The product of the roots is given by c/a = 2/3.

The product of the roots is c/a = 6/1 = 6.

The product of the roots is given by c/a = 6/1 = 6.

The product of the roots is given by c/a = 24/1 = 24.

The product of the roots is given by c/a = 15/1 = 15.

proj_B(A) = (A · B / |B|^2)B = ((3*1 + 4*1) / (1^2 + 1^2))(i + j) = (7/2)(i + j) = 3.5.

DNA ligase is an enzyme that joins DNA fragments together, which is essential for creating recombinant DNA molecules in genetic engineering.

A promoter is a DNA sequence that initiates transcription of a gene, allowing for the expression of the inserted gene in the host organism.

A promoter is a DNA sequence that initiates transcription of a particular gene, driving the expression of the inserted gene in a recombinant DNA molecule.

Selectable markers are genes that confer resistance to antibiotics or other substances, allowing for the identification of cells that have successfully taken up the vector.

Selectable markers are genes that confer resistance to antibiotics or other substances, allowing researchers to identify cells that have successfully taken up the recombinant DNA.

A vernier caliper is used to measure lengths with high precision.

Biopesticides are used to control pests through natural organisms, making option 'To control pests using natural organisms' the correct answer.

CRISPR technology is primarily used for gene editing, allowing precise modifications to DNA.

DNA fingerprinting is used to identify individuals based on their unique DNA profiles, making it crucial in forensic science.

Restriction enzymes are used to cut DNA at specific sequences, which is essential for cloning and genetic engineering.

Circumference = 2πr; 62.8 = 2πr; r = 10 cm.

Area = πr²; 154 = 22/7 * r²; r² = 154 * 7/22 = 49; r = 7 units.

Circumference = 2πr; 31.4 = 2πr; r = 31.4/(2π) ≈ 5 m.

Circumference = 2πr; 62.8 = 2πr; r = 62.8/(2π) ≈ 10 cm.

Radius is half of the diameter. Therefore, radius = 14 cm / 2 = 7 cm.

For a first-order reaction, k = 0.693 / t₁/₂. Here, t₁/₂ = 10 min, so k = 0.693 / 10 = 0.0693 min⁻¹.

For a first order reaction, the rate law is directly proportional to the concentration of the reactant, hence Rate = k[A].

The rate law for a reaction is determined by the order with respect to each reactant. For a first order with respect to A and second order with respect to B, the rate law is Rate = k[A][B]^2.

For a second order reaction with respect to A, the rate law is expressed as Rate = k[A]^2.

The rate law is determined by the order of the reaction with respect to each reactant. For first order in A and second order in B, the rate law is Rate = k[A][B]^2.

For a second order reaction with respect to A, the rate law is expressed as Rate = k[A]^2.

Reactance (X_L) = 2πfL = 2π(50)(0.1) = 31.4 Ω.

The reactance of an inductor in an AC circuit is given by the formula X_L = 2πfL.

The real part of the complex number 4 + 5i is 4.