These essential MCQ questions are selected from the most important topics in the KVPY (Kishore Vaigyanik Protsahan Yojana) aptitude test 2026, funded by the Department of Science and Technology, Government of India. Sections include Physics, Chemistry, Biology and Mathematics for SX (Class 12), SA (Class 11) and SB (1st year UG) streams. For truely unlimited daily MCQ practice, visit Vooo AI Education.
🔭 KVPY Science
1KVPY fellowship is awarded to pursue research in:
Answer: B — Basic science subjects
KVPY (Kishore Vaigyanik Protsahan Yojana) is a national fellowship programme funded by DST (Department of Science and Technology) to encourage students to pursue research careers in basic sciences — Physics, Chemistry, Biology and Mathematics. Fellows receive monthly stipends and contingency grants throughout their BSc/BS/MS/Integrated MSc studies.
KVPY (Kishore Vaigyanik Protsahan Yojana) is a national fellowship programme funded by DST (Department of Science and Technology) to encourage students to pursue research careers in basic sciences — Physics, Chemistry, Biology and Mathematics. Fellows receive monthly stipends and contingency grants throughout their BSc/BS/MS/Integrated MSc studies.
2The De Broglie wavelength of a particle is given by λ = h/mv. If mass doubles and velocity halves:
Answer: A — Wavelength stays same
λ = h/mv. If mass doubles (2m) and velocity halves (v/2), then mv = 2m × v/2 = mv (unchanged). Therefore λ = h/mv remains the same. De Broglie wavelength depends on momentum (p = mv), not mass or velocity individually. This concept is fundamental to quantum mechanics and wave-particle duality.
λ = h/mv. If mass doubles (2m) and velocity halves (v/2), then mv = 2m × v/2 = mv (unchanged). Therefore λ = h/mv remains the same. De Broglie wavelength depends on momentum (p = mv), not mass or velocity individually. This concept is fundamental to quantum mechanics and wave-particle duality.
3The hybridisation of carbon in benzene (C₆H₆) is:
Answer: B — sp²
Each carbon in benzene is sp² hybridised, forming three sigma bonds (two C-C and one C-H) and contributing one p-orbital electron to the delocalised π system. The 6 p-orbital electrons form a delocalised π cloud above and below the ring, giving benzene its aromatic stability. Bond angles are 120°, and the molecule is planar.
Each carbon in benzene is sp² hybridised, forming three sigma bonds (two C-C and one C-H) and contributing one p-orbital electron to the delocalised π system. The 6 p-orbital electrons form a delocalised π cloud above and below the ring, giving benzene its aromatic stability. Bond angles are 120°, and the molecule is planar.
4Which of the following is an example of convergent evolution?
Answer: C — Eyes of vertebrates and octopus
Convergent evolution occurs when unrelated organisms independently evolve similar traits. The camera-type eye of vertebrates and octopus evolved independently (they are not closely related) — a classic example. Forelimbs of humans and horses are homologous structures (divergent evolution from a common ancestor). Wings of bats (mammals) and butterflies (insects) also show convergent evolution.
Convergent evolution occurs when unrelated organisms independently evolve similar traits. The camera-type eye of vertebrates and octopus evolved independently (they are not closely related) — a classic example. Forelimbs of humans and horses are homologous structures (divergent evolution from a common ancestor). Wings of bats (mammals) and butterflies (insects) also show convergent evolution.
5If f(x) = x² - 3x + 2, the roots of f(x) = 0 are:
Answer: A — 1 and 2
To solve x² - 3x + 2 = 0, factorise: (x-1)(x-2) = 0. Therefore x = 1 or x = 2. Verification: f(1) = 1-3+2 = 0 ✓, f(2) = 4-6+2 = 0 ✓. Alternatively use the quadratic formula: x = [3 ± √(9-8)]/2 = [3 ± 1]/2, giving x = 2 or x = 1.
To solve x² - 3x + 2 = 0, factorise: (x-1)(x-2) = 0. Therefore x = 1 or x = 2. Verification: f(1) = 1-3+2 = 0 ✓, f(2) = 4-6+2 = 0 ✓. Alternatively use the quadratic formula: x = [3 ± √(9-8)]/2 = [3 ± 1]/2, giving x = 2 or x = 1.
6The Heisenberg Uncertainty Principle states that:
Answer: B — Position and momentum cannot both be precisely measured simultaneously
Heisenberg's Uncertainty Principle: Δx·Δp ≥ h/4π, where Δx is uncertainty in position and Δp is uncertainty in momentum. The more precisely we measure position, the less precisely we can know momentum, and vice versa. This is a fundamental property of quantum systems, not a measurement limitation.
Heisenberg's Uncertainty Principle: Δx·Δp ≥ h/4π, where Δx is uncertainty in position and Δp is uncertainty in momentum. The more precisely we measure position, the less precisely we can know momentum, and vice versa. This is a fundamental property of quantum systems, not a measurement limitation.
7Glycolysis occurs in which part of the cell?
Answer: C — Cytoplasm
Glycolysis (splitting of glucose) occurs in the cytoplasm/cytosol of the cell. It is the first step of cellular respiration (both aerobic and anaerobic). One glucose molecule is broken down into two pyruvate molecules, producing 2 ATP and 2 NADH. Glycolysis does not require oxygen.
Glycolysis (splitting of glucose) occurs in the cytoplasm/cytosol of the cell. It is the first step of cellular respiration (both aerobic and anaerobic). One glucose molecule is broken down into two pyruvate molecules, producing 2 ATP and 2 NADH. Glycolysis does not require oxygen.
8The number of unpaired electrons in Fe²⁺ ion is:
Answer: C — 4
Fe has electron configuration [Ar]3d⁶4s². Fe²⁺ loses two 4s electrons: [Ar]3d⁶. In the 3d⁶ configuration using Hund's rule: the 5 d-orbitals fill as ↑↓, ↑, ↑, ↑, ↑ — giving 4 unpaired electrons. Fe²⁺ has 4 unpaired electrons, making it paramagnetic.
Fe has electron configuration [Ar]3d⁶4s². Fe²⁺ loses two 4s electrons: [Ar]3d⁶. In the 3d⁶ configuration using Hund's rule: the 5 d-orbitals fill as ↑↓, ↑, ↑, ↑, ↑ — giving 4 unpaired electrons. Fe²⁺ has 4 unpaired electrons, making it paramagnetic.
9A convex lens of focal length 20 cm forms an image at 60 cm. Object distance is:
Answer: A — 30 cm
Using lens formula: 1/v - 1/u = 1/f. Given v = +60 cm (real image), f = +20 cm (convex lens). 1/u = 1/v - 1/f = 1/60 - 1/20 = 1/60 - 3/60 = -2/60. So u = -30 cm. Object distance = 30 cm (negative sign means object is on the same side as incident light — standard convention).
Using lens formula: 1/v - 1/u = 1/f. Given v = +60 cm (real image), f = +20 cm (convex lens). 1/u = 1/v - 1/f = 1/60 - 1/20 = 1/60 - 3/60 = -2/60. So u = -30 cm. Object distance = 30 cm (negative sign means object is on the same side as incident light — standard convention).
10Which of the following is not a greenhouse gas?
Answer: D — N₂
Nitrogen (N₂) is NOT a greenhouse gas. It makes up 78% of Earth's atmosphere but does not absorb infrared radiation. The main greenhouse gases are CO₂ (carbon dioxide), CH₄ (methane), N₂O (nitrous oxide), water vapour (H₂O) and fluorinated gases. Greenhouse gases trap outgoing infrared radiation, warming the Earth.
Nitrogen (N₂) is NOT a greenhouse gas. It makes up 78% of Earth's atmosphere but does not absorb infrared radiation. The main greenhouse gases are CO₂ (carbon dioxide), CH₄ (methane), N₂O (nitrous oxide), water vapour (H₂O) and fluorinated gases. Greenhouse gases trap outgoing infrared radiation, warming the Earth.
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