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Transposons (Transposable elements or mobile elements) are DNA sequence able to insert itself at a new location in the genome without having any sequence relationship with the target locus and hence transposons are called walking genes or jumping genes. They are used as genetic tools for analysis of gene and protein functions, that produce new phenotype on host cell. The use of transposons is well studied in Arabidopsis thaliana and bacteria such as Escherichia coli.

Correct option is (a) Mukti Bahini

(i) False

If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.

Because let us consider an example 6 divide 30, but 6 divides none of 13 and 17 as both are prime numbers.

(ii) True

If a number divides three numbers exactly, it must divide their sum exactly.

Because if x, y and z are three numbers, each of x, y and z is divided by a number (say q), then (x + y + z) is also divisible by q.

(iii) False

If two numbers are co-prime, at least one of them must be a prime number.

Because 16 and 21 are co-prime but none of them is prime.

(iv) True

The sum of two consecutive odd numbers is always divisible by 4.

Because 3+5=8 which is divisible by 4.

Correct option is (A) a² + ab + b²

\((a^3-b^3)\div(a-b)\) \(=\frac{a^3-b^3}{a-b}\)

\(=\frac{(a-b)(a^2+ab+b^2)}{a-b}\)

= \(a^2+ab+b^2\)

A) a² + ab + b²

Correct option is (C) 3

\(\because\) \(n^3-n=n(n^2-1)\) = n (n-1) (n+1)

Whenever a number is divided by 3, the obtained remainder is either 0 or 1 or 2.

\(\therefore\) For any number n,

n = 3p or 3p+1 or 3p+2, where p is same integer.

If n = 3p, then n is divisible by 3.

If n = 3p+1 then n-1 = (3p+1)-1 = 3p is divisible by 3.

If n = 3p+2 then n+1 = (3p+2)+1 = 3p+3 = 3(p+1) is divisible by 3.

So, we can say that for any number n, one of the numbers among n, n-1 and n+1 is always divisible by 3.

\(\therefore\) n (n-1) (n+1) is always divisible by 3 for any n.

\(\Rightarrow\) \(n^3-n\) is always divisible by 3.

Correct option is  C) 3

Alkaline phosphate is a DNA modifying enzymes and adds or removes specific phosphate group at 5’ terminus of double stranded DNA (dsDNA) or single stranded DNA (ssDNA) or RNA. Thus it prevents self ligation. This enzyme is purified from bacteria and calf intestine.

(b) A is right R is wrong.

(c) Alkaline phosphate

The following are the features that are required to facilitate cloning into a vector.

1. Origin of replication (ori): This is a sequence from where replication starts and piece of DNA when linked to this sequence can be made to replicate within the host cells.

2. Selectable marker: In addition to ori the vector requires a selectable marker, which helps in identifying and eliminating non-transformants and selectively permitting the growth of the transformants,

3. Cloning sites: In order to link the alien DNA, the vector needs to have very few, preferably single, recognition sites for the commonly used restriction enzymes.

Allahabad High Court passed a judgment declaring Indira Gandhi’s election to the Lok Sabha invalid.

Correct option is (b) Jayprakash Narayan

Chandrashekhar – Mandal Commission

Correct option is (C) A & B

If a number is divisible by 5 then its unit digit be either 0 or 5.

Correct option is  C) A & B

(d) all the above

Bacterial Artificial Chromosome (BAC) Vector is a shuttle plasmid vector, created for cloning large-sized foreign DNA. BAC vector is one of the most useful cloning vector in r-DNA technology they can clone DNA inserts of upto 300 Kb and they are stable and more userfriendly.

(i) Following incidents paved the way of Indira Gandhi back to power:

• Allahabad High Court verdict against Indira Gandhi 
• Nation – wide strikes and protest led by Jai Prakash Narayan
• Imposition of National Emergency (1975-77) fundamental rights suspended 
• Opposition parties came together to form Janata Party. 
• Short lived governments of Morarji Desai and Charan Singh. 
• Elections conducted in 1980 – Congress back to power.

(ii) Sikkim voted to join the Indian Republic and it became a full – fledged state of Indian Republic in 1975.

(iii) India conducted Nuclear tests for two reasons: 

(i) to keep Pakistan’s aggression under check post 1971 war. 

(ii) To initiate peaceful and constructive use of atomic energy

Given : c > a 

To show : cba – abc = 99(c – a) 

Proof: 

cba = 100c + 106 + a ……….(i)

(By using property 3) 

abc = 100a + 106 + c ………(ii) 

(By using property 3) 

Subtracting (ii) from (i) 

cba – abc= 100c+ 106 + a- 100a- 106-c 

=> cba – abc = 99c – 99a 

=> cba – abc = 99(c – a) 

Hence proved.

Given, a > c 

To show : abc – cba = 99(a – c) 

Proof: abc = 100a + 10b + c ……….(i) (By using property 3) 

cba = 100c + 10b + a ………..(ii) 

(By using property 3) 

Subtracting, equation (ii) from (i), we get 

abc – cba = 100a + c – 100c – a abc – 

cba = 99a – 99c abc – cba = 99(a – c) Hence proved.

Given : a = c 

To show : cba – abc = 0 

Proof:

cba = 100c + 106 + a …………(i) 

(By using property 3) 

abc = 100a + 106 + c …………(ii) 

(By using property 3) 

Since, a = c,

Substitute the value of a = c in equation (i) and (ii), 

we get cba = 100c + 10b + c ……….(iii) 

abc = 100c + 10b + c …………(iv) 

Subtracting (iv) from (iii), we get

cba – abc – 100c + 106 + c – 100c – 106 – c 

=> cba – abc = 0 

=> cba = abc 

Hence proved.

If the sum of the digits of a number is divisible by 9, then the number is divisible by 9. 

∴ 2791A = 2 + 7 + 9 + 1 + A = 9 x 3 

⇒ 19 + A = 9 x 3 = 27 

⇒ A = 27 – 19 = 8 

∴ A = 8

If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.

∴ 345A7 ⇒ 3 + 4 + 5 + A + 7 = 19 + A 19 + A = 3 x 7 

⇒ A = 21 – 19 = 2 ⇒ A = 24 – 19 = 5

A + 19 = 3 x 8

⇒ A = 24 – 19 = 5

A + 19 = 3 x 9

⇒ A = 27 – 19 = 8

∴ A = {2,5,8}

Yes, it is possible to transfer a suitable desired gene to a host plant using certain chemicals, microinjection method, electroporation or by biolistics.

An antibiotic resistance marker is a gene that produces a protein that provides cells with resistance to an antibiotic. Bacteria with transformed DNA can be identified by growing on a medium containing an antibiotic. Recombinants will grow on these medium as they contain genes encoding resistance to antibiotics such as amphicillin, chloroamphenicol, tetracycline or kanamycin, etc., while others may not be able to grow in these media, hence it is considered useful selectable marker.

(c) Solvent extraction is an upstream process of fermentation.

1. Bioventing is the process that increases the oxygen or air flow to accelerate the degradation of environmental pollutants. 

2. Bioaugmentation is the addition of selected microbes to speed up degradation process.

Fermentation refers to the metabolic process in which organic molecules (normally glucose) are converted into acids, gases, or alcohol in the absence of oxygen or any electron transport chain.

The correct answer is option (c) 18

Explanation:

The general form of abc is 100a+10b+c

The genera form of cba is

Now (abc- cba) = (100a+10b+c ) – (100c+10b+a) =99a-99c

= 99(a – c)

Now, abc – cba is divisible by 99, because 99 is the factor of abc – cba

So, all the numbers which are the factors of 99 will also be divisible by abc-cba

Here, 9, 11 and 33 are the factors of 99. But 18 is not a factor of 99. Hence abc- cba is not divisible by 18.

Correct option is (D) 10

abc is a 3-digit number

\(\therefore\) abc = 100a+10b+c

Now abc+bca+cab = (100a+10b+c) + (100b+10c+a) + (100c+10a+b)

= (100a+10a+a) + (100b+10b+b) + (100c+10c+c)

= 111a + 111b + 111c

= 111 (a+b+c)

= 3 \(\times\) 37 (a+b+c)

\(\therefore\) 3, 37 & (a+b+c) are factors of abc+bca+cab.

Thus, abc+bca+cab is divisible by 3, 37 and a+b+c, but not divisible by 10.

Correct option is  D) 10

The correct answer is option (d) 1001

Explanation:

From the given question, the number should be of the form abcabc

So the general form of abcabc is 1000000a+100000b+1000c+100a+10b+c

Now, abcabc = is 1000000a+100000b+1000c+100a+10b+c

By simplifying the above expression, we will get

abcabc = 1001(100a+10b+c)

Hence, the six digit number should be divisible by 1001.

(a) Competent cells

1. Depending upon the type of product, bioreactor is selected. 

2. A suitable substrate in liquid media is added at a specific temperature, pH and then diluted. 

3. The organism (microbe, animal/plant cell, sub-cellular organelle or enzyme) is added to it.

4. Then it is incubated at a specific temperature for the specified time. 

5. The incubation may either be aerobic or anaerobic. 

6. Withdrawal of product using downstream processing methods.

(b) Statement 1 is correct and Statement 2 is incorrect.

(i) If a number is divisible by 3, it must be divisible by 9. 

False, as any number following criteria of 9n + 3 or 9n + 6 violates the statement. 

For example, 6, 12,… 

(ii) If a number is divisible by 9, it must by divisible by 3. 

True, as 9 is multiple of 3. 

Hence, every number which is divisible by 9 must be divisible by 3. 

(iii) If a number is divisible by 4, it must by divisible by 8. 

False, as any number following criteria of 8n + 4 violates the statement. 

For example, 4, 12,20,…. 

(iv) If a number is divisible by 8, it must be divisible by 4. 

True, as 8 is multiple of 4. 

Hence, every number which is divisible by 8 must be divisible by 4. 

(v) A number is divisible by 18, if it is divisible by both 3 and 6. False, for example 48, which is divisible to both 3 and 6 but not divisible with 18 

(vi) If a number is divisible by both 9 and 10, it must be divisible by 90. 

True, as 90 is the GCD of 9 and 10. 

Hence, every number which is divisible by both 9 and 10, it must be divisible by 90. 

(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately. 

False, for example 6 divides 30, but 6 divides none of 13 and 17 as both are prime numbers. 

(viii) If a number divides three numbers exactly, it must divide their sum exactly. 

True, if x,y and z are three numbers, where each of x, y and z is divided by a number (say s), then (x+y+z) is divided by s 

(ix) If two number are co-prime, at least one of them must be a prime number. 

False, as 16 and 21 are co prime but none of them is prime. 

(x) The sum of two consecutive odd numbers is always divisible by 4. True.

The correct answer is option (a) 9

Explanation:

We know that the general form of abc is 100a+10b+c

Then the given number is abc – a – b – c =100a+10b+c – a – b- c

By simplifying the above expression, we will get

abc – a – b – c = 9(11a+b)

Hence, then number abc – a – b – c is divisible by 9.

The correct answer is option (d) 9

Explanation:

By simplifying the general form of abc, bca and cab, we will get

= abc+bca+cab = 111(a+b+c)

Hence, abc+bca+cab is divisible by 111 and also it is divisible by the factors of 111.

Here, 3 and 7 are the factors of 111, and a+b+c is also a factor of 111(a+b+c).

But 9 is not the factor of 111.

Blue- White Colony Selection Method is a powerful method used for screening of recombinant plasmid. In this method, a reporter gene lacZ is inserted in the vector. The lacZ encodes the enzyme P-galactosidase and contains several recognition sites for restriction enzyme.P-galactosidase breaks a synthetic substrates called X-gal (5-bromo-4-chloroindolyl- P-D- galacto-pyranoside) into an insoluble blue coloured product. If a foreign gene is inserted into lacZ, this gene will be inactivated.

Therefore, no-blue colour will develop (white) because P-galactosidase is not synthesized due to inactivation of lacZ. Therefore, the host cell containing r-DNA form white coloured colonies on the medium contain X-gal, whereas the other cells containing non-recombinant DNA will develop the blue coloured colonies. On the basis of colony colour, the recombinants can be selected.

11

Explanation:

Let “a”, “b” and “c” be the digits, then X = abc

By reversing the digits, then take Y =cba

Therefore sum of digits in X is 100a+10b+c

Sum of digits in Y is 100c+10b+a

By subtracting X and Y, we get

99(x-z) = (9)(11)(x-z)

Therefore, the number is divisible by 9 and 11.

9

Explanation:

Let “a” and “b” be the digits, then X = ab

By reversing the digits, then take Y =ba

Therefore sum of digits in X is 10a+b

Sum of digits in Y is 10b+a

By subtracting X and Y, we get

9a – 9a = 9(ab)

Therefore, the number is divisible by 9.

(1) 2 but not by 4. 

Any number which follows criteria of 4n + 2 is an example of a number divisible by 2 but not by 4. 

For example, 6 , where n= 1. 

(2) 3 but not by 6. 

Any number which follows criteria of 6n + 3 is an example of a number divisible by 3 but not by 6. 

For example, 9 , where n= 1. 

(3) 4 but not by 8. Any number which follows criteria of 8n + 4 is an example of a number divisible by 4 but not by 8. 

For example, 12 , where n= 1. 

(4) both 4 and 8 but not by 32 

Any number which follows criteria of 32n + 8 or 32n + 16 or 32n +24 is an example of a number divisible by both 4 and 8 but not by 32 For example, 40 , where n= 1.

(1) Here, we observe that 69 and 96 are having ten’s and unit place interchanged, ie they are having reverse digits. 

Hence, sum of digits is 15. 

We know that when ab + ba is divided by 11, quotient is (a + b). 

∴ The sum of 69 and 96 is divided by 11, we get 15 (sum of digits) as our quotient. 

(2) Here, we observe that 69 and 96 are having ten’s and unit place interchanged, ie they are having reverse digits. 

Hence, sum of digits is 15. 

We know that when ab + ba is divided by (a + b), quotient is 11. 

∴ The sum of 69 and 96 is divided by 15 (sum of digits) , we get 11 as our quotient.

False

Explanation:

If a number with three digits and if the unit digit is an even number, then the number is said to be an even number. A number is divisible by 5, only if the unit digit is either 0 or 5 (divisibility test of 5)

11

Explanation:

Let “a” and “b” be the digits, then X = ab

By reversing the digits, then take Y =ba

Therefore sum of digits in X is 10a+b

Sum of digits in Y is 10b+a

By adding X and Y, we get

11a+11b = 11(a+b)

Therefore, the number is divisible by 11.

True

Explanation:

In case, if a number is divisible by 6, it is also divisible by 2 and 3.

If c is an even number, then the sum of digits is divisible by 3.

True

Explanation:

If a number with two digits and the number in the unit place is even, then the number is said to be an even number and it is divisible by 2 (using the divisibility test of 2).

The number is divisible by 11 if and only if the difference between the sum of the digits in the odd places and the sum of the digits in the even places is divisible by 11. 

(a + b) – (4 + 3) = 0 (a + b) – 7 = 0 

or (a + b) – 7 = 11 a + b = 7 or a + b = 11 + 7 = 18 

(a + b) – 7 cannot be equal to 22 because it a + b – 7 = 22 then a + b = 29 

since a and b are digits their sum cannot be 29.

Magic sum is 27 

Central number is 9 

We have ⇒ 27 = 3 × 9 

Magic sum is 3 times the central number.

(c) 5′ GAATTC 3′ CTTAAG 5′

Restriction exonuclease are the restriction enzyme used to cut nucleotides from the terminal end of DNA. Whereas, restriction endonucleases cut the internal phospho diester bond with DNA molecule.

A 4 digit Palindrome i so f the form \(\bar{abba}\) sum of the digits in the odd places is a + b.

Correct option is (D) 11

A palindrome number is a number that remains same when digits are reversed.

If total number of digits are even in palindrome number.

Then difference of the sum of digits at even place and the sum of digits at odd place is 0.

Thus, it is divisible by 11.

Hence, every palindrome number with an even number of digits is divisible by 11.

Correct option is  D) 11