Explore topic-wise InterviewSolutions in Current Affairs.

Formula:-

ⁿC_r=ⁿC_n-r

¹⁵C₈+¹⁵C₉-¹⁵C₆-¹⁵C₇

=¹⁵C_15-8+¹⁵C_15-9-¹⁵C₆-¹⁵C₇

=¹⁵C₇+¹⁵C₆-¹⁵C₆-¹⁵C₇=0

8 men can be seated around a table in (8 – 1)! = 7! ways.

No two women should sit together.

There are 8 gaps created by 8 men’s seats.

∴ Women can be seated in 8 gaps in P ways.

∴ Required number of arrangements = 7! x ⁸P₆

Answer is (A)

Number of men = 4; Number of women = 6

It is given that committee includes at least two men and exactly twice as many women as men.

So, we can select either 2 men and 4 women or 3 men and 6 women.

∴ Required number of committee formed = ⁴C₂ x ⁶C₄ + ⁴C₃ x ⁶C₆

= 6×15 + 4×1=94

(c) 17

Let the number of participants in the beginning be n. 

Total number of games played by the 2 players who fell ill = 6 + 6 = 12 

Number of remaining players is (n – 2) 

Number of games played by (n – 2) players with each other = ^n–2C₂ 

∴ Total number of games played = ^n–2C₂ + 12 

Given ^n–2C₂ + 12 = 117 

⇒ ^n–2C₂ ⇒ \(\frac{n-2!}{(n-4)!2!}\) = 105

⇒ \(\frac{(n-2)(n-3)}{2}\) = 105 ⇒ n² – 5n – 204 = 0 

⇒ (n – 17) (n + 12) 0 ⇒ n = 17 (Neglecting –ve value)

(a) 100

If a particular student is excluded, then the committee has to be chosen as: 2 professors from 5 professors and 3 students from 5 students (as one student is excluded) 

∴ Total number of ways of forming the committee 

= ⁵C₂ × ⁵C₃ 

= \(\frac{5!}{2!3!}\times\frac{5!}{3!2!}\) 

= \(\frac{5\times4}{2}\) x \(\frac{5\times4}{2}\) = 100.

(b) 25 

If at least one woman has to be included then the committee can be formed as: 

• 1 woman and 2 men 

• 2 women and 1 man 

∴ Number of ways of forming the committee 

= ²C₁ × ⁵C₂ + ²C₂ × ⁵C₁ 

= 2 × 10 + 1 × 5 = 20 + 5 = 25.

(a) 385

As there are 4 candidates to be elected and the voter votes for at least one candidate, the voter can vote for 1 or 2 or 3 or 4 candidates out of 10 candidates. 

∴ Total number of ways in which the voter can vote 

= ¹⁰C₁ + ¹⁰C₂ + ¹⁰C₃ + ⁴C₄ 

= \(10+\frac{10\times9}{2\times1}+\frac{10\times9\times8}{3\times2\times1}+\frac{10\times9\times8\times7}{4\times3\times2\times1}\)

= 10 + 45 + 120 + 210 = 385.

(c) 186

A committee of 5 persons, including at most two ladies can be constituted in the following ways : 

I. Selecting 5 gents only out of 6 gents. 

II. Selecting 4 gents out of 6 gents and 1 lady out of 4 ladies. 

III. Selecting 3 gents out of 6 gents and 2 ladies out of 4 ladies. 

∴ Total number of ways of forming the committee 

= ⁶C₅ + ⁶C₄ × ⁴C₁ + ⁶C₃ × ⁴C₂ 

= \(6+\frac{6\times5}{2}\times4+\frac{6\times5\times4}{3\times2}\times\frac{4\times3}{2}\) 

= 6 + 60 + 120 = 186.

Correct answer is 26.25

We will separate the mixture of wheat, barley & com on the basis of their identification by picking with our hands.

(a) hand picking

Two or more substances mixed in indefinite proportion make mixture.

(b) heterogeneous mixture

(d) winnowing

Correct answer is Rs 200

5 rupees 5 paise = Rs 5.05

(i) Mixture of Sand and husk : Sand and husk can be separated by the method of winnowing 

(ii) Mixture of Wheat , sugar and stalk : For separating stalk from the mixture we should follow the winnowing method Wheat and sugar can be seperated by sieving because they are in different sizes. 

(iii) Mixture of Water and petrol (oil) : Water does not dissolve in petrol, so it can be separated by the use of separating funnel or decanatation method. 

(iv) Mixture of Rice and salt : Rice and salt can be separated by sieving. 

(v) Mixture of Sand and salt : Sand and salt is mixed with water, salt dissolves in water and sand can be seperated by sedimentation and decantation followed by Alteration After that using evaporation common salt is seperated.

Sugar is a substance whereas sand is a mixture.

Following are the method to separate mixture of sand, salt and iron fillings/chips

Step 1:

Magnetic separation:

First of all, the mixture is spread on a piece of paper and magnet is moved around it again and again. By this, iron fillings cling to the magnet. Iron filings are now separated from magnet.

Step 2:

Sedimentation:

Now, in the mixture sand and salt are left. The mixture is dissolved in water and left for sometime., Sand accumulates at the bottom of the container. Now, upper layer of salt solution is separated by decantation.

Step 3:

Vaporisation:

Now the solution contains only salt and water. Mixture is heated in a broad bottom container. Water is evaporated in the form of vapour and salt remains in the beaker. In this way, all the three components of the mixture are separated.

(c) sand dissolved in water

(a) The method of separating seeds of paddy from its stalks is called threshing.
(b) When milk, cooled after boiling, is poured onto a piece of cloth the cream (malai) is left behind on it. This process of separating cream from milk is an example of churning.
(c) Salt is obtained from seawater by the process of evaporation.
(d) Impurities settled at the bottom when muddy water was kept overnight in a bucket. The clear water was then poured off from the top. The process of separation used in this example is called sedimentation and decantation.

Weight of potatoes = 3.350 kg 

Weight of tomatoes = 2.250 kg 

Weight of total items = 10.250 kg 

Weight of onions = ? 

Weight of (potatoes + tomatoes + onions) = 10.250 kg 

(3.350 + 2.250) + onions weight = 10.250 

5.600 + onions weight = 10.250 

Onions weight = 10.250 – 5.600 

∴ Weight of onions = 4.650 kg.

(d) Threshing

(ii) Decantation
(iii) Filtration

Following steps are required to obtain clear water from muddy water:
1. Allow muddy water to stand undisturbed in a container.
2. After sometime, mud settles at the bottom of the container. This process is called sedimentation.
3. Upper layer is clear water.
4. Pour the clear water gently in another container. This process is called decantation.
5. To remove finer impurities we can filter this water again with the help of filter paper. This process is called filtration.

Correct option is A) Air

Correct option is B) Leather

Correct option is C) Pot

Correct option is D) Pot

(b) Sieving, Answer is correct 

B) i – b, ii – c, iii – a

Correct option is C) Mirror

Transferring the clear liquid into an other container using a glass rod is called Decantation.

Correct option is C) both A & B

Correct option is B) transparent

Correct option is C) sediment

Source: Streptococcus.

Streptokinase is a clot buster, i.e., it removes clot from the blood vessels of patients who had a heart attack.

Correct option is C) Petrol

Correct option is B) insoluble

Correct option is A) opaque

Correct option is D) Sawdust

Correct option is A) solid mixture

Correct option is D) handpicking

Correct option is A) vitamin

Correct option is C) separating funnel

Correct option is B) decantation

Correct option is D) threshing

Correct option is B) Sieving

Correct option is D) Cornflakes in milk