half the digit in the 4^th place.

What is his ATM PIN?

• 24863
• 24683
• 26483
• 23468

Answer

Hence, required number is ‘24863’.

So, Option A

3. Refer to the sequence of letters given below and answer the questions that follow.

N F C I O R O O I U M N T S M C T U A A N R T 1 E I C T O A N N T I

If all the vowels from the given sequence arc removed, then which letter will be the 8th letter to the right of the 5^th letter to the left of the 10th letter from the right?

• R
• T
• C
• S

Answer

Sequence of letters after removing all vowel.

N F C R M N T S M C T N R T C T N N T

Letter which is 8^th to the right of the 5^th to the left of the 10^th from the right end = 10 + 5 – 8 = 7^th from the right and that is letter ‘R’.

So, Option A

4. A traveller travels 10 km towards the East from Pune. He then turns 90 degrees towards his right and travels 5 km and again takes a 90 degrees turn towards his right and walks 5 km. What direction is he now with respect to Pune?

• South-West
• South-East
• North-West
• North-East

Answer

Hence, person is in south-east from Pune city.

So, Option B

Read the given information and answer the following questions:

Eight people A, B, C, D, E, F, G and H are sitting on 8 chairs kept symmetrically around a circular table and equidistant from each other. All of them are facing towards the centre of the table. Some information about the order in which they are sitting is provided as follows:

• F is sitting exactly opposite to C.
• D is not next to F.
• H is the only one sitting between G and C.
• E is sitting two places to the right of B and is not next to F.

5. Which of the following is the correct position of H?

• Left of C
• Exactly Opposite of B
• Exactly Opposite of E
• Cannot Be Determined

Answer

B is exactly opposite to H

So, Option B

6. Which of the following statements is not correct?

• B is to the immediate right of F.
• G is sitting two places to the light of F.
• There are only six persons whose sitting positions can be exactly determined.
• All of these.

Answer

Sitting position of all eight people can be exactly determined

So, Option C

1.There are six persons A, B, C, D, E and F. C is the sister of F. B is the brother of E’s husband. D is the father of A and the grandfather of F. There are two lathers, three brothers and a mother in the group. How many male members are there in the group?

• One
• Two
• Three
•  Four

Answer

male members in the group are D, A, B and F. Hence, there are 4 males in the family.

So, Option D

2. Directions: In the following question, a part of the figure is missing. Find out from the given options (a, b, c and d), the right figure to fit in the missing figure.

• 
• 
• 
• 

Answer

Option C

 

3. A piece of paper is folded and punched as shown below in the question figures. From the given answer figures, indicate how it will appear when opened.

• 
• 
• 
• 
• 

Answer

Option C

 

4.  I. Yes: Studies have shown that breathing in vehicular pollution reaches dangerous levels when the exposure to such pollution has been more than five hours in a day.

II. No. Breathing in vehicular pollution for more than five hours a day does not lead to lung cancer as was revealed in a study to analyze the effect of vehicular pollution.

• Only I is strong.
• Only II is strong.
• Both I and II are strong
• Neither I nor II are strong.

Answer

Here, statement I is wrong.

So, Option A

1.Choose the odd term in the following series

DIM; GLP; JOT; MRV; PUY; SXB

• MRV
• DIM
• GLP
• JOT

2. Choose the pair similar to the following

ITWN : LQZK

• JZFY : MWIV
• MBTZ : OLQS
• IJSX : LWBJ
• FGMO : PLKE

3. Select the figure that will replace the question mark (?), from the following figure series.

• 
• 
• 
• 

4. Given below is a question followed by two statements, I and II, each containing some information. Decide which of the statement(s) is/are sufficient to answer the question

Among six members of the family, O, P, Q, R, S and T, how many are females?

Statements

1. Q is wife of P and mother of T, R is grandmother of O and mother of P
2. T is granddaughter of S.

• Statement I alone is sufficient
• Statement II alone is sufficient
• Both I and II together are sufficient
• Both I and II together are not sufficient

1.Given below is a question followed by two statements, I and II, each containing some information.

Decide which of the statement(s) is/are sufficient to answer the question.

How far is Janny from her starting point? If

1. Janny moves 4 km towards South, then 3 km towards right, 5 km towards left, 3 km towards left and 3 km towards right and stop.
2. Janny moves 7 km towards South, then 4 km towards left, 2 km towards right, 4 km towards right and finally 3 km towards left and stop.

• The data in statement I alone is sufficient to answers the question.
• The data in statement II alone is sufficient to answer the question.
• The data of both statement I alone and statement II alone are sufficient to answer the question.
• The data in both statements I and II together are necessary to answer the question.

2. Determine whether the following data is sufficient for the statements maintained on its basis.

A home delivery retail provision store sells goods around ₹ 1,500 per day, Of the total number of food item sold in a month, they sell around 1000 loaves of bread, 80 kg of sugar, 100 packets of tea leaves, 100 kg of flour, 50 packets of coffee and 200 kg of detergents, 25 litres of cooking oil. The sale of toiletries is far more than that of cereals.

1. The ratio of the sale of toiletries as compared to food items is 1:2
2. The income from tea, coffee and sugar is more than the sale earnings from flour.

• Sufficient for both A and B
• Sufficient for B but not for A
• Sufficient for A but not for B
• Sufficient neither for A nor B

3. I a coded form, A # B means A is the paternal grandfather of B, A $ B means A is the son of B and A @ B means A is the brother of B. Which of the following equations shows that P is the father of S?

• P @ Q $ R # S
• P # Q @ R $ S
• P # Q $ R @ S
• P $ Q # R @ S

4. The age of the mother is twice of her son. If the sum of their ages is 60, what is the age of the mother?

• 30 years
• 40 years
• 48 years
• 36 years

5. There are five persons in a group Raju, Sanjay, Deepak, Suresh and Mukesh. Deepak is elder to Raju, but not tall as Suresh, Suresh is younger to Sanjay and taller that Mukesh and Raju. Sanjay is taller than Mukesh but not younger than Raju. Mukesh is elder to Sanjay but is the shortest of all the friends. Who among the following is the eldest?

• Sanjay
• Deepak
• Suresh
• Either Deepak or Mukesh

1.Study the given information carefully.

For a job selection in a company the following conditions need to be fulfilled.

The candidate must:

• be at least 23 years and at most 28 years as on 01 December 2020.
• have at least 65% marks in written exam and 40% marks in interview.
• possess a graduation degree with minimum 60% marks.
• have one-year work experience.

• In case a candidate who fulfils all conditions except (iv) but possess 80% marks in graduation then case is to be referred to manager.

In the following question, details of candidates are given. Select the appropriate option accordingly.

Anshika was born on 07 March 1997. She completed her graduation with 75% marks. She has a work experience of 2 years. She scored 70% marks in written exam and 55% marks in interview.

• If candidate is to be selected
• If candidate is to be rejected
• If case is to be referred to manager
• If data is insufficient to conclude.

2. The following are the criteria of selecting a Lawyer for a legal firm.

The candidates must:

• have completed LLB with at least 75% marks.
• be more than 28 years and less than 35 years of age as on October 1, 2020
• have secured more than 85% marks in the interview and at least 70% marks in the written test.

However, if the candidate fulfils all the above criteria EXCEPT

criterion (d) at (b), but has 3 years experience of practicing in district court, his/her case is to be referred to the Chief Manager

criterion (e) at (c), but has secured more than 80% marks in L.L.M., his/her case is to be referred to the Chief Legal Advisor. 

Sakshi Kuman has obtained 81% marks in L.L.M. and 75% marks in L.L.B. She was 26 years of age when she completed her L.L.B. in 2013. She has obtained 66% marks in the written test and 75% marks in interview. He also has 3 years experience of practicing in district court.

• She would be selected
• She would not be selected
• Her case is to be referred to the Chief Manager
• Her case is to be referred to the Chief Legal Advisor

3. A statement is followed two assumptions numbered I and II. Consider the statement and decide which of the given assumption(s) is/are implicit in the statement.

Statement:

The educational framework now requires to go through a process of change so as to cater to individuals according to their interests and talents.

Assumptions:

I. The current education system is geared to mainstream individuals without due regard to their unique potentialities.

II. Learners find less scope for nurturing their individual interests and talents in the present system.

• Only I is implicit
• Only II is implicit
• Both I and II are implicit
• Neither I nor II is implicit

4. Two Statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.

Statements: 

No cylinder is a drum.

All balls are cylinders.

I. No drum is a cylinder.

II. Some cylinders are balls.

III. No ball is drum.

• Only conclusion I and II follows.
• Only conclusion II and III follow.
• Only conclusion I and III follow.
• All of the conclusions follow

5.  In the following diagram, the circle stands for ‘farmers’, the hexagon stands for ‘tax-payers’, the square stands for ‘females’, the triangle stands for ‘folk-artists’. The numbers in different segments show the number of persons for that segment.

How many farmers are tax-payers also but are neither folk-artists nor females?

• 15
• 20
• 10
• 6

1. In the following figure, the triangle represents researchers, the square represents historians, the rectangle represents lectures and the circle represents singers. Find the researcher who is neither historian nor lecturer but singer and the lecturer who is researcher and singer but not historian.

• R,T
• K, P
• W, M
• N, R

2. How many dots are there opposite to the side having ‘four’ dots?

• Two
• One
• Five
• Six

3. The figure marked ‘X’ lying flat with patterns on it is folded to form a box such that the patterns/blanks show on the faces of the box. Four possible boxes A, B, C and D are given below some of which can be formed and some cannot be formed. Choose from the alternatives the boxes that can be formed.

• A and C only
• C and D only
• B and D only
• A and D only

4. The sequence of folding a piece of square paper and the manner in which the folded paper has been cut is shown in the figures marked X, Y and Z. How would the paper look when unfolded?

• 
• 
• 
•