CMAT 2018 Slot 2 Question Paper

Probability = Expected number of outcomes/ Total number of outcomes.

Total number of outcomes we get in a single throw of two dice = $$6\times 6$$ = 36.

Possible cases of getting 'nine' in a single throw of two dice:

                  dice 1           dice 2

                  three             six..................(1)

                  six                three................(2)

                  four              five..................(3)

                  five              four...................(4)

So, total of 4 cases.

Possible cases of getting 'ten' in a single throw of two dice:

                dice 1            dice 2

                four                six.....................(1)

                 six                 four....................(2)

                five                 five....................(3)

So, total of 3 cases.

Expected number of outcomes = Total possible cases of getting 'nine' or 'ten'  in a single throw of two dice = 4 + 3 = 7 .

So, Probability = $$\frac {7} {36}$$

Let the breadth(b) of the room be 'x' metres.

then, length(l) of the room = x+2 metres.

Area(A) = $$l\times b$$ = x(x+2) $$m^2$$

Given, length is increased by 4 meters and the breadth decreased by 2 meters

Then, new length(l') of the room = x+6 metres

new breadth(b') of the room = x-2 metres

New Area(A') of the room = $$l'\times b'$$ = (x+6)(x-2) $$m^2$$

Also given that, A = A'

$$\Rightarrow x(x+2) = (x+6)(x-2)$$

$$\Rightarrow x^2+2x = x^2+4x-12$$

$$\Rightarrow 2x = 12$$

$$\Rightarrow x = 6$$

Therefore the length of the room (l) = 8 metres

and breadth of the room (b) = 6 metres

and given height of the room (h) = 3 metres

Since the room will be in the shape of a cuboid, Surface area = 2 ($$l\times b+b\times h+l\times h$$)

But the Surface area of Walls = Total Surface area - Area of Roof and Floor = 2 ($$l\times b+b\times h+l\times h) - 2 (l\times b) = 2 (8\times 3+6\times 3) = 84 m^2$$

Hence, Surface Area of walls = 84 $$m^2$$.

Average  Speed = Total  distance  covered $$\div$$ Total  time  taken

Total distance travelled = 50 + 50 + 30 = 130 km.

Total time taken = Time taken to travel first 50 km + Time taken to travel next 50 km + Time taken to travel next 30 km = $$40 + 50\div 2 + 30\div 1 = 95$$ minutes = $$\frac{95}{60}$$ hours.

$$\Rightarrow$$ Average Speed = $$130\div \frac{95}{60} = 82.1$$ kmph

First wheel makes 60 revolutions in 1 minute

$$\Rightarrow$$ It makes 60 revolutions in 60 seconds

$$\Rightarrow$$ It makes 1 revolution in 1 second.

This implies, after every 1 second the certain point at which the wheel started its revolution reaches its initial position.

Similarly, Second wheel and Third wheel makes 36 and 24 revolutions in 1 minute respectively.

$$\Rightarrow$$ Second and Third wheel makes 1 revolution in $$\frac{5}{3} and \frac{5}{2}$$ seconds respectively.

So for all the multiples of $$\frac{5}{3} and \frac{5}{2}$$ seconds the certain point of second wheel and third wheel reaches its initial position respectively.

After LCM {1, $$\frac{5}{3}, \frac{5}{2}$$} seconds all the three wheels will come together in the same position.

LCM of fractions = LCM of numerators/ HCF of denominators 

$$\Rightarrow$$ LCM {1,$$\frac{5}{3}, \frac{5}{2}$$} = LCM {1,5,5}$$\div$$HCF {1,3,2} = 5$$\div$$1 = 5.

Hence, after 5 seconds all the wheels will come again together in the same position.

If the  principle amount 'P' when compounded annually for 'n' years at 'R%" interest rate per annum becomes P'.

Then $$P' = P {[1 +\frac{R}{100}]}^{n}$$

Given P' = 2000, n = 2 years, R = 10% 

$$\Rightarrow P = P'\div {[1 +\frac{R}{100}]}^{n}$$

$$\Rightarrow P = 2000\div {[1 +\frac{10}{100}]}^{2}$$ 

$$\Rightarrow P = 2000\div 1.21$$

$$\Rightarrow P = 1653$$

Hence the initial amount P = Rs. 1,653.

The Volume of the right circular cone of base radius 'r' and height 'h' is given by 'V' = $$\frac{1}{3} \pi r^2h$$

Given 'h' has been increased by 200%

$$\Rightarrow$$ New height h' = h[1 +$$\frac{200}{100}$$] = 3h

also,radius of the base is reduced by 50%

$$\Rightarrow$$ New base radius r' = r[1 - $$\frac{50}{100}$$] = $$\frac{r}{2}$$  

New Volume of the cone with new base radius r' and new height h' is given by V' = $$\frac{1}{3} \pi r'^2h'$$ = $$\frac{1}{3} \pi (\frac{r}{2})^2(3h) = \frac{3V}{4}$$.

Change in Volume = $$\frac{New Volume - Old Volume}{Old Volume}\times 100  = \frac{\frac{3V}{4} - V}{V}\times 100 = -25$$

Hence the new volume decreased by 25 %.

Initial price is given as 'I' = Rs. 600

After the first reduction, the initial price is reduced by 10%

$$\Rightarrow$$ the new price I' = $$600[1 - \frac{10}{100}] = 540$$

After second reduction, I' is reduced by 10%

$$\Rightarrow$$ the new price I'' = $$540[1 - \frac{10}{100}] = 486$$

After third reduction, I'' is reduced by 10%

$$\Rightarrow$$ the new price I''' = $$486[1 - \frac{10}{100}] = 437.4$$

Hence the Current price after three successive reductions is Rs. 437.4

Let say,

The number mobiles sold in last year of the brands LG, SAMSUNG, NOKIA, SONY, MICRO-MAX be A, B, C, D, and E respectively.

Given that A+B+C+D+E = 1 crore.

But from the given data, the values of A, B, C, D, and E cannot be found out.

So the number of LG sets sold last year cannot be determined.

$$\sqrt{188+ \sqrt{51+ \sqrt{169}}}$$ = $$\sqrt{188+ \sqrt{51+13}}$$ = $$\sqrt{188+ \sqrt{64}}$$ = $$\sqrt{188+ 8}$$ = $$\sqrt{196}$$ = 14

If the principle amount 'P' when compounded half-yearly at R% interest rate per annum for 'n' years, the new amount is P'.

then $$P' = P{[1 + \frac{R}{2\times 100}]}^{n}$$

Given P' = 6,632.55, P = 6,250 and R = 4%

$$\Rightarrow 6,632.55 = 6,250{[1 + \frac{4}{2\times 100}]}^{n}$$

$$\Rightarrow 1.061 = {1.02}^{n}$$

Taking logarithm on both sides we get,

n = log(1.061)$$\div$$log(1.02) = 3

Since n refers to half a year in this case, the number of years will be $$\frac{3}{2}$$ years.

Average Salary Expenditure (in Lakh Rupees) per annum = Total salary expenditure in all these years$$\div$$Total number of years

= $$\frac{576+682+648+672+740}{5}$$

= 663.6

Option A:

In 2011, number of Refrigerators sold =60

        number of Cell phones sold = 336

$$\Rightarrow$$  number of refrigerators sold as a percentage of number of cell phones sold = $$\frac{60}{336}\times 100 = 17.85$$   

Option B:

In 2012, number of Refrigerators sold = 79

             number of Cell phones sold = 404

$$\Rightarrow$$  number of refrigerators sold as a percentage of number of cell phones sold = $$\frac{79}{404}\times 100$$ = 19.5

Option C:

In 2013,number of Refrigerators sold = 93

             number of Cell phones sold = 411

$$\Rightarrow$$  number of refrigerators sold as a percentage of number of cell phones sold = $$\frac{93}{411}\times 100$$ = 22.6

Option D:

In 2014, number of Refrigerators sold = 112

              number of Cell phones sold = 442

$$\Rightarrow$$  number of refrigerators sold as a percentage of number of cell phones sold = $$\frac{112}{442}\times 100$$ = 25.33

Hence Option D is the correct answer.

SInce PQ is the diameter, the angle subtended by it at R is 90 deg. i.e., $$\angle$$ PRQ = 90 deg.

Let $$\angle$$ RPQ = $$\theta$$, then $$\angle$$RQP = 90 - $$\theta$$

As the angles subtended by a chord in same segment are equal, $$\angle$$RPQ = $$\angle$$RSQ = $$\theta$$

In triangle RSQ, $$\angle$$QRS + $$\angle$$RSQ + $$\angle$$RQS = 180 

$$\Rightarrow$$ $$\angle$$QRS + $$\theta$$ + 35 + 90 - $$\theta$$ = 180

$$\Rightarrow$$ $$\angle$$QRS = 180 - 125 = 55 deg.

Hence $$\angle$$QRS = 55 deg.

Given  x = $$\sqrt[6]{5}$$ and y = $$\sqrt[5]{4}$$

which can also be written as x = $$5^{\frac{5}{30}}$$ and y = $$4^{\frac{6}{30}}$$    

which can be further written as x = $$\sqrt[30]{5^5}$$ and y = $$\sqrt[30]{4^6}$$

As we know $$4^6 > 5^5$$

$$\Rightarrow \sqrt[30]{4^6}  > \sqrt[30]{5^5} $$

$$\Rightarrow$$ y > x                     

Given, If a and b are positive real numbers then a * b denotes √ab

Consider 4 * 16 = $$\sqrt{4\times 16} = \sqrt64 = 8$$

then 8 * 8 = $$\sqrt{8\times 8} = \sqrt64 = 8$$

Hence the value of  8 * (4 * 16) = 8

Given the proportion of ages of three men are 3:5:7.

Let their ages be 3k, 5k, 7k ,where k is any constant.

Given average of ages of three men = 50 

$$\Rightarrow \frac{3k+5k+7k}{3} = 50$$

$$\Rightarrow \frac{15k}{3} = 50$$

$$\Rightarrow 5k = 50$$

$$\Rightarrow k = 10$$

Therefore the ages of three men are 30, 50, and 70 years.

The age of the youngest men is 30 years.

If 64 mangoes are sold at Rs.2000, each mango will be sold at Rs. $$\frac{2000}{64}$$

Hence Selling price (S.P) of each mango = Rs. 31.25

Given loss percentage of vendor at this S.P = 40%

Loss percentage = $$\frac{C.P - S.P}{C.P}\times 100$$ 

$$\Rightarrow \frac{40}{100} = \frac{C.P - S.P}{C.P}$$

$$\Rightarrow S.P = 0.6\times C.P$$

$$\Rightarrow C.P = \frac{31.25}{0.6} = 52$$

Therefore Cost Price of 1 mango (C.P) = Rs. 52

Let us calculate the S.P of each mango in order to get a 20% gain.

Gain percentage = $$\frac{S.P - C.P}{C.P}\times 100$$

$$\Rightarrow \frac{20}{100} = \frac{S.P - C.P}{C.P}$$

$$\Rightarrow S.P = 1.2\times C.P$$

$$\Rightarrow S.P = 62.5$$

So, to get a gain of 20% we need to sell each mango at Rs. 62.5 

Let say we sold 'x' number of mangoes.

Selling price of these 'x' number of mangoes (S.P) = Rs. 62.5x

But given that this S.P = Rs. 1000

$$\Rightarrow 62.5x = 1000$$

$$\Rightarrow x = \frac{1000}{62.5} = 16$$.

Therefore a total of 16 mangoes are to be sold for Rs. 1000 to get a gain of 20%.

Area of triangular metal plate with base(b) = 88 cm and altitude(h) = 64 cm is given as A = $$\frac{1}{2} b\times h = \frac{1}{2} 88\times 64 = 2816 cm^2$$

Given this area is to be reduced to one-fourth by making a hole in the shape of circle

$$\Rightarrow$$ Reduction in the area of the triangle = Area of the circular hole

$$\Rightarrow\frac{3}{4}\times A=\pi r^2$$

$$\Rightarrow \frac{\frac{3}{4}\times 2816}{\pi} = r^2$$

$$\Rightarrow r = \sqrt672 = 4\sqrt42 $$

So, the radius of the circular hole = $$4\sqrt42$$ cm.

Let us consider $$\frac{2 + \sqrt3}{2 - \sqrt3}$$ 

Rationalising the denominator by multiplying and diving with 2+$$\sqrt3$$ we get,

$$\frac{(2 + \sqrt3)\times (2 + \sqrt3) }{(2 - \sqrt3)\times (2 + \sqrt3) } = \frac {(2 + \sqrt3)^2}{4 - 3} = (2 + \sqrt3)^2$$

Now,

 $$\sqrt{\frac{2 + \sqrt3}{2 - \sqrt3}} = \sqrt{(2 + \sqrt3)^2} = 2 + \sqrt3 = 2 + 1.732 = 3.732$$

Initial amount of Kerosene(I) = 5% of 5 kg mixture of petrol and kerosene = $$\frac{5}{100}\times 5000 = 250$$ grams 

Let say 'x' gm of Kerosene is added to the mixture.

The final amount of Kerosene in the mixture after the addition is given as 10%.

$$\Rightarrow \frac{250 + x}{5000 + x} = \frac{10}{100}$$

$$\Rightarrow 2500 + 10x = 5000 + x$$

$$\Rightarrow 9x = 2500$$

$$\Rightarrow x = 275$$ gm approximately.

Therefore additionally 275 gm of kerosene is to be added to the mixture to make it 10%.

Let the maximum number of marks be 'x' and minimum passing marks be 'y'.

Given, A student who gets 20% marks fails by 20 marks.

$$\Rightarrow \frac{20}{100}\times x = y - 20$$

$$\Rightarrow 20x = 100y - 2000$$.................(1)

Also given that, another student who gets 36% marks gets 44 marks more than minimum passing marks.

$$\Rightarrow \frac{36}{100}\times x = y + 44$$

$$\Rightarrow 36x = 100y + 4400$$....................(2)

(2) - (1) $$\Rightarrow$$ 16x = 6400

$$\Rightarrow$$ x = 400

From (1) or (2), we get y = 100

Hence, maximum number of marks = x = 400

Percentage necessary for passing = $$\frac{y}{x}\times 100$$ = 25%

Let amount eaten by each horse and each bullock in one day be 'h' units and 'b' units respectively.

So Total fodder = Total effciency$$\times$$Total number of days 

$$\Rightarrow$$ Total work =  26$$\times$$h$$\times$$170 = 20$$\times$$b$$\times$$170

$$\Rightarrow$$ b = 1.3h............(1)

The amount of fodder eaten by 10 horses and 8 bullocks in one day = 10h + 8b = 10h + 8(1.3h) = 20.4h

Time taken by them to eat the same amount of fodder = total fodder/amount eaten by them in one day

= $$\frac{ 26\times h\times 170}{20.4h}$$

= 216.67 days

Let the speed of the boat in still water be V and speed of the stream be V'.

Relative speed of boat in upstream = V - V', as water stream flows against the direction of boat.

whereas Relative speed of boat in downstream = V + V', as water stream flows in the direction of boat.

Case (1)

Given Total time taken = Time taken during upstream + Time taken during downstream = 8 hours.

$$\Rightarrow \frac{24}{V - V'} + \frac{72}{V + V'} = 8$$

$$\Rightarrow 3 [\frac{1}{V - V'} + \frac{3}{V + V'}] =1$$.............(1)

$$\Rightarrow 3 [4V - 2V'] = V^2 - V'^2$$......................(2)

Case (2)

Given Total time taken = Time taken during upstream + Time taken during downstream = 14 hours

$$\Rightarrow \frac{48}{V - V'} + \frac{108}{V + V'} = 14$$

$$\Rightarrow 6 [\frac{4}{V - V'} + \frac{9}{V + V'}] = 7$$

$$\Rightarrow 6[13V - 5V'] = 7 [V^2 - V'^2]$$...................(3)

Dividing equation (3) by (2), we get

$$\frac{2 [13V - 5V']}{4V - 2V'} = 7$$

$$\Rightarrow 26V - 10V' = 28V - 14V'$$

$$\Rightarrow V = 2V'$$

Substituting this value in equation (1) we get,

$$\Rightarrow 3 [\frac{1}{V'} + \frac{1}{V'}] =1$$

$$\Rightarrow V' = 6$$

$$\Rightarrow V = 12$$

Hence, Speed of the boat in still water = 12 km/h.

and Speed of the stream = 6 km/h.

Let say cost price(C.P) of 1 kg(1000 g) of rice be Rs. 100

Given Shopkeeper is selling rice  at cost price,

$$\Rightarrow$$ Selling price(S.P) = C.P = Rs. 100

If he had used correct weight of 1000 g then C.P would have also been Rs. 100.

But given that he uses false weight. Let the weight he had used be  'x' g.

For 1000 g of rice  the C.P = Rs. 100

$$\Rightarrow$$ For '1' g of rice the C.P will be Rs. $$\frac{1}{10}$$

$$\Rightarrow$$ For 'x' g of rice the C.P will be Rs. $$\frac{x}{10}$$

Given that, by using this false weight the shop keeper gains 20%.

Gain percentage = $$\frac{S.P - C.P}{C.P}\times 100$$

$$\Rightarrow \frac{20}{100} = \frac{S.P - C.P}{C.P}$$

$$\Rightarrow S.P = 1.2\times C.P$$

$$\Rightarrow 100 = 1.2\times \frac{x}{10}$$

$$\Rightarrow x = 833.33$$ 

Hence the false weight used is 833.33 g 

Let the efficiencies of Rakesh, Prakash, and Ashok be 'r' 'p' and 'a' respectively.

GIven that Rakesh can do a job an hour quicker than Prakash.

So let time taken by Prakash be 't' hours, then time taken by Rakesh will be 't-1' hours.

Total work(W) = Efficiency$$\times$$ Time taken = p$$\times$$ t = r$$\times$$ (t-1)

$$\Rightarrow$$ t = $$\frac{r}{r-p}$$....................(1)

Given that, Working together, Rakesh, Prakash and Ashok can finish the same job in an hour.

$$\Rightarrow$$ Total work(W) = (r+p+a) (1) units.............(2)

Also given that,  if Prakash works for an hour, and then Ashok works for four hours, the job will be completed.

$$\Rightarrow$$ Total work(W) = p(1) + a(4) units...........(3)

Equating (2) and (3), we get

(r+p+a) (1) = p(1) + a(4)

$$\Rightarrow$$ r = 3a..............(4)

Substituting this value in equation (1), we get

t = $$\frac{3a}{3a-p}$$.............(5)

As the Total work is always constant, p$$\times$$ t = p(1) + a(4)

$$\Rightarrow$$ t = 1 + 4$$\frac{a}{p}$$.......(6)

Equating (5) and (6), we get

 $$\frac{3a}{3a-p} = 1 + 4\frac{a}{p}$$

Let $$\frac{a}{p}$$ = 'k'

$$\Rightarrow \frac{3k}{3k-1} = 1 + 4k$$

$$\Rightarrow 3k = 12k^2 + 3k - 4k -1$$

$$\Rightarrow 12k^2 - 4k - 1 = 0$$

Solving for k, we get k = $$\frac{1}{2} or -\frac{1}{6}$$[which is not possible]

Hence k = $$\frac{1}{2}$$

$$\Rightarrow$$ p =2a.............(7) 

Substituting (4) and (7) in equation (2) we get,

Total work(W) = 6a units.

Time taken by Ashok alone to do the job = Total work/ Efficiency of Ashok

= 6a/a

=6 hours.

Elder brother of Raj's father = Raj's uncle

Now, Sweety is grand-daughter of Raj's uncle.

=> Sweety is Raj's niece.

=> Ans - (A)

The minimum number of people taking classes after school is 3.

The minimum number of people taking classes before school is 2.

Hence the maximum number of people taking classes during lunch must be 2.

Hence the number of people taking classes during lunch and after school cannot be equal.

Option D is the correct answer.

To find : A's wife = ?

It is given that R and S are A's sisters.

Also, W is wife of E and V is wife of B. 

Thus, we have : (A,) (B,V) (C,) (D,) (EW)

Also, T is married neither to C nor to D, => T is wife of A.

=> Ans - (C)

If southeast becomes east and northwest becomes west, thus we have to tilt the direction $$45^\circ$$ clockwise. (to the right)

Thus, direction of north will be northeast.

=> Ans - (D)

Case 1 : If Kalia speaks truth

=> Raza is the thief, which means Raza's first statement is a lie.

Case 1(a) : Raza speaks lie and truth alternatively.

=> Second statement cannot be true.

Case 1(b) : Raza always lies.

=> Raza is a thief, and the other ones are not.

This can only mean Shera speaks truth and lie alternatively, which positively concludes above statements.

$$\therefore$$ Raza is the thief.

=> Ans - (C)

According to the statements,

If A visited Delhi and Lucknow, then B can only visit two of Chennai, Kolkata, Hyderabad or Mumbai.

=> Ans - (D)

W is greater than C but less than M, : M > W > C

Y is greater than D but not less than M, : Y > D and Y $$\geq$$ M

Combining above statements, we get : Y $$\geq$$ M > W > C and Y > D

Thus, either Y or M is the greatest.

=> Ans - (D)

No group can have more than four students. No two groups can have the same number of students.

=> The four groups will have 1,2,3,4 students respectively.

I should be alone and is in one group, => $$G_1=I$$

Given : A, D, F and J form a group, => $$G_4=A,D,F,J$$

Also, C and G must be in the same group. B and E cannot be in the same group.

=> B belongs with C and G, => $$G_3=B,C,G$$

and $$G_2=E,H$$

=> Ans - (C)

If he inspects B, he cannot inspect C immediately, => C cannot be to the immediate right of B, and thus first two options are eliminated.

If he inspects A, he cannot go to E after that, similarly third option is also not possible.

Thus, proper order : D,C,B,E,A

=> Ans - (D)

(A) : The two statements (A & C) are contradictory, hence it is invalid.

(B) : This also contain A and C, hence it is also invalid.

(C) : The statements are B and F are again contradictory, hence it is also invalid.

(D) : All honest person are obese, and all obese are good natured, hence all honest persons are good natured.

=> Ans - (D)

The road map when we connect all the 1-way roads is :

Thus, the shortest route to go from R1 to R7 : R1-R6-R7

=> Ans - (D)

Comparing the rods on the basis of weight

A is lighter than C, which is lighter than D, : D > C > A

B is heavier than D, : B > D

E is heavier than D, : E > D

It is given that B is the heaviest, and combining above statements, we get : B > E > D > C > A

Thus, A is the shortest.

=> Ans - (B)

DT screens film B in the first slot and PVR exhibits film C in the third slot

This means only Regal can exhibit the remaining film A in the remaining slot, i.e. second slot.

=> Ans - (C)

We get the following :

We can say none of the given options are connected directly
so D is the correct answer.

The middle number is the sum of numbers assigned to their adjacent alphabets as, A=1, B=2, C=3,.......,Z=26

EJO + TYE $$\equiv5+10+15+20+25+5=80$$

DHL + PTX $$\equiv4+8+12+16+20+24=84$$

Similarly, CFI + LOR $$\equiv3+6+9+12+15+18=63$$

=> Ans - (A)

Chair A is along the side joining the corner P and R. S is to the immediate right of P, => R is to the left of P.

R is between P and T, => Q is to the immediate right of S.

Chair B is along the side of Q and T. Chairs D and E are next to B on either side. => C is to the immediate right of A.

Thus, the corners that join the side where the chair C is placed are : P and S.

=> Ans - (D)

Punita and Kabir are in the same row 
So jai is in opposite row , Neetu and Lakshya will also be in the same row as Jai.
we get the arrangement as :

Option C is the correct answer.

G goes to Ram only and it is given that EFG go together so they will go together to Ram. Now A does not go with F so A goes to Deepak, I do not go with E so I go to Deepak F and B do not go to same so B goes to Deepak 
so we have 
Ram - F,G,E
Deepak - A,I,B,H
Now D can go to both
And as per options the correct answer is Deepak - D, I, H or D, B, H

Given that there are 3 boxes of green blue red colours

According to the given condition,that the box color toy is not present in respective box,

green box has blue and red toys

Blue box has Green and  red toys

Red box has Green and blue toy

There are 10 chocolates The least number of chocolates are in red box. Given that atleast one chocolate in red box

and maximum possible number of chocolates in Green box

that is 7 is the maximum number of chocolates because 2 chocolates are kept in blue box.

Therefore, option D is correct that is the box which has green and red toys has 2 chocolates. such box is Blue box which has 2 chocolates in it.

Given : If A buys R, then B does not but P or S.

Now A buys R and T, then B cannot buy P and S, thus the only two items left for him to buy are Q and U.

=> Ans - (B)

(A) : The statements are clearly contradictory, hence it is invalid.

(B) : Again the statements, this is morning and this is not morning are invalid.

(C) : The order CB is not logically consistent with the given statement.

(D) : This order is valid, and states this is not morning, hence you cannot catch the bus.

=> Ans - (D)

a+b: a is the sister of b
b-c: b is the brother of c
c+d: c is the sister of d
d-e : d is the brother of e
e*f: e is the daughter of f.
We can state that a(female), b(male),c(female), d(male), e (female), f(male or female).
Hence D is the correct answer.

Three coins are tossed in the air and two of the coins land with tails face upwards.

Assuming that the coins are fair and the first part does not try to indicate that they are not fair. The outcomes that make at least two coins heads are : 

HHT, HHH, HTH, THH 

Thus, outcome is 4 out of 8 = 50%

=> Ans - (A)

Given that F is a grandmother and travels with her granddaughter D in Audi. Similarly, A travels with her daughter in a honda. Since A doesn't belong to the first generation as F is the grandmother and each car must have at least one female.

We are provided 2 cars and each car has 2 females each. Hence the third car with the father and son must have a female in order to satisfy the condition of one female each in the car.

Hence one female must be traveling along with E and B who are father and son. The only possible way in order to fill the two married couples are :

E must be the grandfather and belongs to the first generation and B must be his son who is married to A.

Hence the two couples are EF, AB

R is not the mother of Q but Q is the son of R

=> R is father of Q

P and R are a married couple

=> P(f) is wife of R(m), and Q(m) is their son.

U is the brother of Q. S is the daughter of P

=> Q(m), U(m) and S(f) are siblings and children of P(f) and R(m).

Also, T is the brother of R

$$\therefore$$ T is S's uncle.

=> Ans - (A)

In the second paragraph of the passage, the author mentions, "People in Haryana tend to count the gold medals of the Hyderabadi shuttler, Saina Nehwal and the Delhi wrestler, Sushil Kumar, in their tally. This is because both of them are Jats. People of this dominant caste form more than 20% of Haryana's population and, therefore, in popular perception, Haryana is Jat-land."

From this, we can observe that option D is the correct answer.

In the first paragraph, the author mentions, "our playfulness is unproductive. But athletes play for profit and contest for prizes."

From this, we can infer that since most people do not play for material benefits like medals, prizes or profits, the author is calling their playfulness, unproductive.

Hence, the answer is option C.

From the third paragraph: "Firstly, the province has a volatile history of continuous aggression due to its geographical location on the frontier. Secondly, the people of Haryana have valued physical strength and perseverance due to its peasant culture."

From the last paragraph: "For the military serving population of Haryana, therefore, such sports come easily."

From the above-mentioned lines, we can infer options B, C and D to be true.

Hence, the answer is option A.

In the last paragraph, the author mentions, "But, in the late 19th century, the colonial strategists honored ordinary peasant castes by calling them 'martial races' in united Punjab. This was a clever way of taming the aggression in this frontier region."

Hence, the answer is option C.

From the second-last paragraph:

1. " Like a horseshoe, Haryana encircles Delhi from three sides and the culture of both is similar."

2. "In the medieval times, Haryana flourished when weak rulers ruled Delhi."

3. "The half-hearted policy does not create achievers but supports the successful ones among them."

Options A, B and C can be inferred from the lines mentioned above. 

Hence, the answer is option D.

From the second-last paragraph: "the sports policy since 2006 has honed the killer athletic spirit in Haryana. The half-hearted policy does not create achievers but supports the successful ones among them."

From this, we can infer option B. Option A is not mentioned in the paragraph.

Hence, the answer is option B.

"Under the new system, sources said states will be encouraged to meet the targets of various schemes or
face the prospects of drying up of the fund flows."

Thus, the funds will be distributed based on the implementation of new schemes by the states. Hence, the answer is option D.

"The official said,“We have patiently waited for the state governments to adopt a number of reform-oriented legislative bills. But our experiences have largely been negative."

Hence, the answer is option C.

The author talks about the new three-year action plan of the NITI Aayog. They also mention the provisions added to make the states follow the new rules. The passage does not talk about the infrastructure development in India or the corruption.

Hence, option A is the answer.

Options A, B, C: Nowhere explicitly mentioned or implied in the passage.

Option D: Since from the first paragraph, "Twenty years ago on Thursday, Moscow started what it thought would be a "blitzkrieg" against secular separatists in Chechnya, a tiny, oil-rich province in Russia's North Caucasus region that had declared its independence.", it can be inferred that the timing of Chechenya's independence and the Russian invasion coincided, the independence of Chechnya can be a possible reason for the invasion.

Thus, out of all the options, option D is the most appropriate one.

The correct option is D.

In the last paragraph it has been mentioned that retreating was such a humiliating experience for the Russians. 

Hence it can be inferred that the Russian military retreated. Option C is the correct answer.

The penultimate paragraph states,"...Western media and politicians dubbed the Chechens "freedom fighters"—an army of Davids fighting the Russian Goliath." This suggests that the Western media shared sympathetic feelings toward the Chechens. 

Option C most appropriately represents the Western media's attitude. None of the other options is implied in the passage.

Thus, the correct option is C.

The passage starts with the importance of smoke detectors and then explains in detail the considerations while installing them.

Option A: Though the passage mentions smoke jumpers in the starting, the main focus of the passage is on smoke detectors. Thus, this option can be eliminated.

Option B: Since the passage explains in detail the importance and considerations while installing the smoke detectors, this option aptly reflects the primary focus of the passage.

Option C: This option can be easily eliminated as this is not the primary focus of the passage.

Option D: This is a distorted inference as smoke detectors detect fires, not thwart them.

Thus, the correct answer is option B.

It can be inferred from these lines of passage, "Because smoke detectors reduce the risk of dying in a fire by half,
smokejumpers often provide audiences with information on how to fix these protective devices in their homes", that smoke detectors increase the survival in case of fire by 50%.

Since option A aptly reflects this inference, it is the correct answer.

Option B is a distorted inference as smoke detectors increase the chances of survival, not decrease the chance of preventing fire.

Options C and D are nowhere explicitly mentioned or implied in the passage.

Thus, the correct answer is A.

From the lines "Smokejumpers are often asked to address to organizations and the public groups about the importance of fire protection, particularly fire deterrence and detection", it can be inferred that one of the responsibilities of the smokejumpers is to spread the awareness about fire protection to organizations and groups.

Option A: Although smoke jumpers provide the information on the installation of smoke detectors, it cannot be inferred from the passage that they install smoke detectors in homes by themselves.

Option B: This is not implied anywhere in the passage.

Option C: Although it can be inferred from the passage that smoke jumpers address the organizations and groups about the importance of fire protection, it would be far-fetched to say that they develop fire safety programs.

Option D: This option aptly represents the responsibility of smoke jumpers given in the starting lines of the passage.

Thus, the correct option is D.

Dormant - lazy, inactive

Opposite to dormant is rampant, which means fast or active. Therefore, Option B is the correct answer.

Couchant: Lying down but alert (not necessarily active).
Potent: Powerful or strong (not directly opposite to dormant).
Prostrate: Lying flat, often weak or inactive (similar to dormant).

exiguous - small, scanty

Opposite of exiguous is large.

Answer is option C.

Soap is used for "rinsing". Thus, we have to choose the option where the second term mentions the use of the object mentioned in the first term.

Among the options, only option A has the required relationship.

The correct sentence is "later, as she is developing her self-portraits in her darkroom Nina enters and apologizes for running away"

The correct order is (6, 4, 3, 8, 5, 1, 7, 9, 2, 10).

Hence, the answer is option A.

The three statements given are inferences since we are drawing conclusions based on known facts.

Statement 1: The speaker does not see Ritu. Ritu had told the speaker that she was tired. From this known information, the speaker is concluding that Ritu must have gone home to bed.

Statement 2: The speaker knows that Ram is going to the gym a lot. From this information, the speaker is inferring that Ram must have been trying to lose weight.

Statement 3: It is known that Shera is a dog and all dogs love belly rubs. The speaker thus, infers from this that Shera must love belly rubs, too.

Hence, the answer is option B.

Cloak and dagger - involving secrecy or mystery

Forty winks - a short sleep

The alpha and the omega - beginning and the end

Lay bare - to reveal something

Option A is the most appropriate one.

Answer is option A.

truant - people who stay away from school without any reason or explanation.

Answer is option C.

"To set aside" means "to declare a legal decision or process to be invalid."

Thus, for the given sentence, option C is the correct choice.

"Evanescent" means "something that fades quickly".

Options A, B and C can be eliminated since they are not things that fade away. Rainbow mentioned in option C is something that fades away quickly.

Hence, the answer is option C.

Option A and Option B have the same meaning and both are gramatically correct.
In case of Option C and Option D, the cause and effect has been reversed while the sentences are gramatically correct.
Even though cause and effect have been reversed, both sentences make logical sense independently.
i.e. when there was an intent to catch lots of fish, seine(fishing net) was hauled(spread across)
And when a seine was spread across, many fish were caught.
Hence, All sentences are gramatically and logically correct.
Hence, the right option is D.