Pre-Board Examination 2026
Subject - Mathematics
Subject - Mathematics
Q.1 Choose the correct option to answer the following multiple choice question (i to xviii) and write in the answer book. (1 × 18 = 18)
(i) What type of reaction is the above?
CaCO₃(s) Heat → CaO(s) + CO₂(g)
✔ Correct Answer : Decomposition Reaction
(ii) A metal reacts with oxygen to form a compound with high melting point. This compound dissolves in water. What could be this element?
✔ Correct Answer : Calcium
(iii) Butenone is a four-carbon compound whose functional group is–
✔ Correct Answer : Ketone
(iv) What happens when dilute hydrochloric acid is added to iron powder?
✔ Correct Answer : Hydrogen gas and iron chloride are formed
(v) Which of the following values of pH gives the value of alkali solution?
✔ Correct Answer : 13
(vi) Pyruvate breaks down into carbon dioxide, water and energy and this reaction occurs at–
✔ Correct Answer : Mitochondria
(vii) Which of the following gases is used in metal welding?
✔ Correct Answer : Acetylene
(viii) The space between two nerve cells is called–
✔ Correct Answer : Synapse
(ix) Where does the fetus get its nutrients in the mother’s uterus?
✔ Correct Answer : Placenta
(x) Sexually transmitted disease is–
✔ Correct Answer : All of the above
(xi) The genotype ratio of a monohybrid cross is–
✔ Correct Answer : 1 : 2 : 1
(xii) A divergent lens will produce–
✔ Correct Answer : Always a virtual image
(xiii) Convex lenses are used to correct which condition?
✔ Correct Answer : Hypermetropia
(xiv) A positively charged alpha-particle projected towards the west is deflected towards the north. The direction of magnetic field is–
✔ Correct Answer : Downward
(xv) A student plots V–I graphs for three samples of nichrome wire with resistances R₁, R₂ and R₃. Choose the correct statement–
✔ Correct Answer : R₃ > R₂ > R₁
(xvi) An electric bulb is rated 220V and 100W. When operated on 110V, the power consumed will be–
✔ Correct Answer : 25W
(xvii) In our houses we receive AC electric power of–
✔ Correct Answer : 220V, 50Hz
(xviii) S.I. unit of resistivity is–
✔ Correct Answer : Ohm meter
Score: 0 / 18
Q.2. Fill in the blanks in the following (i to vi) (½ × 10 = 5)
(i) __________ gas is formed by reacting granulated zinc with dilute sulfuric acid.
(ii) The pH value of milk of magnesia is __________.
(iii) Reflex reactions are carried out by __________.
(iv) Energy in the human body is stored in the form of __________.
(v) The number of autosomes in a human body cell is __________.
(vi) __________ are the units responsible for the transmission of traits.
(i) __________ gas is formed by reacting granulated zinc with dilute sulfuric acid.
(ii) The pH value of milk of magnesia is __________.
(iii) Reflex reactions are carried out by __________.
(iv) Energy in the human body is stored in the form of __________.
(v) The number of autosomes in a human body cell is __________.
(vi) __________ are the units responsible for the transmission of traits.
Q.3. Very short Answer Type Question –(i to xii))
(i) Write an example of a precipitation reaction.
(ii) What is water crystallization?
(iii) Write an example of two amphoteric oxides.
(iv) Define biomagnifications.
(v) Name of the part of the brain affected by alcohol.
(vi) What happens at the synapse between two neurons?
(vii) How does the creation of variations in a species promote survival?
(viii) Draw a diagram showing the inheritance of traits up to F₂ progeny between pure tall (TT) and pure short (tt) plants.
(ix) What is the pattern of magnetic field lines around a straight current-carrying conductor?
(x) What is determined by Fleming's left hand rule?
(xi) List the image characteristics formed by plane mirrors.
(xii) In the phenomenon of refraction of light, if sin i = a and sin r = b, then what will be the refractive index of the medium.
(ii) Express 336 as a product of its prime factors.
(i) Write an example of a precipitation reaction.
(ii) What is water crystallization?
(iii) Write an example of two amphoteric oxides.
(iv) Define biomagnifications.
(v) Name of the part of the brain affected by alcohol.
(vi) What happens at the synapse between two neurons?
(vii) How does the creation of variations in a species promote survival?
(viii) Draw a diagram showing the inheritance of traits up to F₂ progeny between pure tall (TT) and pure short (tt) plants.
(ix) What is the pattern of magnetic field lines around a straight current-carrying conductor?
(x) What is determined by Fleming's left hand rule?
(xi) List the image characteristics formed by plane mirrors.
(xii) In the phenomenon of refraction of light, if sin i = a and sin r = b, then what will be the refractive index of the medium.
(ii) Express 336 as a product of its prime factors.
Q.4.
(i) Why do ionic compounds have high melting points?
(ii) Explain the formation of MgO by electron transfer.
(ii) Explain the formation of MgO by electron transfer.
Solution:
(i) Ionic compounds have high melting points because the oppositely charged ions are held together by strong electrostatic forces of attraction. A large amount of energy is required to break these forces.
(ii) Magnesium loses two electrons to form Mg²⁺ ion and oxygen gains two electrons to form O²⁻ ion. These oppositely charged ions attract each other to form magnesium oxide (MgO).
Mg → Mg²⁺ + 2e⁻
O + 2e⁻ → O²⁻
Mg²⁺ + O²⁻ → MgO
(i) Ionic compounds have high melting points because the oppositely charged ions are held together by strong electrostatic forces of attraction. A large amount of energy is required to break these forces.
(ii) Magnesium loses two electrons to form Mg²⁺ ion and oxygen gains two electrons to form O²⁻ ion. These oppositely charged ions attract each other to form magnesium oxide (MgO).
Mg → Mg²⁺ + 2e⁻
O + 2e⁻ → O²⁻
Mg²⁺ + O²⁻ → MgO
Q.5. Write the IUPAC names of the following compounds.
Solution:
(i) CH₃–CH(CH₃)–CH₂–CH₃ → 2-Methylbutane
(ii) H–COOH → Methanoic acid
(iii) CH₃–CH₂–CH(Cl)–CH₃ → 2-Chlorobutane
(iv) CH₃–CO–CH₃ → Propanone
(i) CH₃–CH(CH₃)–CH₂–CH₃ → 2-Methylbutane
(ii) H–COOH → Methanoic acid
(iii) CH₃–CH₂–CH(Cl)–CH₃ → 2-Chlorobutane
(iv) CH₃–CO–CH₃ → Propanone
Q.6. Explain the breakdown of glucose by different pathways.
Solution:
Glucose first breaks down into pyruvate in the cytoplasm. In the presence of oxygen, pyruvate is completely oxidised to carbon dioxide, water and energy in mitochondria. In the absence of oxygen, pyruvate is converted into ethanol and carbon dioxide in yeast or into lactic acid in muscle cells.
Glucose first breaks down into pyruvate in the cytoplasm. In the presence of oxygen, pyruvate is completely oxidised to carbon dioxide, water and energy in mitochondria. In the absence of oxygen, pyruvate is converted into ethanol and carbon dioxide in yeast or into lactic acid in muscle cells.
Q.7. How is the movement of leaves of mimosa plant different from the movement of shoots towards light?
Solution:
The movement of mimosa leaves is a nastic movement caused by change in turgor pressure and is not directional. The movement of shoots towards light is a phototropic movement which is directional and involves growth.
The movement of mimosa leaves is a nastic movement caused by change in turgor pressure and is not directional. The movement of shoots towards light is a phototropic movement which is directional and involves growth.
Q.8. Explain budding in hydra with the help of labelled diagram.
Solution:
Budding in hydra is an asexual reproduction process. A small bud develops on the parent body due to repeated cell division. The bud grows, develops tentacles and finally detaches to form a new hydra.
Budding in hydra is an asexual reproduction process. A small bud develops on the parent body due to repeated cell division. The bud grows, develops tentacles and finally detaches to form a new hydra.
Q.9.
(i) Create a food chain of the following organisms.
Insect, Hawk, Grass, Snake, Frog
(ii) Name the organism at the third trophic level.
(iii) Which organism will have the highest concentration of non-biodegradable chemicals?
(i) Create a food chain of the following organisms.
Insect, Hawk, Grass, Snake, Frog
(ii) Name the organism at the third trophic level.
(iii) Which organism will have the highest concentration of non-biodegradable chemicals?
Solution:
(i) Grass → Insect → Frog → Snake → Hawk
(ii) Frog
(iii) Hawk
(i) Grass → Insect → Frog → Snake → Hawk
(ii) Frog
(iii) Hawk
Q.10. A wire of resistance 4 Ω has length L and area A. Find the resistance of another wire of the same material having length L/2 and area 2A.
Solution:
Resistance R ∝ L/A
New resistance = (L/2)/(2A) = L/4A
R = 4/4 = 1 Ω
Resistance R ∝ L/A
New resistance = (L/2)/(2A) = L/4A
R = 4/4 = 1 Ω
Q.11. A circular loop carries current clockwise. Find the direction of magnetic field inside and outside the loop.
Solution:
Using the right-hand thumb rule, the magnetic field inside the loop is directed into the plane of the table and outside the loop it is directed out of the plane.
Using the right-hand thumb rule, the magnetic field inside the loop is directed into the plane of the table and outside the loop it is directed out of the plane.
Q.12. What is meant by the power of accommodation of the eye?
Solution:
The power of accommodation of the eye is the ability of the eye lens to change its focal length so that objects at different distances can be seen clearly.
The power of accommodation of the eye is the ability of the eye lens to change its focal length so that objects at different distances can be seen clearly.
Q.13. A convex mirror has radius of curvature 3.0 m. A bus is placed at 5.0 m from it. Find the position, nature and size of image.
Solution:
Radius of curvature R = 3.0 m
Focal length f = R/2 = 1.5 m
Using mirror formula, the image is formed at about 1.15 m behind the mirror.
Nature of image: Virtual and erect
Size of image: Diminished
Radius of curvature R = 3.0 m
Focal length f = R/2 = 1.5 m
Using mirror formula, the image is formed at about 1.15 m behind the mirror.
Nature of image: Virtual and erect
Size of image: Diminished
Q.14. Write balanced equations for the following chemical reactions.
(i) Barium chloride + Aluminium sulphate → Barium sulphate + Aluminium chloride
(ii) Sodium + Water → Sodium hydroxide + Hydrogen
OR
Compound (X) and aluminium are used to join railway tracks.
(i) Identify compound (X).
(ii) Name the reaction.
(iii) Write the reaction.
(i) Barium chloride + Aluminium sulphate → Barium sulphate + Aluminium chloride
(ii) Sodium + Water → Sodium hydroxide + Hydrogen
OR
Compound (X) and aluminium are used to join railway tracks.
(i) Identify compound (X).
(ii) Name the reaction.
(iii) Write the reaction.
Solution:
(i) 3BaCl₂ + Al₂(SO₄)₃ → 3BaSO₄ + 2AlCl₃
(ii) 2Na + 2H₂O → 2NaOH + H₂↑
OR
(i) Compound (X) is Ferric oxide (Fe₂O₃).
(ii) The reaction is called Thermite reaction.
(iii) Fe₂O₃ + 2Al → Al₂O₃ + 2Fe + Heat
(i) 3BaCl₂ + Al₂(SO₄)₃ → 3BaSO₄ + 2AlCl₃
(ii) 2Na + 2H₂O → 2NaOH + H₂↑
OR
(i) Compound (X) is Ferric oxide (Fe₂O₃).
(ii) The reaction is called Thermite reaction.
(iii) Fe₂O₃ + 2Al → Al₂O₃ + 2Fe + Heat
Q.15. Write reactions of ethanol with:
(i) Sodium (Na)
(ii) Hot concentrated H₂SO₄
(iii) Acidified K₂Cr₂O₇ with heat
OR
(i) Draw electron dot structure of: Ethanoic acid, Propanone, H₂S, CO₂
(ii) What is micelle? Explain the cleaning action of soap.
(iii) Write differences between soap and detergent.
(i) Sodium (Na)
(ii) Hot concentrated H₂SO₄
(iii) Acidified K₂Cr₂O₇ with heat
OR
(i) Draw electron dot structure of: Ethanoic acid, Propanone, H₂S, CO₂
(ii) What is micelle? Explain the cleaning action of soap.
(iii) Write differences between soap and detergent.
Solution:
(i) 2C₂H₅OH + 2Na → 2C₂H₅ONa + H₂↑
(ii) C₂H₅OH → C₂H₄ + H₂O (in presence of conc. H₂SO₄)
(iii) C₂H₅OH + [O] → CH₃COOH (Acidified K₂Cr₂O₇)
OR
(ii) Micelle is a cluster of soap molecules formed in water. The hydrophobic tail attaches to grease while the hydrophilic head remains in water, removing dirt effectively.
(iii) Soap is biodegradable and works in soft water, whereas detergents are non-biodegradable and work in hard water also.
(i) 2C₂H₅OH + 2Na → 2C₂H₅ONa + H₂↑
(ii) C₂H₅OH → C₂H₄ + H₂O (in presence of conc. H₂SO₄)
(iii) C₂H₅OH + [O] → CH₃COOH (Acidified K₂Cr₂O₇)
OR
(ii) Micelle is a cluster of soap molecules formed in water. The hydrophobic tail attaches to grease while the hydrophilic head remains in water, removing dirt effectively.
(iii) Soap is biodegradable and works in soft water, whereas detergents are non-biodegradable and work in hard water also.
Q.16.
(i) What is fertilisation? Draw labelled diagram of male reproductive organ.
(ii) Name the mechanical methods of preventing pregnancy.
OR
(i) Draw labelled diagram of cross section of a flower.
(ii) What is vegetative propagation? Why is it used?
(i) What is fertilisation? Draw labelled diagram of male reproductive organ.
(ii) Name the mechanical methods of preventing pregnancy.
OR
(i) Draw labelled diagram of cross section of a flower.
(ii) What is vegetative propagation? Why is it used?
Solution:
(i) Fertilisation is the fusion of male and female gametes to form a zygote.
(ii) Mechanical methods include condoms, diaphragm and intrauterine devices.
OR
(ii) Vegetative propagation is asexual reproduction using roots, stems or leaves. It is used to grow plants which do not produce seeds or produce weak seeds.
(i) Fertilisation is the fusion of male and female gametes to form a zygote.
(ii) Mechanical methods include condoms, diaphragm and intrauterine devices.
OR
(ii) Vegetative propagation is asexual reproduction using roots, stems or leaves. It is used to grow plants which do not produce seeds or produce weak seeds.
Q.17. Draw a circuit diagram of parallel combination of resistors R₁, R₂ and R₃ and derive the formula for equivalent resistance.
OR
An electric lamp of resistance 20Ω and a conductor of 4Ω are connected to a 6V battery. Calculate:
(a) Total resistance
(b) Current through the circuit
(c) Potential difference across the lamp.
OR
An electric lamp of resistance 20Ω and a conductor of 4Ω are connected to a 6V battery. Calculate:
(a) Total resistance
(b) Current through the circuit
(c) Potential difference across the lamp.
Solution:
For parallel combination:
1/R = 1/R₁ + 1/R₂ + 1/R₃
OR
Total resistance = 20Ω + 4Ω = 24Ω
Current I = V/R = 6/24 = 0.25 A
Potential difference across lamp = I × R = 0.25 × 20 = 5V
For parallel combination:
1/R = 1/R₁ + 1/R₂ + 1/R₃
OR
Total resistance = 20Ω + 4Ω = 24Ω
Current I = V/R = 6/24 = 0.25 A
Potential difference across lamp = I × R = 0.25 × 20 = 5V
Q.18. Draw ray diagrams for a concave mirror and explain image formation:
(i) Object at C
(ii) Object between C and F
OR
Draw ray diagrams for convex lens and explain image formation.
(i) Object at C
(ii) Object between C and F
OR
Draw ray diagrams for convex lens and explain image formation.
Solution:
(i) At C: Image is formed at C, real, inverted and same size.
(ii) Between C and F: Image is beyond C, real, inverted and enlarged.
(i) At C: Image is formed at C, real, inverted and same size.
(ii) Between C and F: Image is beyond C, real, inverted and enlarged.
Q.19.
(i) Draw labelled diagram of human digestive system.
(ii) How are oxygen and carbon dioxide transported in humans?
(iii) Explain artificial dialysis.
OR
Explain double circulation with diagram and define blood pressure.
(i) Draw labelled diagram of human digestive system.
(ii) How are oxygen and carbon dioxide transported in humans?
(iii) Explain artificial dialysis.
OR
Explain double circulation with diagram and define blood pressure.
Solution:
(ii) Oxygen is transported by haemoglobin, carbon dioxide mainly by plasma.
(iii) Artificial dialysis removes waste materials from blood using a dialysis machine.
(ii) Oxygen is transported by haemoglobin, carbon dioxide mainly by plasma.
(iii) Artificial dialysis removes waste materials from blood using a dialysis machine.
Q.20.
(i) Draw setup for preparation and test of hydrogen gas.
(ii) Explain limewater test for CO₂.
OR
(i) What is pH scale?
(ii) Electrolysis of brine gives gases X and Y.
(i) Draw setup for preparation and test of hydrogen gas.
(ii) Explain limewater test for CO₂.
OR
(i) What is pH scale?
(ii) Electrolysis of brine gives gases X and Y.
Solution:
(i) Zn + H₂SO₄ → ZnSO₄ + H₂↑
(ii) CO₂ + Ca(OH)₂ → CaCO₃ ↓ (white ppt.)
CaCO₃ + CO₂ → Ca(HCO₃)₂
OR
Gas X = Hydrogen, Gas Y = Chlorine
2NaCl + 2H₂O → 2NaOH + H₂ + Cl₂
Ca(OH)₂ + Cl₂ → CaOCl₂ + H₂O
(i) Zn + H₂SO₄ → ZnSO₄ + H₂↑
(ii) CO₂ + Ca(OH)₂ → CaCO₃ ↓ (white ppt.)
CaCO₃ + CO₂ → Ca(HCO₃)₂
OR
Gas X = Hydrogen, Gas Y = Chlorine
2NaCl + 2H₂O → 2NaOH + H₂ + Cl₂
Ca(OH)₂ + Cl₂ → CaOCl₂ + H₂O
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