Explore topic-wise InterviewSolutions in Current Affairs.

DNA fingerprint, the method of individual identification using DNA, is based on the fact that the DNA of every individual (with exception of identical twins and individual clones) contains nucleotide sequences exclusive to each individual.

Although normal individuals of the same species have the same genes in their chromosomes, each individual has different alleles and even in the inactive portions of the chromosomes (heterochromatin) there are differences in nucleotide sequences among individuals.

The recombinant DNA technology and the nucleus transplantation technology (cloning) are extremely dangerous since they are able to modify, in a very short time, the ecological balance that evolution has taken millions of years to create on the planet. During the evolutionary process, under the slow and gradual action of mutations, genetic recombinations and of natural selection species emerged and were modified and genetic patrimonies were formed. With genetic engineering however humans can mix and modify genes, making changes of unpredictable long term consequences, risking creating new plant or animal diseases, new types of cancers and new disease outbreaks. It is a field as potentially dangerous as the manipulation of nuclear energy.

There are Four types of e-commerce.

• Click the compose button on the left side of the Gmail page. 
• Fill the intending username in the “To” text box. “Cc” button allows you to add users whose response are welcomed but not required. “Bcc” option allows you to hide recipient addresses from one another. 
• Summarize the purpose of the mail in the “subject” text box. 
• Enter the content of the mail in the large field below the subject line text box. 
• Use “send” button at the button left of the Compose Mail Screen to send the mail to the recipient.

DNA ligases are enzymes specialized in tying the complementary DNA chains that form the DNA double helix. These enzymes are used in the recombinant DNA technology to insert pieces of DNA cut by restriction enzymes into other DNA molecules submitted to the action of the same endonucleases. 

AutoSum option is available in Editing group under the Home tab.

The correct answer is 61.

• The ODD function rounds a positive number up to the nearest odd integer. 
• The EVEN function rounds a positive number up to the nearest even integer.
• ODD(20) equals 21.
• EVEN(39) equals 40.
• Hence, the Sum is 61.

• The ISEVEN function returns TRUE if a number is even and FALSE if a number is odd.
• The ISODD function returns TRUE if a number is odd and FALSE if a number is even. 

There are Four Views in Power Point Presentation.

(i) Notes:
1.Important schools of yoga – expounded by Patanjali
1.1. Raja Yoga-teaching of other six
1.2. Hatha Yoga-body exercises to stimulate the mental and spiritual faculties
1.3. devotion
1.4. Bhakti Yoga ritualistic course of meditation

2. The objective of different yogas
2.1. common objective
2.2. self-knowledge
2.3. internal & mental balance

3. Yoga is attained
by studying the fluctuations of the mind.

4. Student of yoga
4.1. strives for self-knowledge & internal mental balance.

5. Yoga encourages devotional approach

(ii) Summary or Abstraction
There are seven schools of yoga. Some of the important schools of yoga are- Raja yoga, Hatha yoga, Mantra yoga, Bhakti yoga, etc. The object of all the yogas is common-that is to gain self-knowledge and internal mental balance. Yoga is attained by studying the fluctuations of the mind. Yoga encourages a devotional approach and stimulates mental and spiritual faculties.
Title – Yoga and Its Importance

By Euclid’s division algorithm

a = bm + r, where 0 ≤ r ≤ b

Put b = 5

a = 5m + r, where 0 ≤ r ≤ 4

If r = 0, then a = 5m

If r = 1, then a = 5m + 1

If r = 2, then a = 5m + 2

If r = 3, then a = 5m + 3

If r = 4, then a = 5m + 4

Now, (5)² = 25m²

= 5(5m²)

= 5q where q is some integer

(5m + 1)² = (5m)² + 2(5m)(1) + (1)²

= 25m² + 10m + 1

= 5(5m² + 2m) + 1

= 5q + 1 where q is some integer

(5m + 1)² = (5m)² + 2(5m)(1)(1)²

= 25m² + 10m + 1

= 5(5m² + 2m) + 1

= 5q + 1 where q is some integer

= (5m + 2)² = (5m)² + 2(5m)(2) + (2)²

= 25m² + 20m + 4

= 5(5m² + 4m) + 4

= 5q + 4, where q is some integer

= (5m + 3)² = (5m)² + 2(5m)(3) + (3)²

= 25m² + 30m + 9

= 25m² + 30m + 5 + 4

= 5(5m² + 6m + 1) + 4

= 5q + 1, where q is some integer

= (5m + 4)² = (5m)² + 2(5m)(4) + (4)²

= 25m² + 40m + 16

= 25m² + 40m + 15 + 1

= 5(5m²) + 2(5m)(4) + (4)²

= 5q + 1, where q is some integer

Hence, the square of any positive integer is of the form 5q or 5q + 1, 5q + 4 for some integer q.

Solution:
Let a be the positive integer and b = 5.
Then, by Euclid’s algorithm, a = 5m + r for some integer m ≥ 0 and r = 0, 1, 2, 3, 4 because 0 ≤ r < 5.
So, a = 5m or 5m + 1 or 5m + 2 or 5m + 3 or 5m + 4.
So, (5m)² = 25m² = 5(5m²)
= 5q, where q is any integer.
(5m + 1)² = 25m² + 10m + 1
= 5(5m² + 2m) + 1
= 5q + 1, where q is any integer.
(5m + 2)² = 25m² + 20m + 4
= 5(5m² + 4m) + 4
= 5q + 4, where q is any integer.
(5m + 3)² = 25m² + 30m + 9
= 5(5m² + 6m + 1) + 4
= 5q + 4, where q is any integer.
(5m + 4)² = 25m² + 40m + 16
= 5(5m² + 8m + 3) + 1
= 5q + 1, where q is any integer.
Hence, The square of any positive integer is of the form 5q, 5q + 1, 5q + 4 and cannot be of the form 5q + 2 or 5q + 3 for any integer q.

The National Council of Educational Research and Training (NCERT) has developed syllabus and textbooks across the subjects to promote gender sensitization in the school curriculum. The textbooks at all stages of school education prioritize gender sensitization in the designing of activities/exercises. 

• "Gender sensitization education" means education based on the teaching that propagates gender equality by improving curriculum and textbooks to include gender-positive material and any other learning activities that promote gender equality.
• It implies a respectful approach towards defining gender roles. It will also imply the idea that an equal balance of man and woman is required in all aspects of life and will remove the stereotype that certain activities are only meant to be done by men and not by women and vice versa.
• Smriti Zubin Irani, Minister of Women and Child Development, in response to MP, Parvesh Sahib Singh, stated in Lok Sabha that the government is taking initiative in implementing various programs/schemes and legislations to address multiple forms of gender discrimination.

​Thus, it is concluded that 'Gender sensitization' in the school curriculum implies a respectful approach towards defining gender roles.

Solution:
Let a be any odd integer and b = 4.
Then, by Euclid’s algorithm, a = 4m + r for some integer m ≥ 0 and r = 0,1,2,3 because 0 ≤ r < 4.
So, a = 4m or 4m + 1 or 4m + 2 or 4m + 3
So, a = 4m + 1 or 4m + 3
Here, a cannot be 4m or 4m + 2, as they are divisible by 2.
=> (4m + 1)² = 16m² + 8m + 1
= 4(4m² + 2m) + 1
= 4q + 1, where q is some integer.
(4m + 3)² = 16m² + 24m + 9
= 4(4m² + 6m + 2) + 1
= 4q + 1, where q is some integer.
Hence, The square of any odd integer is of the form 4q + 1, for some integer q.

See this answer

Show that the square of any odd integer is of the form 4q + 1, for some integer q.

Solution: Let √3+√5 be any rational number x

x=√3+√5

squaring both sides 

x²=(√3+√5)²

x²=3+5+2√15

x²=8+2√15

x²-8=2√15

(x²-8)/2=√15

As x is a rational number 

so x² is also a rational number, 8 and 2 are rational numbers. , 

so √15 must also be a rational number as quotient of two rational numbers is rational 

But this contradicts the fact that √5 is irrational

This contradiction arose because of our false assumption
so √3+√5 is not a rational number.
So √3+√5 is irrational.

\(S = 1 + \frac56 + \frac{12}{6^2} + \frac{22}{6^3} + \frac{35}{6^4} + \frac{51}{6^5} + \frac{70}{6^6} + ...\)    ....(1)

\(\frac S6 = \frac16 + \frac5{6^2} + \frac{12}{6^3} + \frac{22}{6^4} + \frac{35}{6^5} + \frac{51}{6^6} + ....\)        .....(2)

Subtract equation (2) from (1), we get

\(S - \frac S6 = 1 + \frac46 + \frac7{6^2} + \frac{10}{6^3} + \frac{13}{6^4} + \frac{16}{6^5}+ \frac{19}{6^6} + ...\)

⇒ \(\frac{5S}{6} = 1 + \frac46 + \frac7{6^2} + \frac{10}{6^3} + \frac{13}{6^4} + \frac{16}{6^5} + \frac{19}{6^6}+...\)     ....(3)

\(\frac{5S}{36} = \frac16 + \frac4{6^2} + \frac7{6^3} + \frac{10}{6^4} + \frac{13}{6^5} + \frac{16}{6^6} +...\)            ....(4)

Subtract equation (4) from (3), we obtain

\(\frac{5S}{6} - \frac{5S}{36} = 1 + \frac36 +\frac3{6^2} + \frac3{6^3}+ \frac3{6^4}+ \frac3{6^5}+ \frac3{6^6}+...\)

⇒ \(\frac{5S}{6}\left(1 - \frac16\right) = 1 + \frac36 \left(1 + \frac16 + \frac1{6^2} + \frac{1}{6^3} + \frac1{6^4}+ \frac1{6^5}+...\right)\)

⇒ \(\frac{25S}{36} = 1 + \frac36 \times \frac1{1 - \frac16} = 1+ \frac36 \times \frac65 = 1 + \frac35\)

⇒ \(S = \frac{36}{25} \times \frac85 = \frac{288}{125}\)

\(\therefore 1 + \frac56 + \frac{12}{6^2} + \frac{22}{6^3} + \frac{35}{6^4} + \frac{51}{6^5} + \frac{70}{6^6} + ... = \frac{288}{125}\)

Solution:

We have polynomial is 4x²+5√2x-3

4x²+5√2x-3=0

a=4

b=5√2

c=-3

D=b²-4ac

D=(5√2)²-4x4x(-3)

D= 50+48

D=98

Apply Quadratic formula 

we got two zeros are -b±√D/2a

- 5✓2 +- ✓ 50+48/2*4
(-5✓2 +- ✓98)/8
therefore zeros of the polynomial are (-5✓2 + ✓98)/8 & (-5✓2 - ✓98)/8

Find the quadratic polynomial whose sum and product of zeroes are - 2 root 3 and -9

Solution:

We have given that sum of zeroes(S)= -2√3

and product of zeroes(P) = -9

so the quadratic polynomial p(x)= k(x² - Sx +P)

p(x) = k(x² - (-2√3)x + (-9))

p(x) = k(x² + 2√3x - 9)

where  k  is any non-zero real number.

Solution: We have 4tanA = 3 so, tanA = 3/4 

Now, (4sinA - cosA)/(4sinA + cosA) 

First of all divide by cosA on both LHS and RHS , 

(4sinA/cosA - cosA/cosA)/(4sinA/cosA + cosA/cosA) 

= (4tanA - 1)/(4tanA + 1)

Now, put tanA = 3/4 

= (4 × 3/4 - 1)/(4 × 3/4 + 1)

= (3 - 1)/(3 + 1) 

= 2/4 = 1/2 

P = principal amount  = Rs. 58750

R = 12% per annum

T = 4 years

\(\therefore \) S. I. = \(\frac{PRT}{100} = \frac{58750\times2\times4}{100}\) = 28200

\(\therefore \) Amount after the end of 4 year is

A = P + S. I. = 58750+ 28200

 = Rs.86950

Short Form Equation - 

Fitness Index = (100 x test duration in seconds) divided by (5.5 x pulse count between 1 and 1.5 minutes). 

Long Form Equation - 

Fitness Index= (100 x test duration in seconds) divided by (2 x sum of heartbeats in the recovery periods).

We have

2 sin² A - cos² A = 2

2 sin² A - cos² A = 2(sin² A + cos² A)

2 sin² A - cos² A = 2sin² A + 2cos² A

3cos² A = 0

cos A = 0, 

or A = 90 deg or 180 deg.

The correct answer is I only.

• Since 2010, Rajasthan state occupies the first position in the country in the micro-irrigation process based on solar energy pumps.

​

• Solar Water Pump Programme 
  • Solar pump along with micro-irrigation systems scheme was started in Rajasthan in the year 2010-11.
  • Farmers who install micro-irrigation systems (Drip, Mini Sprinkler, and Sprinkler) on their fields are only eligible for the solar pump subsidy.
  • Department of Horticulture is the Implementing Agency and the Director, Horticulture is the Mission Director of the State. 
  • Since 2010, Rajasthan state occupies the first position in the country in the micro-irrigation process based on solar energy pumps. Hence statement 1 is correct.
  • 4 stages of the scheme:
    • ​1st stage
      • ​50 pumps (2010-2011)
    • 2nd stage
      • ​​500 pumps (2011-2012)
    • ​3rd stage
      • ​​2200 pumps (2012-2013). Hence statement 3 is not correct.
    • ​4th stage
      • ​​10000 pumps (2013-2018)

​

• Tamilnadu state occupies the first position in the country in harvesting wind energy. Hence statement 2 is not correct.
• Rajasthan had secured the third position in the country in harvesting wind energy.
• Rajasthan Wind and Hybrid Energy Policy, 2019​
  • The Wind and Hybrid Energy Policy, 2019 promotes developing new wind as well as hybrid projects, repowering of existing wind projects, and hybridization of existing wind and solar power plants.
  • The policy will also promote the blending of renewable power with thermal power, thus helping in reducing fuel consumption and carbon-emission.

Cucurbitaceous vegetables: 

Pumpkin, cucumber, round melon, musk melon, water melon, karela, tori etc.

Major plant nutrients: 

N,P,K, Ca, Mg, S etc.

Bio-fertilizers commercially used in India: 

Rhizobium, VAM, Azotobacter, PSB

Two points to be kept in mind while selecting area:

Ginger 

1.Smooth knobs 

2.Firm and shinny skinned

b) Celery 

1.Stems should be firm and crisp 

2.Leaves should be fresh green

Correct option is B) feel sorry for them

Given Principal amount P = Rs. 10

 Time T = 4 months

 Rate of interest R = 3 ps

 Interest I = PTR/100 = (10 x 4 x 3)/100 = 12/10 = 1.2 paise.

Correct option is C) begin before the others

Correct option is B) is tough and powerful

First multiple after 50 = 55

Last multiple before 200 = 195

therefore, a = 55, d = 5

a_n = 195 

=> 55+(n-1)5 = 195

(n-1)5 = 195-55

(n-1)5 = 140

(n-1) = 140/5

n = 28+1 = 29

therefore, S₂₉ = 29/2 x (55+195)

S₂₉ = 29x250/2

S₂₉ = 29X125

S₂₉ = 3625

Hence, the sum of all the multiples of 5 greater than 50 but less than 200 is 3625

Correct option is (D) all of these

\(I = \int\limits^{\frac\pi2}_{\frac{-\pi}2} (4\lambda sin^4x + 54 sin^5x + 72 sin^7x)dx\)

\(= 2 \int\limits^\frac\pi2_0 4\lambda sin^4 x \,dx\)

\( = 8\lambda \frac{\Gamma\left(\frac52\right) + \Gamma\left(\frac12\right)}{2\Gamma(3)}\)      (By gamma beta function)

\(= 8\lambda \frac{\frac32.\frac12\,\Gamma\left(\frac12\right) \Gamma\left(\frac12\right)}{2\times 2!}\)   \((\because \Gamma (n + 1) = n \Gamma (n))\) 

\(= \frac{3\lambda}{2}\sqrt{\pi}. \sqrt\pi\)            \((\because \Gamma\left(\frac12\right) = \sqrt\pi )\)

\(= \frac{3\pi\lambda}{2}\)

∴ \(I \propto \lambda\)     (∵ \(\frac{3\pi}{2}\) is constant)

Similarly \(I \propto 2\lambda\), \(I \propto 3\lambda\), \(I \propto 4\lambda\).

use the relation sec(theta)=±√(1+tan²(theta)) to get the answer