A convex lens has a focal length of 20 cm. An object is placed at a distance of 30 cm from the lens. What is the nature and position of the image formed?
A. Real, inverted, 60 cm from the lens on the opposite side.
B. Virtual, erect, 60 cm from the lens on the same side.
C. Real, inverted, 30 cm from the lens on the opposite side.
D. Virtual, erect, 30 cm from the lens on the same side.
Correct Answer: A Using the lens formula 1/f = 1/v - 1/u, where f = 20 cm and u = -30 cm (object distance is negative). 1/20 = 1/v - 1/(-30) => 1/v = 1/20 - 1/30 = (3-2)/60 = 1/60. So, v = 60 cm. Since v is positive, the image is real and formed on the opposite side. The magnification m = v/u = 60/(-30) = -2, indicating an inverted image.
Q2. Physics
The direction of induced current is given by:
A. Ampere's law
B. Biot-Savart law
C. Lenz's law
D. Ohm's law
Correct Answer: C Lenz's law determines direction: induced current opposes change in flux.
Q3. Biology
Which of these is a vestigial organ in humans?
A. Liver
B. Heart
C. Appendix
D. Kidney
Correct Answer: C Appendix is a vestigial organ (remnant of larger cecum in herbivore ancestors).
Q4. Physics
A convex mirror always forms which type of image?
A. Real and inverted
B. Virtual and erect
C. Real and erect
D. Virtual and inverted
Correct Answer: B Convex mirrors always form virtual, erect, and diminished images regardless of object position.
Q5. Physics
A body of mass 2 kg is moving with velocity 3 m/s. Its kinetic energy is:
A. 3 J
B. 9 J
C. 6 J
D. 18 J
Correct Answer: B KE = ½mv² = ½ × 2 × 9 = 9 J.
Q6. Physics
A wire of length L and area A has resistance R. If length is halved and area doubled, new resistance is:
A. R/2
B. R/4
C. R
D. 2R
Correct Answer: B R' = Ï(L/2)/(2A) = (ÏL/A)/4 = R/4.
Q7. Physics
A particle of mass m is released from rest at a height h above a horizontal surface. If it falls under gravity, and experiences a resistive force proportional to its velocity (F_r = -kv), where k is a positive constant, what is the terminal velocity it approaches?
A. mg/k
B. √(2gh)
C. k/mg
D. mgh/k
Correct Answer: A Terminal velocity is reached when the net force on the particle is zero. The forces acting on the particle are gravity (mg downwards) and the resistive force (-kv upwards). Thus, mg - kv_t = 0, which gives v_t = mg/k.
Q8. Chemistry
Which of these is a double displacement reaction?
A. 2H₂ + O₂ → 2H₂O
B. NaCl + AgNO₃ → AgCl + NaNO₃
C. Zn + H₂SO₄ → ZnSO₄ + H₂
D. CaCO₃ → CaO + CO₂
Correct Answer: B Double displacement: two compounds exchange ions → new compounds.
Q9. Biology
During DNA replication, which enzyme is responsible for synthesizing the new DNA strand by adding nucleotides complementary to the template strand?
A. DNA ligase
B. DNA helicase
C. DNA polymerase
D. Primase
Correct Answer: C During DNA replication, several enzymes play crucial roles:* **DNA ligase:** Joins the Okazaki fragments on the lagging strand by forming phosphodiester bonds.* **DNA helicase:** Unwinds the DNA double helix by breaking the hydrogen bonds between complementary base pairs, creating the replication fork.* **DNA polymerase:** This is the primary enzyme responsible for synthesizing new DNA strands. It adds deoxyribonucleotides one by one to the growing DNA strand, using the existing template strand as a guide to ensure complementary base pairing (A with T, G with C).* **Primase:** Synthesizes short RNA primers, which are necessary for DNA polymerase to initiate DNA synthesis, as DNA polymerase cannot start a new strand from scratch.
Q10. Physics
A thin uniform ring of mass M and radius R is rotating about an axis perpendicular to its plane and passing through its center with an angular velocity ω. Two point masses, each of mass m, are gently attached at diametrically opposite points on the ring. The new angular velocity of the system will be:
A. Mω / (M + 2m)
B. Mω / (M + m)
C. (M + 2m)ω / M
D. Mω / (M + m/2)
Correct Answer: A According to the principle of conservation of angular momentum:Initial angular momentum (L_initial) = I_initial * ωFor the ring, I_initial = MR²So, L_initial = MR²ωWhen two point masses 'm' are attached at diametrically opposite points, the new moment of inertia (I_final) will be:I_final = I_ring + I_two_point_masses = MR² + mR² + mR² = (M + 2m)R²Let the new angular velocity be ω'.Final angular momentum (L_final) = I_final * ω' = (M + 2m)R²ω'Equating initial and final angular momentum:MR²ω = (M + 2m)R²ω'ω' = MR²ω / ((M + 2m)R²)ω' = Mω / (M + 2m)
Q11. Physics
A body starts from rest and moves with uniform acceleration of 2 m/s². The distance covered in 5 seconds is:
A. 10 m
B. 25 m
C. 50 m
D. 5 m
Correct Answer: B s = ut + ½at² = 0 + ½ × 2 × 25 = 25 m.
Q12. Biology
A person suffers from abnormally high blood glucose levels, frequent urination, and excessive thirst. Which of the following conditions is most likely causing these symptoms?
A. Diabetes insipidus
B. Hypothyroidism
C. Diabetes mellitus
D. Addison's disease
Correct Answer: C The symptoms described are classic indicators of Diabetes Mellitus.* **High blood glucose levels (hyperglycemia):** This is the hallmark of diabetes mellitus, caused by insufficient insulin production or insulin resistance, leading to glucose accumulation in the blood.* **Frequent urination (polyuria):** High glucose levels in the blood lead to glucose excretion in the urine, drawing water with it due to osmosis, resulting in increased urine output.* **Excessive thirst (polydipsia):** The loss of fluids through frequent urination leads to dehydration, triggering a sensation of intense thirst.Let's look at the other options:* **Diabetes insipidus:** Characterized by frequent urination and thirst, but it is due to a deficiency of ADH (vasopressin) or kidney's inability to respond to ADH, and does not involve high blood glucose levels.* **Hypothyroidism:** Caused by low thyroid hormone levels, leading to symptoms like weight gain, fatigue, cold intolerance, and slow metabolism, not primarily high blood glucose.* **Addison's disease:** Results from adrenal insufficiency, affecting cortisol and aldosterone production, leading to symptoms like fatigue, weight loss, low blood pressure, and skin hyperpigmentation, not typically high blood glucose.
Q13. Chemistry
The correct order of increasing acidic strength for the following compounds is:
A.
B.
C.
D.
Correct Answer: B Ethanol is a very weak acid. Phenol is more acidic than ethanol due to resonance stabilization of the phenoxide ion. Acetic acid is a carboxylic acid, much stronger than phenol. Chloroacetic acid is more acidic than acetic acid due to the electron-withdrawing inductive effect (-I effect) of the chlorine atom, which stabilizes the carboxylate anion further. Therefore, the order is Ethanol < Phenol < Acetic acid < Chloroacetic acid.
Q14. Chemistry
Which of the following is a saturated hydrocarbon?
A. Câ‚‚Hâ‚„
B. C₃H₈
C. Câ‚‚Hâ‚‚
D. C₆H₆
Correct Answer: B Propane (C₃H₈) follows CₙH₂ₙ₊₂ → saturated alkane.
Q15. Chemistry
Which of the following is NOT a polymer?
A. Nylon
B. Cellulose
C. Glucose
D. PVC
Correct Answer: C Glucose is a monomer (monosaccharide), not a polymer. Nylon, cellulose, PVC are polymers.
Q16. Chemistry
Which of the following reagents would distinguish between ethanal and propanone?
A. Tollen's reagent
B. Fehling's solution
C. Benedict's solution
D. All of the above
Correct Answer: D Ethanal (CH3CHO) is an aldehyde, while propanone (CH3COCH3) is a ketone. Aldehydes can be easily oxidized to carboxylic acids by mild oxidizing agents, whereas ketones are generally resistant to oxidation by mild agents. Tollen's reagent (ammoniacal silver nitrate), Fehling's solution (alkaline solution of CuSO4 and sodium potassium tartrate), and Benedict's solution (alkaline solution of CuSO4 and sodium citrate) are all mild oxidizing agents used to detect aldehydes.Ethanal, being an aldehyde, will give a positive test with Tollen's reagent (forming a silver mirror), Fehling's solution (forming a red precipitate of Cu2O), and Benedict's solution (forming a red precipitate of Cu2O).Propanone, being a ketone, will not react with any of these mild oxidizing agents.Therefore, all the listed reagents can distinguish between ethanal and propanone.
Q17. Chemistry
Which catalyst is used in the Haber process for ammonia synthesis?
A. Vanadium pentoxide
B. Iron
C. Nickel
D. Platinum
Correct Answer: B Haber process uses finely divided iron with promoters (K₂O, Al₂O₃) as catalyst.
Q18. Biology
Which of these is a prokaryote?
A. Amoeba
B. Bacteria
C. Yeast
D. Paramecium
Correct Answer: B Bacteria are prokaryotes (no membrane-bound nucleus/organelles).
Q19. Physics
Which of the following has the highest specific heat capacity?
A. Iron
B. Copper
C. Water
D. Lead
Correct Answer: C Water has the highest specific heat capacity (4200 J/kg°C) among common substances.
Q20. Chemistry
Which of the following is a noble gas?
A. Hydrogen
B. Nitrogen
C. Argon
D. Chlorine
Correct Answer: C Argon (Ar) is a noble gas in Group 18 with a full valence shell.
Q21. Biology
DNA replication is which type of process?
A. Conservative
B. Semiconservative
C. Dispersive
D. Random
Correct Answer: B DNA replication follows the semiconservative model as demonstrated by Meselson and Stahl.
Q22. Chemistry
Which of these is a greenhouse gas?
A. Nâ‚‚
B. Oâ‚‚
C. CHâ‚„
D. Hâ‚‚
Correct Answer: C Methane (CH₄) is a potent greenhouse gas (~25× more effective than CO₂).
Q23. Biology
The pigment responsible for skin color is:
A. Chlorophyll
B. Haemoglobin
C. Melanin
D. Carotene
Correct Answer: C Melanin produced by melanocytes determines skin, hair, and eye color.
Q24. Physics
If the speed of light is 3 × 10⸠m/s, the distance traveled by light in one year (light year) is approximately:
A. 9.46 × 10¹² km
B. 9.46 × 10¹² km
C. 9.46 × 10¹ⵠkm
D. 3 × 10⸠km
Correct Answer: B 1 light year = 9.46 × 10¹² km.
Q25. Chemistry
The most stable allotrope of carbon is:
A. Diamond
B. Graphite
C. Fullerene
D. Coal
Correct Answer: B Graphite is the most stable allotrope of carbon at room temperature.
Correct Answer: C Ideal voltmeter has infinite resistance to draw zero current.
Q27. Chemistry
Which of the following shows paramagnetism?
A. Hâ‚‚
B. Nâ‚‚
C. Oâ‚‚
D. Fâ‚‚
Correct Answer: C O₂ has two unpaired electrons in its MO configuration → paramagnetic.
Q28. Physics
The reason of mirage in desert is:
A. Reflection
B. Total internal reflection
C. Diffraction
D. Interference
Correct Answer: B Mirage occurs due to total internal reflection of light in layers of different refractive indices.
Q29. Physics
A solid cylinder of mass M and radius R rolls without slipping on a horizontal surface with a linear velocity v. The kinetic energy of the cylinder is:
A. (1/2)Mv^2
B. (3/4)Mv^2
C. Mv^2
D. (1/4)Mv^2
Correct Answer: B The total kinetic energy (KE_total) of a body rolling without slipping is the sum of its translational kinetic energy (KE_translational) and rotational kinetic energy (KE_rotational).KE_total = KE_translational + KE_rotationalKE_translational = (1/2)Mv^2KE_rotational = (1/2)Iω^2For a solid cylinder, the moment of inertia I = (1/2)MR^2.For rolling without slipping, the linear velocity v and angular velocity ω are related by v = Rω, so ω = v/R.Substituting these into the rotational kinetic energy equation:KE_rotational = (1/2) * ((1/2)MR^2) * (v/R)^2KE_rotational = (1/4)MR^2 * (v^2/R^2)KE_rotational = (1/4)Mv^2Now, sum the translational and rotational kinetic energies:KE_total = (1/2)Mv^2 + (1/4)Mv^2KE_total = (2/4)Mv^2 + (1/4)Mv^2KE_total = (3/4)Mv^2
Q30. Physics
Which of the following is a scalar quantity?
A. Force
B. Velocity
C. Energy
D. Acceleration
Correct Answer: C Energy has magnitude only (no direction), hence scalar. Force, velocity, acceleration are vectors.