AP PGECET 2024 Biotechnology Question Paper with Answer Key PDF

Question 1:

Which of the following cells of the immune system do not perform phagocytosis?

• (1) Macrophage
• (2) Neutrophil
• (3) Eosinophil
• (4) Basophil

Which of the following cell organelles is present in animal cells and absent in plant cells?

• (1) Nucleus
• (2) Centrosome
• (3) Chloroplast
• (4) Endoplasmic reticulum

Which regulatory body oversees the guidelines for mass cultivation of animal cell culture in the United States?

• (1) FDA (Food and Drug Administration)
• (2) WHO (World Health Organization)
• (3) EMA (European Medicines Agency)
• (4) USDA (United States Department of Agriculture)

Name the cell which is recruited first at the place of infection.

• (1) NK cells
• (2) Basophils
• (3) Neutrophils
• (4) Macrophages

Prostaglandins and leukotrienes are produced by:

• (1) B cells
• (2) Mast cells
• (3) Macrophages
• (4) NK cells

The electron source for the Chemolithoheterotrophs type of microorganism is:

• (1) Sunlight
• (2) CO₂
• (3) Reduced inorganic compounds
• (4) Organic carbon

Blue-white screening is performed to select .......... in vector-based molecular cloning.

• (1) Vectors from plasmid
• (2) Gram-positive bacteria from Gram-negative bacteria
• (3) Antibiotic-resistant bacteria
• (4) Recombinant bacteria from non-recombinant bacteria

Which of the following helps in opening of DNA double helix in front of replication fork?

• (1) Topoisomerase
• (2) DNA polymerase I
• (3) DNA gyrase
• (4) DNA ligase

Nitrogen is an essential component of:

• (1) Proteins
• (2) Sugars
• (3) Carbohydrates
• (4) Lipids

Which are the major modes of active transport?

• (1) Exocytosis, endocytosis, and pumps
• (2) Simple diffusion, endocytosis, and exocytosis
• (3) Simple diffusion, facilitated diffusion, and osmosis
• (4) Exocytosis, endocytosis, and osmosis

What is the primary role of shear forces in a stirred-tank bioreactor?

• (1) Enhance oxygen transfer to cells
• (2) Improve nutrient uptake by cells
• (3) Prevent cell aggregation
• (4) Damage cells and affect cell viability

The following process involves transferring naked DNA fragments from the surroundings into the bacteria:

• (1) Transfection
• (2) Transformation
• (3) Transduction
• (4) Conjugation

............ is stirred with sugar beet juice in batch stirred tank reactors to remove raffinose.

• (1) Kluyveromyces lactis
• (2) Bacillus licheniformis
• (3) Mortierella vinacea
• (4) Bacillus acidopullulyticus

A purified protein sample contains 10 µg of protein and has an enzyme activity of 1 mole of ATP synthesized/sec (1 unit). What is the specific activity of the final purified sample?

• (1) 1,000 units/mg
• (2) 10,000 units/mg
• (3) 100,000 units/mg
• (4) 1,000,000 units/mg

.............. bacterium can withstand the dosage of radiation, which are several times higher than what human cells can tolerate.

• (1) Escherichia coli
• (2) Conus magus
• (3) Deinococcus radiodurans
• (4) Staphylococcus aureus

Gel permeation chromatography is based on:

• (1) Size
• (2) Charge
• (3) Affinity
• (4) Sedimentation rate

The order for the construction of cDNA fragment from mRNA is to:

• (1) bind oligo-dT, treatment with reverse transcriptase, digest with RNase, add G residues to the 3' end, bind oligo-dC, treat with DNA polymerase
• (2) treat with reverse transcriptase, digest with RNase, add G residues to the 3' end, bind oligo-dC, treat with DNA polymerase and bind oligo-dT
• (3) digest with RNase, add G residues to the 3' end, treat with reverse transcriptase, add G residues to the 3' end and treat with DNA polymerase
• (4) bind oligo-dC, treat with reverse transcriptase, digest with RNase, add G residues to the 3' end, bind oligo-dT and treat with DNA polymerase

When populations are small, gene frequencies can change from generation to generation and some alleles may become fixed in a population. This is called ............

• (1) Assortative mating
• (2) Inbreeding
• (3) Heterosis
• (4) Genetic drift

Which tool is utilized for motif identification?

• (1) BLAST
• (2) COPIA
• (3) PROSPECT
• (4) FASTA

Which one of the following is required for the development of B-cells in the bone marrow?

• (1) Stromal cells
• (2) Dendritic cells
• (3) Kupffer cells
• (4) NK cells

Which of the following is untrue about the Loop Modeling Step?

• (1) The gaps cannot be directly modeled
• (2) Loop modeling is required for closing the gaps
• (3) In the sequence alignment for modeling, there are no regions producing gaps in sequence alignment
• (4) In the sequence alignment for modeling, there are often regions caused by insertions and deletions producing gaps in sequence alignment

With regard to the ABO blood group typing system, if a father is of blood group AB and a mother is of blood group O, what are the possible blood groups that a son of the couple have?

• (1) O only
• (2) Either A or B
• (3) AB only
• (4) AB, A, B, and O

Identify autoimmune disorder

• (1) Alzheimer’s disease
• (2) Rheumatoid arthritis
• (3) Chronic gum disease
• (4) AIDS

Which of the following is NOT correct about FASTA?

• (1) It was in fact the first database similarity search tool developed, preceding the development of BLAST
• (2) FASTA uses a ‘hashing’ strategy to find matches for a short stretch of identical residues with a length of k
• (3) The string of residues is known as blocks
• (4) It stands for FAST ALL

What is the function of the lysozyme present in mucus?

• (1) Degrade bacterial peptidoglycan
• (2) Bind to iron
• (3) To generate toxics
• (4) Secretes an antibody

Antigen binding sites are present in ...............

• (1) Fab regions of an antibody
• (2) Fc region of an antibody
• (3) Only in the light chain
• (4) Only in the heavy chain

Who is the Father of Microbiology?

• (1) Gregor Johann Mendel
• (2) Aristotle
• (3) Antonie van Leeuwenhoek
• (4) Louis Pasteur

The production of secondary metabolites requires the use of ............

• (1) Meristem tips
• (2) Protoplasts
• (3) Axillary buds
• (4) Cell suspensions

The average size of plant mitochondrial DNA range between .............. Kilo base pairs.

• (1) 2 to 20
• (2) 20 to 200
• (3) 200 to 2000
• (4) 2000 to 20000

Which of the following technique is commonly used in animal cloning?

• (1) Polymerase Chain Reaction (PCR)
• (2) CRISPR-Cas9
• (3) Somatic Cell Nuclear Transfer (SCNT)
• (4) Gel Electrophoresis

The computational methodology that tries to find the best matching between two molecules, a receptor and a ligand, is called?

• (1) RASMOL
• (2) Molecular matching
• (3) Molecular modelling
• (4) Molecular docking

Sodium-Potassium pump present on the cell membrane is a classic example of ..............

• (1) Primary active transport
• (2) Primary passive transport
• (3) Secondary active transport
• (4) Secondary passive transport

............. is NOT an indigenous microbe used for bioremediation.

• (1) Pseudomonas aeruginosa
• (2) Piscirickettsia salmonis
• (3) Phanerochaete sordida
• (4) E. coli

Lack of independent assortment of two genes is due to .............

• (1) Recombination
• (2) Crossing over
• (3) Linkage
• (4) Repulsion

In a batch process, 70 Kg of H₂O and 10 Kg of NaOH and some other reactants enters the vessel. If 100 Kg of the product leaves the vessel, what is the percentage of H₂O in the product?

• (1) 10%
• (2) 30%
• (3) 70%
• (4) 100%

Cell division occurs in ............

• (1) S phase
• (2) G₁ phase
• (3) G₂ phase
• (4) M phase

Isoschizomers recognize ..................

• (1) Same recognition sequence but different recognition site
• (2) Same recognition site and same recognition sequence
• (3) Same recognition site and different recognition sequence
• (4) Different recognition site and different recognition sequence

In which phase is penicillin produced?

• (1) Lag phase
• (2) Log phase
• (3) Exponential phase
• (4) Stationary phase

All of the following interactions occur between antigen-antibody reaction except .................

• (1) Ionic bond
• (2) Covalent bond
• (3) Hydrogen bond
• (4) Vander waal force

One of the following is NOT an antigen presenting cell.

• (1) B cells
• (2) Dendritic cells
• (3) Macrophages
• (4) T cells

The melting temperature (Tm) of DNA is higher when the content of

• (1) A: T base pair is lower
• (2) G:C base pair is lower
• (3) G:C base pair is higher
• (4) A: T base pair is higher

The batch fermentation can be used to produce

• (1) Organic acids
• (2) Amino acids
• (3) Single cell protein
• (4) Antibiotics

A living microbe with reduced virulence that is used for vaccination is considered as

• (1) A toxoid
• (2) Dormant
• (3) Virulent
• (4) Attenuated

In homology modeling, the most suitable BLAST is

• (1) PSI-BLAST
• (2) PHI-BLAST
• (3) Geo-BLAST
• (4) Rp-BLAST
• (1) PSI-BLAST (Position-Specific Iterative BLAST):
   

Genotype of dominant plant can be determined by

• (1) Pedigree analysis
• (2) Back cross
• (3) Test cross
• (4) Dihybrid cross
• (1) Test Cross:
   

The presence of transposons can lead to genome instability due to their ability to cause ..........

• (1) Gene disruption
• (2) Gene regulation
• (3) Chromosome inversions
• (4) DNA replication errors

T cells and macrophages are involved in which type of hypersensitivity?

• (1) Type I
• (2) Type II
• (3) Type III
• (4) Type IV

Polymorphism in RAPD is observed because ................

• (1) DNA used is from different chromosomes of same species
• (2) DNA used is from same chromosomes of same species
• (3) DNA used is from different chromosomes of different species
• (4) DNA used is from complementary chromosomes of same species

Which of the following gas is produced in large amounts during sludge digestion?

• (1) Methane
• (2) Carbon dioxide
• (3) Hydrogen
• (4) Nitrogen

.............. bacteria are cold loving and have optimal temperature for growth lower than 15°C.

• (1) Mesophilic
• (2) Thermophilic
• (3) Psychrophilic
• (4) Acidophilic

Which of the following is true about phosphodiester linkage?

• (1) 3’-phosphate group of one nucleotide unit is joined to the 5’-hydroxyl group of the next nucleotide
• (2) 3’-phosphate group of one nucleotide unit is joined to the 3’-hydroxyl group of the next nucleotide
• (3) 5’-phosphate group of one nucleotide unit is joined to the 3’-hydroxyl group of the next nucleotide
• (4) 5’-phosphate group of one nucleotide unit is joined to the 5’-hydroxyl group of the next nucleotide

Which one of the following techniques can be used to compare the expression of a large number of genes in two biological samples in a single experiment?

• (1) Polymerase chain reaction
• (2) DNA microarray
• (3) Northern hybridization
• (4) Southern hybridization

Which is the major factor(s) determining whether glucose is oxidized by aerobic or anaerobic glycolysis?

• (1) Presence of high AMP
• (2) NADH and the ATP/ADP ratio
• (3) Ca\(^2\)
• (4) FADH\(_2\)

The best way to determine the location of protein in the purification scheme is to measure the

• (1) Rate of ATP synthesis
• (2) Changes in the refractive index
• (3) UV absorption
• (4) Mass spectroscopy of the protein

The reduction of NADP\(^+\) to NADPH occurs in

• (1) HMP shunt
• (2) Calvin Cycle
• (3) Glycolysis
• (4) EMP (1988)

Which is the first antibody produced in the primary immune response?

• (1) IgM
• (2) IgA
• (3) IgG
• (4) IgD

Saul Needleman and Christian Wansch postulated an algorithm which is useful for

• (1) Multiple sequence alignment
• (2) Global alignment of sequence
• (3) Local alignment of sequence
• (4) Progressive alignment

Parthenogenic embryos in plants are those which are formed by

• (1) Unfertilized eggs
• (2) Fertilized eggs
• (3) Sporophytic cells
• (4) Male gametophyte

The Yield factor (Y) is the measure of the efficiency of

• (1) Conversion of anyone substrate into biomass
• (2) Conversion of all the substrates into biomass
• (3) The affinity of an enzyme to the substrate
• (4) Number of microbes which produced the biomass

Which of the following function of DNA is necessary for the purpose of evolution?

• (1) Mutation
• (2) Replication
• (3) Translation
• (4) Transcription

The enzymes required for the glycolysis pathway are localized in

• (1) Rough endoplasmic reticulum
• (2) Smooth endoplasmic reticulum
• (3) Cytoplasm
• (4) Mitochondria

All of the following statements about hybridoma technology are true except

• (1) Specific antibody-producing cells are integrated with myeloma cells
• (2) Myeloma cells with mutation in salvage pathway grow well in HAT medium
• (3) Aminopterin, a folate antagonist, inhibits de-novo pathway
• (4) HGPRTase and thymidylate synthetase are required for the salvage pathway

The bench-top bioreactor comes under which type of bioreactor?

• (1) Solid-state bioreactor
• (2) Photo bioreactors
• (3) Airlift bioreactors
• (4) Stirred tank bioreactors

Cryoprotectants are used to ................ in cryopreservation.

• (1) Prevent ice formation
• (2) Increase ice formation
• (3) Increase the freezing temperature
• (4) Reduce the freezing temperature

Which one of the following can NOT be a limiting substrate if Monod's growth kinetics is applicable?

• (1) Extracellular carbon source
• (2) Extracellular nitrogen source
• (3) Dissolved oxygen
• (4) Intracellular carbon source

Which of the following restriction enzyme produce blunt ends?

• (1) Sal I
• (2) Eco RV
• (3) Xho I
• (4) Hind III

The biomass concentration is at the highest level in which phase?

• (1) Lag phase
• (2) Log phase
• (3) Exponential phase
• (4) Stationary phase

What is the size of the human genome?

• (1) 3 billion base pairs
• (2) 2 billion base pairs
• (3) 4 billion base pairs
• (4) 6 trillion base pairs

The following bacterium is considered as a natural genetic engineer:

• (1) E. coli
• (2) Pseudomonas aeruginosa
• (3) Agrobacterium tumefaciens
• (4) Xanthomonas axonopodis

Which is the first enzyme to be immobilized by adsorption method?

• (1) Protease
• (2) Glucose isomerase
• (3) Invertase
• (4) Amylase

Buffers are mixtures of a ..............

• (1) Weak acid and weak base
• (2) Weak acid and their conjugate base
• (3) Strong base and their conjugate acid
• (4) Strong acid and weak base

RNA interference helps in

• (1) Cell proliferation
• (2) Micropropagation
• (3) Cell defence
• (4) Cell differentiation

Which among the following is a pathogenic alga for humans?

• (1) Cephaleuros
• (2) Acanthopeltis
• (3) Chlorella
• (4) Prototheca

What is the primary function of the protein collagen in the human body?

• (1) Structural support in connective tissues
• (2) Enzyme catalysis
• (3) Transport of oxygen in the blood
• (4) Muscle contraction

Match separation methods in Group I with associated properties in Group II.


GROUP-I                GROUP-II
 
A. Centrifugation   (1) Density
 
B. Dialysis             (2) Diffusivity
 
C. Solvent extraction   (3) Size
 
D. Ultrafiltration      (4) Solubility
 

• (1) A-4, B-2, C-1, D-3
• (2) A-3, B-1, C-2, D-4
• (3) A-1, B-3, C-2, D-4
• (4) A-1, B-2, C-4, D-3

Logistic growth model describes which type of growth?

• (1) Product-based growth
• (2) Non-growth
• (3) Substrate-based growth
• (4) Maintenance-based growth

A culture vessel in which physical, physicochemical and physiological conditions, as well as cell concentration, are kept constant is known as

• (1) Cell concentrator
• (2) Biostat
• (3) Batch bioreactor
• (4) Incubator

How many molecules of ATP are required to fix one molecule of nitrogen?

• (1) 12
• (2) 20
• (3) 6
• (4) 16

Which of the following can be used as a measure to construct a linkage map of the Hfr chromosome?

• (1) Frequency of recombination
• (2) Time of entry
• (3) Locus of mutation
• (4) Transfer of F factor

Microtubules are composed of

• (1) Tubulin
• (2) Actin
• (3) Niacin
• (4) Myosin

Which of these would not be used to introduce DNA in animal cells?

• (1) Liposomes
• (2) Electroporation
• (3) Microinjection
• (4) Ti-plasmid

Where does respiration take place in woody plants?

• (1) Phloem tissue
• (2) Peripheral tissue
• (3) Lenticles
• (4) Xylem tissues

Which of the following signal molecules does not interact with cell surface receptors?

• (1) Insulin
• (2) Gastrin
• (3) Glucagon
• (4) Testosterone

Which promoter is used for yeast cell expression?

• (1) Polyhedrin
• (2) Alcohol oxidase
• (3) Cauliflower mosaic virus 35S
• (4) T7 polymerase

Which is the source of energy used to make ATP by oxidative phosphorylation?

• (1) Oxygen
• (2) High-energy phosphate bonds
• (3) The proton motive force
• (4) Inorganic phosphate

Which of the following transcribes protein-coding genes in plants?

• (1) DNA polymerase II
• (2) DNA polymerase I
• (3) RNA polymerase II
• (4) RNA polymerase I

Error-free repair of double strand breaks in DNA is accomplished by

• (1) Non-homologous end-joining
• (2) Base excision repair
• (3) Non-homologous recombination
• (4) Mismatch repair

Which part of the compound microscope helps in gathering and focusing light rays on the specimen to be viewed?

• (1) Condenser lens
• (2) Magnifying lens
• (3) Objective lens
• (4) Eyepiece lens

Histopathology deals with

• (1) Cells
• (2) Tissues
• (3) Muscles
• (4) Organs

Which solution is used to maintain sterility in laboratories?

• (1) Sodium chloride
• (2) Sodium hypochlorite
• (3) Sodium cyanide
• (4) Sodium sulphate

Enzymes that remove nucleotides one at a time from the end of a DNA molecule are called

• (1) Ligases
• (2) Exonucleases
• (3) Endonucleases
• (4) DNases

Which of the following is NOT a thermostable polymerase?

• (1) pfu polymerase
• (2) Taq polymerase
• (3) Vent polymerase
• (4) DNA polymerase III

Cell theory was proposed by ...........?

• (1) Theodor Schwann, Watson and Robert Hooke
• (2) Theodor Schwann, Matthias Schleiden and Robert Hooke
• (3) Theodor Schwann, Matthias Schleiden and Rudolf Virchow
• (4) Theodor Schwann, Rudolf Virchow and Robert Hooke

Which of the following polysaccharide is not present in the eukaryotic plant cell wall, it is __?

• (1) Chitin
• (2) Hemicellulose
• (3) Pectin
• (4) Cellulose

Which of the following cells are pluripotent?

• (1) Embryonic stem cells
• (2) Nucleosomes
• (3) Hepatocytes
• (4) Neurons

Which leaching agent is used for the slow decomposition of refractory gold ores?

• (1) Nickel
• (2) Sulphur
• (3) Cyanide
• (4) Molybdenum

A colour-blind mother and normal father would have

• (1) Colour blind sons and daughters
• (2) Colour blind sons and normal/carrier daughters
• (3) All normal
• (4) All colour blind

.................... enzyme that catalyzes the transfer of the gamma-phosphate from ATP to the 5'-OH group of single- and double-stranded DNA, RNA, oligonucleotides, and nucleoside 3'-monophosphates.

• (1) T4 polynucleotide kinase
• (2) Endonuclease
• (3) Exonuclease
• (4) DNA ligase

Which of the following is not part of the growth medium for animal cell culture?

• (1) Starch
• (2) Serum
• (3) Carbon source
• (4) Inorganic salts

Which technique is used to separate and analyze DNA fragments that are of different lengths?

• (1) Gel electrophoresis
• (2) DNA sequencing
• (3) Site-directed mutagenesis
• (4) Polymerase chain reaction (PCR)

All the statements are true regarding RFLP and RAPD except

• (1) RAPD is a quick method compared to RFLP
• (2) RFLP is more reliable than RAPD
• (3) Species specific primers are required for RAPD
• (4) Radioactive probes are not required in RAPD

The correct order of taxonomic groups from higher to lower rank is?

• (1) Kingdom -- Order -- Class -- Family -- Division -- Genus -- Species
• (2) Kingdom -- Order -- Class -- Division -- Family -- Genus -- Species
• (3) Kingdom -- Order -- Division -- Family -- Class -- Genus -- Species
• (4) Kingdom -- Division -- Class -- Order -- Family -- Genus -- Species

The process by which extracellular messages translate into intracellular changes is termed

• (1) Cell transport
• (2) Cell adhesion
• (3) Signal transduction
• (4) Cell transformation

Abscisic acid regulates \hspace{2cm}

• (1) Wilting of leaves and seed dormancy
• (2) Cell division
• (3) Cell elongation and cell wall formation
• (4) Shoot elongation

Vero cell line is obtained from kidney cells of

• (1) African green monkey
• (2) Chinese hamster
• (3) Calf
• (4) Swine

Phylogenetic relationships can be shown by

• (1) Dendrogram
• (2) Gene Bank
• (3) Data retrieving tool
• (4) Data search tool

Bacteriophages that can enter into stable, long-term relationships with their hosts are called

• (1) Lytic phages
• (2) Defective phages
• (3) Virulent phages
• (4) Temperate phages

For one of the following, recombinant vaccine is available in the market

• (1) Hepatitis B virus
• (2) Polio virus
• (3) Rubella virus
• (4) Dengue virus

The following system has non-trivial solution \( px + qy + rz = 0, qx + ry + pz = 0, rx + py + qz = 0 \) then which one of the following is TRUE?

• (1) \( p - q + r = 0 \) or \( p = q = -r \)
• (2) \( p + q - r = 0 \) or \( p = -q = r \)
• (3) \( p + q + r = 0 \) or \( p = q = r \)
• (4) \( p - q - r = 0 \) or \( p = -q = -r \)

If A is \[ A = \begin{bmatrix} 8 & 7
5 & 6 \end{bmatrix} \]
then the value of \( det(A^{121} - A^{120}) = ? \)

• (1) 0
• (2) 1
• (3) 120
• (4) 121

If \[ A = \begin{bmatrix} 2 & 3 & 4
0 & 4 & 2
0 & 0 & 3 \end{bmatrix} \]
then the eigenvalues of \( adj(A) \) are

• (1) 12, 5, 3
• (2) 12, 6, 8
• (3) 10, 2, 3
• (4) 2, 3, 4

Let A be square matrix of order m, then nullity of A is

• (1) \( 2 \cdot Rank of [A] - m \)
• (2) \( m + Rank of [A] \)
• (3) \( m \)
• (4) \( m - Rank of [A] \)

The function \( (1 + \cos x) \sin x \) is maximum at

• (1) \( x = \frac{\pi}{3} \)
• (2) \( x = \pi \)
• (3) Both at \( x = \frac{\pi}{3} \) and \( x = \pi \)
• (4) \( x = 2\pi \)

Evaluate the limit \[ \lim_{x \to \infty} \frac{\sin x}{x} \]

• (1) 1
• (2) -1
• (3) \( \infty \)
• (4) zero

The integrating factor of equation \[ \sec^2 y \frac{dy}{dx} + x \tan y = x^3 \] is

• (1) \( e^{x^2/2} \)
• (2) \( e^{-x^2/2} \)
• (3) \( e^{x/2} \)
• (4) \( e^{-x/2} \)

Consider the differential equation \[ \frac{dy}{dx} + a y = e^{-bt} \quad with \quad y(0) = 0. \]
Then the Laplace transform of \( y(t) \) is

• (1) \( \frac{1}{(s+a)(s+b)} \)
• (2) \( \frac{1}{(s+a)b} \)
• (3) \( \frac{1}{a(s+b)} \)
• (4) \( \frac{e^{-a} - e^{-b}}{b - a} \)

Let \( u(x,t) \) satisfy the initial boundary value problem \[ \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2}, \quad x \in (0,1), t > 0 \]
given that \[ u(x, 0) = \sin(\pi x), \quad x \in [0,1], \quad u(0,t) = u(1,t) = 0, \quad t > 0. \]
Then \( u \left( x, \frac{1}{\pi^2} \right) \) for \( x \in (0,1) \) is

• (1) \( e \sin(\pi x) \)
• (2) \( e^{-1} \sin(\pi x) \)
• (3) \( \sin(\pi x) \)
• (4) \( \sin(\pi^{-1} x) \)

The standard deviation for the following frequency is
Class Interval   Frequency
0-4                         4
4-8                          8
8-12                        2
12-16                      1
 

• (1) 3.20
• (2) 3.22
• (3) 3.26
• (4) 3.28

The probability of getting 4 heads in 6 tosses of a fair coin is.

• (1) \( \frac{2}{3} \)
• (2) \( \frac{1}{64} \)
• (3) \( \frac{15}{64} \)
• (4) \( \frac{3}{64} \)

Solution of the differential equation \((D^2 + 9)y = \sin 2x\) is:

• (1) \( y = a \cos 3x + b \sin 3x + \frac{1}{5} \sin 2x \)
• (2) \( y = a \cos 9x + b \sin 9x + \frac{1}{5} \sin 2x \)
• (3) \( y = a \cos 3x + b \sin 3x + \frac{1}{5} \cos 2x \)
• (4) \( y = a \cos 3x + b \sin 3x - \frac{1}{9} \sin 2x \)