Explore topic-wise InterviewSolutions in Current Affairs.

Dear Mom and Dad,

Chennai 

01.02.19

I’m fine. I hope all are fine at home. I wish to join the karate class. Mr. Saravanan is the instructor. The charges are only two hundred rupees per month. The classes start next Monday. Please give me permission.

Thank you,

Yours lovingly, 

XYZ

To 

Mr. Mukesh, 

12, Railway Station Road, 

Nagercoil

Answer: 4/3 + i10

Z = x + iy and 3x + (3x - y)i = 4 - 6i 

3x = 4, 3x - y = 6 

∴ z = 4/3 + i10 

soft diet is the most appropriate food for old person.

16 March, 2019 

Roshan M. 

12, Gandhi Nagar 

Chennai 

The Director 

Success Institute 

10-A, Race Course Road, Guindy 

Chennai

Sir, 

Sub: Coaching for NEET 

Kindly refer to your advertisement in the Deccan Times dated 14 March. I would like more information and details about NEET coaching the institute offers, facilities available, timings, fee structure and size of classes/groups. I need special coaching in Physics and Chemistry. Please let me know if coaching is available in all these subjects and what is the schedule. Does your institute cater to individual difficulties or do you discuss and resolve general problems?

Kindly enlighten me on all the above points. In case you have a detailed information booklet, do send it to my address given above.

Yours faithfully 

Roshan M.

To 

The Director 

Success Institute 

10-A, Race Course Road, Guindy 

Chennai

Booster doses of DPT and Polio are given at the age of 16 - 24 months. 

05 Jan, 2019 

B. Amrita Chettinad School 

Ramapuram 

Chennai

Cultural Program Co-ordinator 

Don Bosco School 

Perambur Sir,

Sub: Information regarding inter-school competitions

We have received the notification about the interschool competitions to be held in your school. Kindly confirm the details that is mentioned in the poster.

1. Participants from school: 25 No.s 

2. Registration fees : Rs. 250/- (DD attached) 

3. Time of entry: 8.30 am 

4. No. of competitions a participant can take part in: 3 

5. No. of teachers to accompany students: 3 

6. Last date for registration: 10.01.2019

The specific conditions and eligibility criteria may please be intimated to us. 

I hope you will provide the necessary information at the earliest.

Yours faithfully 

B. Amrita 

Sports Secretary

To 

Cultural Program Co-ordinator 

Don Bosco School, 

Perambur Chennai

Dear Grandma,

Chennai 

09.03.19

How are you my dear grandma? I’m fine and am waiting for my vacation. I am coming to visit you and spend the vacation with you, listening to your stories and having your handmade delicacies. I’ll reach Trichy on 25.04.2019. Anxiously waiting to meet you. Love you, grandma.

Thank you,

Yours lovingly, 

To 

Mrs. Seema Mani, 

15, MG Road,

 TrichyXYZ

Night blindness is caused by deficiency of Vitamin A. 

Purple colour is Secondary. 

The medium of audio is radio. 

\(f(x) = \frac{2 x -1}{x -2}\)

Let \(f(x_1) \ne f(x_2)\) & \(x_1 \ne 2, x_2 \ne 2.\)

\(\therefore \frac{2x_1-1}{x_1-2}\ne \frac{2x_2-1}{x_2-2}\)

⇒ \((2x_1 -1) (x_2-2) \ne (2x_2-1)(x_1-2)\)

⇒ \(2x_1x_2 - 4x_1 - x_2 + 2\ne 2x_1x_2 - 4x_2 - x_1 + 2\)

⇒ \(-3x_1 \ne -3x_2\)

⇒ \(x_1 \ne x_2\)

\(\therefore\) Function f(x) is one-one.

Let \(y = \frac{2x - 1}{x - 2}\) 

⇒ \(xy - 2y = 2x - 1\)

⇒ \(xy - 2x = 2y-1\)

⇒ \(x(y - 2) = 2y - 1\)

⇒ \(x = \frac{2y -1}{y - 2}\)

⇒ \(f^{-1}(y) = \frac{2y - 1}{y - 2}\)

⇒ \(f^{-1}(x) = \frac{2y - 1}{y - 2}\)

\(\therefore \) Range of function f(x) is R-{2}

which is codomain  of f(x).

\(\therefore \) f(x) is onto.

Hence, given function f(x) is both one-one & onto.

(i) \(\{x\in N; x^2 < 25\} = \{1,2,3,4\}\)

\(\because 1^2 = 1 < 25, 2^2 = 4<25, 3^2 = 9< 25, 4^2 = 16 < 25 \;\text{but}\; 5^2 = 25\)

(ii) \(\{x\in N; x\) is a prime number and \(10 < x < 20\}\)

\(\because \) 11, 13, 17 & 19 are prime numbers between 10 & 20.

\(\{x\in N; x\) is a prime number and \(10 < x < 20\} = \{11, 13, 17, 19\}\) 

(iii) 17, 26, 35, 44, 53, 62 & 71 are two digit numbers whose sum of digits is 8.

\(\therefore\) {x : x is a two digit number such that the sum of its digits is 8} = {17, 26, 35, 44, 53, 62, 71}.

(iv) 9, 18, 27, 36, 45, ...... are positive integer which are divisor of 9.

\(\therefore\) {x : x is a positive integer and a divisor of 9} = {9, 18, 27, 36, 45, .....}

(v) \(|x| \le 2\)

⇒ \(-2 \le x \le 2\)

-2, -1, 0, 1 & 2 are integer which belongs to \(-2 \le x \le 2\).

\(\therefore \{x: x\in Z\;and\;|x| \le 2\}= \{-2, -1, 0, 1, 2\}\)

(ix) \(a_{n +2} = a_{n + 1} + a_n \) & \(a_1 = a_2 = 1\)

\(\therefore a_3 = a_2 + a_1= 1+1=2\)

\(a_4 = a_3+a_2 = 2+1= 3\)

\(a_5 = a_4+ a_3 = 3+2 = 50\)

\(a_6 = a_5 + a_4 = 5 + 3= 8\)

\(\therefore \{a_n : n\in N, a_{n + 2} = a_{n + 1} + a_n \;and\; a_1 = a_2 = 1\}= \{1,1,2,3,5,8,...\}\)

(x) \(a_{n + 1} = 3a_n \) & \(a_1 = 2\)

\(\therefore a_2 = 3a_1 = 3 \times 2 = 6 = 2\times 3\)

\(a_3 = 3a_2 = 3 \times 6 = 18 = 2\times 3^2\)

\(a_4 = 3a_3 = 3\times 18 = 54= 2 \times 3^3\)

\(a_n = 2\times 3^{n -1}\)

\(\therefore \{a_n : n\in N, a_{n + 1} = 3a_n \; and\; a_1 = 2\}= \{{2, 6, 18, 54,..., 2\times 3^{n -1},...\}}\)

A = {1, 2, 3, 4, 6}, R = {(a, b): a, b ∈ A, b is exactly divisible by a} 

(i) R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (6, 6)} 

(ii) Domain of R = {1, 2, 3, 4, 6} 

(iii) Range of R = {1, 2, 3, 4, 6} 

A = {1, 2, 3, 5} and B = {4, 6, 9} 

R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B} 

∴ R = {(1, 4), (1, 6), (2, 9), (3, 4), (3, 6), (5, 4), (5, 6)} 

The value of sin² 45º will be 1/2

R = {(x, y): y = x + 5, x is a natural number less than 4, x, y ∈ N} 

The natural numbers less than 4 are 1, 2, and 3. 

∴ R = {(1, 6), (2, 7), (3, 8)} The domain of R is the set of all first elements of the ordered pairs in the relation. 

∴ Domain of R = {1, 2, 3} The range of R is the set of all second elements of the ordered pairs in the relation. 

∴ Range of R = {6, 7, 8} 

Leakage of Income – Leakage represents that income which is saved and not returned back to income flow. If factors of production do not spend their entire income on purchasing goods and service is called the leakage of income. Similarly if firms do not spend their income and keep away a part of their income as undistributed income and profit it will also be called leakage from income flow. Thus “ Leakage of income is that income which is not returned to circular flow as an expenditure and is kept away from the flow.” In other words “ Leakage gives the squeezing affect on national income.” Injection of Income : - Injection of income is that income addition which takes place in circular flow from outsources other than circular flow. Injection of income causes an increase in the process of income generation in the economy. In other words “ Injection gives the expanding effect on National income.”

Concept:

Let f(x) be any function.

f (x) is onto if range of f (x ) = Codomain  

The function f is said to be many-one functions if there exist two or more than two different elements in X having the same image in Y.

Calculations:

Given function f : R → {0, 1} such that \(f(x)=\left\lbrace \begin{matrix} 1 \ \text{if} \ x \ \text{is rational} \\\ 0 \ \text{if} \ x \ \text{is irrational} \end{matrix} \right.\)

Codomain = {0, 1}

Since, on taking a straight line parallel to the x-axis, the group of given function intersect it at many points. 

⇒ f (x) is many-one. 

Range of function is {0, 1}

As range of f (x ) = Codomain 

⇒ f (x) is onto. 

Hence, f (x) is many-one onto

CONCEPT:

Product property of logarithms is given by \(\log a + \log b = \log (a \times b)\)

CALCULATION:

Given that \(\\log \frac{x}{y} + \log \frac{y}{x} = \log (x + y)\)

\(\begin{gathered} \log \frac{x}{y} + \log \frac{y}{x} = \log (x + y) \hfill \\ ⇒ \log (x + y) = \log (\frac{x}{y} \times \frac{y}{x}) \hfill \\ \end{gathered} \)

⇒ log (x + y) = log (1)

∴ x + y = 1

Therefore  option (1) is the correct answer.

CONCEPT:

• Basic Quotient property of logarithms is given by \(\ln (\frac{x}{y}) = \ln (x) - \ln (y)\).

CALCULATION:

Given is log(6x) − log(6−x) = log(3).

By Quotient property of logarithms we can write it as -

\( ⇒ \log \left( {\frac{{6x}}{{6 - x}}} \right) = \log 3\)

On dropping log from both the sides we get \(\left( {\frac{{6x}}{{6 - x}}} \right) = 3\).

 ⇒  6x = 3(6 - x)

 ⇒  9x = 18

 ⇒ x = 2

Therefore, option (3) is the correct answer.

Let point (x, y) on parabola y² = 4ax is nearest point to focus of parabola.

\(\therefore\) distance between (x, y) & focus(a, 0)

\(\leq a\) (\(\because\) a is distance between focus & vertex)

⇒ (x - a)² + (y - 0)² \(\leq a^2\)

⇒ y² + (x - a)² \(\leq a^2\) 

⇒ 4ax + (x - a)² \(\leq a^2\) (\(\because\) y² = 4ax)

⇒ (x + a)² \(\leq a^2\)

⇒ |x + a| \(\leq a\)

⇒ -a \(\leq \) x + a \(\leq \) a

⇒ - 2a \(\leq \) x \(\leq \) 0

But x \(\geq\) 0 for given parabola

\(\therefore\) x = 0 is only possibility

If x = 0 then y = 0

\(\therefore\) (0,0) is nearest point to focus which is vertex of the parabola.

Hence proved.

Given:

The pairs are (35, 51), (75, 104), (49, 133), (63, 95)

Concept Used:

A co-prime number is a set of numbers or integers which have only 1 as their common factor.

Calculation:

(i) (35, 51)

35 = 5 × 7

51 = 3 × 17 

No common factor other than 1 ⇒ 35 and 51 are co-prime numbers

(ii) (75, 104)

75 = 3 × 5²

104 = 2³ × 13

No common factor other than 1 ⇒ 75 and 104 are co-prime numbers

(iii) (49, 133)

49 = 7²

133 = 7 × 19

Common factor is 7 ⇒ 49 and 133 are not co-prime numbers

(iv) (63, 95)

63 = 3² × 7

95 = 5 × 19

No common factor other than 1 ⇒ 63 and 95 are co-prime numbers

∴ 49 and 133 are not co-prime numbers

Let the quantity of alcohol and water be 4x litres and 3x litres respectively 

4x/(3x+5)=4/5 

20x=4(3x+5)

8x=20 

x=2.5 

Quantity of alcohol = (4 x 2.5) litres = 10 litres. 

Given:

A sold an item to B at 20% gain 

B sold it to C at 8% gain 

C sold it to D at 25% loss 

If the difference between the profit of A and B is Rs. 260 

Concept used:

S.P = C.P × (100 + P%)/100

S.P = C.P × (100 – L%)/100 

P = S.P – C.P

Where,

S.P → Selling price 

C.P → Cost price 

P% → Profit% 

L% → Loss%  

Calculations:

Let the cost price of A be 100x 

Cost price of B = Selling price of A = 100x × 120/100 = 120x 

Profit of A = 120x – 100x = 20x 

Cost price of C = Selling price of B = 120x × 108/100 = 129.60x 

Profit of B = 129.60x – 120x = 9.6x 

Difference between profit of A and B = 20x – 9.6x = 10.4x 

⇒  10.4x = 260 

⇒ x = 25 

Cost price of D = Selling price of C = 129.60x × 75/100 = 97.20x 

Cost price of D = 97.20 × 25 = 2430

∴ Cost price of D is Rs. 2,430

|sinx| is non differentiable where sinx =0.

Given :

Rate of Rice of quality 1 = Rs. 55

Quantity = 20 kg

Rate of Rice of quality 2 = Rs. 50

Quantity = 25 kg

Rate of Rice of quality 3 = Rs. 60

Quantity = 35 kg

Money spent on transportation = Rs. 150

Selling price of mixed Rice = Rs. 62.56

Formula used :

Profit = Selling price - Cost price

Profit% = (profit/cost price) × 100

Solution :

Cost price of Rice of quality 1 = 55 × 20

⇒ Cost price of Rice of quality 1 = 1100

Cost price of Rice of quality 2 = 50 × 25

⇒ Cost price of Rice of quality 2 = 1250

⇒  Cost price of Rice of quality 3 = 60 × 35

Cost price of Rice of quality 3 = 2100

⇒ Total quantity of mixed rice = 20 + 25 + 35

⇒ Total quantity of mixed rice = 80 kg

Final cost price including transportation = 1100 + 1250 + 2100 + 150

⇒ Final cost price including transportation = 4600

⇒ Cost price of 1 kg of mixed rice = 4600/80

⇒ Cost price of 1 kg of mixed rice = 57.5

⇒ Selling price of 1 kg of mxed rice = 62.56

⇒ Profit = 62.56 - 57.5

⇒ Profit = 5.06

⇒ Profit% = (5.06/57.5) × 100

⇒ Profit% = 8.8%

∴ His profit percent in the entire transaction is 8.8%

Given:

Length of wall = 3m 50cm = 7/2 m

Height of wall = 4m

Calculation:

Area of wall = 7/2 × 4 = 14 m²

As we dont know area of square tiles, so number of largest possible tiles would be in multiple of 14 as 28, 42, 56....

∴ From options, 56 tiles needed to cover wall.

Correct option is B) on

(b) Radha siad to Ravi, "Where is your father?'

Correct option is D) in / in

Correct option is A) on

A lot of energy was wasted on finding the treasure.

Correct option is D) for

(c) A novel is being read by Marsha.

Correct option is C) on

(b) A novel had read by Marsha.

Correct option is C) in / at