Greenvaley Scholarship Test

Test Instructions

This test consists of 45 multiple-choice questions divided into three sections.
Each question has four options, with only one correct answer.
Answer all questions to the best of your ability.
You will receive section-wise scores after submission.
The test is timed, so manage your time efficiently.

🦮 Mathematics

1. Match the following:

Column A (Equation/Expression)          Column B (Value/Result)
(i) sin⁴θ + cos⁴θ                                                   (a) 1/4
(ii) tan θ + cot θ                                                     (b) 1 − 2 sin²θ cos²θ
(iii) sin 2θ / (1 + cos 2θ)                                   (c) 2 / sin 2θ
(iv) sin 30° · cos 60°                                   (d) tan θ

A) (i)-(b), (ii)-(c), (iii)-(d), (iv)-(a)
B) (i)-(d), (ii)-(a), (iii)-(b), (iv)-(c)
C) (i)-(a), (ii)-(d), (iii)-(c), (iv)-(b)
D) (i)-(a), (ii)-(b), (iii)-(c), (iv)-(d)

2. Match the following:

Column A (Figure/Concept)          Column B (Property/Formula)
(i) Section Formula                                    (a) 2πrh
(ii) Volume of a Cylinder                    (b) 2π(r + h)
(iii) Surface Area of a Cylinder             (c) √[(x₂ − x₁)² + (y₂ − y₁)²]
(iv) Distance Formula                       (d) (mx + nx)/(m+n), (my + ny)/(m+n)

A) (i)-(b), (ii)-(c), (iii)-(d), (iv)-(a)
B) (i)-(d), (ii)-(a), (iii)-(b), (iv)-(c)
C) (i)-(a), (ii)-(d), (iii)-(c), (iv)-(b)
D) (i)-(a), (ii)-(b), (iii)-(c), (iv)-(d)

3. Assertion (A): The quadratic equation x² + px + q = 0 has real and distinct roots if p² − 4q > 0.
Reason (R): The discriminant of a quadratic equation ax² + bx + c = 0 is b² − 4ac.

A) Both A and R are true and R is the correct explanation of A.
B) Both A and R are true but R is not the correct explanation of A.
C) A is true but R is false.
D) A is false but R is true.

4. If α and β are the roots of the equation 2x² − 3x + 5 = 0, then (1/α) + (1/β) is:

A) 3/5
B) −3/5
C) 5/3
D) −5/3

5. The sum of the first n terms of an AP is 2n² + 3n + 5. The 16th term is:

A) 96
B) 98
C) 100
D) 102

6. If the points (a,0), (0,b), and (1,1) are collinear, then 1/a + 1/b is:

A) 0
B) 1
C) 2
D) −1

7. A solid sphere of radius r is melted and recast into a cone of height h. Then, the radius of the base of the cone is:

A) √(4r³/h)
B) √(2r³/h)
C) √(r³/h)
D) √(r²/h)

8. If tan θ + sec θ = l, then sec θ is:

A) (l² + 1)/(2l)
B) (l² − 1)/(2l)
C) (l² + 1)/l
D) (l² − 1)/l

9. The probability of getting a sum of 9 from two throws of a dice is:

A) 1/9
B) 1/6
C) 1/12
D) 1/18

10. If the radii of the ends of a frustum of a cone are r₁ and r₂ (r₁ > r₂), and the height is h, then the volume of the frustum is:

A) (1/3)πh(r₁² + r₂² + r₁r₂)
B) (1/3)πh(r₁² + r₂² − r₁r₂)
C) πh(r₁² + r₂² + r₁r₂)
D) πh(r₁² + r₂² − r₁r₂)

11. The median of the data set: 25, 15, 23, 40, 27, 25, 23, 42 is:

A) 24
B) 25
C) 26
D) 27

12. Case-Based: A lighthouse is 100 meters high. The angles of depression of two ships are 30° and 45°. If the ships are on the same side of the lighthouse:

(i) What is the distance of the first ship from the lighthouse?
(ii) What is the distance of the second ship from the lighthouse?
(iii) What is the distance between the ships?
(iv) Which ship is closer to the lighthouse?

A) (i) 100√3 m, (ii) 100 m, (iii) 100(√3−1) m, (iv) Second ship
B) (i) 100 m, (ii) 100√3 m, (iii) 100(√3−1) m, (iv) First ship
C) (i) 100√3 m, (ii) 100 m, (iii) 100(√3+1) m, (iv) Second ship
D) (i) 100 m, (ii) 100√3 m, (iii) 100(√3+1) m, (iv) First ship

13. Case-Based: A metallic sphere of radius 10 cm is melted into a wire of diameter 2 mm.

(i) What is the volume of the sphere?
(ii) What is the radius of the wire?
(iii) What is the length of the wire?
(iv) If bent into a circle, what is the radius of the circle?

A) (i) (4/3)π(10)^3 cm³, (ii) 0.1 cm, (iii) 400000/3 cm, (iv) 200000/(3π) cm
B) (i) (4/3)π(10)^3 cm³, (ii) 0.2 cm, (iii) 400000/3 cm, (iv) 200000/(2π) cm
C) (i) 4000 cm³, (ii) 0.1 cm, (iii) 400000 cm, (iv) 200000π cm
D) (i) (4/3)π(10)^3 cm³, (ii) 0.1 cm, (iii) 420000 cm, (iv) 200000/(3π) cm

14. Case-Based: A quadratic polynomial p(x) has zeroes α and β such that α + β = 6, αβ = 4.

(i) Find the quadratic polynomial p(x).
(ii) Find the value of α² + β².
(iii) Find the value of (1/α) + (1/β).
(iv) Find the value of α³ + β³.

A) (i) x² − 6x + 4, (ii) 28, (iii) 3/2, (iv) 144
B) (i) x² + 6x + 4, (ii) 28, (iii) 3/2, (iv) 180
C) (i) x² − 6x − 4, (ii) 28, (iii) −3/2, (iv) 180
D) (i) x² − 6x + 4, (ii) 32, (iii) 3/2, (iv) 198

15. Case-Based: A box contains 5 red balls, 8 white balls, and 4 green balls. One ball is drawn at random:

(i) Probability of drawing a red ball?
(ii) Probability of drawing a white ball?
(iii) Probability of drawing a green ball?
(iv) Probability of drawing a red or white ball?

A) (i) 5/17, (ii) 8/17, (iii) 4/17, (iv) 13/17
B) (i) 5/17, (ii) 8/17, (iii) 4/17, (iv) 12/17
C) (i) 5/17, (ii) 9/17, (iii) 4/17, (iv) 13/17
D) (i) 6/17, (ii) 8/17, (iii) 4/17, (iv) 13/17

🔬 Physics

1. Match the following:

Column A (Quantity/Concept)      Column B (Unit/Formula)
(i) Power of Lens                                         (a) Ohm
(ii) Resistance                                           (b) Dioptre
(iii) Magnetic Field                                (c) Volt
(iv) Potential Difference                     (d) Tesla

A) (i)-(a), (ii)-(d), (iii)-(c), (iv)-(b)
B) (i)-(b), (ii)-(a), (iii)-(d), (iv)-(c)
C) (i)-(a), (ii)-(b), (iii)-(c), (iv)-(d)
D) (i)-(d), (ii)-(a), (iii)-(b), (iv)-(c)

2. Match the following:

Column A (Device/Component)      Column B (Function/Principle)
(i) Electric Generator                          (a) Heating Effect of Current
(ii) Electric Motor                                   (b) Electromagnetic Induction
(iii) Fuse                                                               (c) Magnetic Effect of Current
(iv) Solenoid                                                     (d) Protection from Overloading

A) (i)-(a), (ii)-(c), (iii)-(b), (iv)-(c)
B) (i)-(d), (ii)-(c), (iii)-(b), (iv)-(a)
C) (i)-(c), (ii)-(b), (iii)-(d), (iv)-(a)
D) (i)-(b), (ii)-(c), (iii)-(d), (iv)-(c)

3. Assertion (A): A convex mirror always forms a virtual, erect, and diminished image.
Reason (R): The focal length of a convex mirror is positive.

A) Both A and R are true and R is the correct explanation of A.
B) Both A and R are true but R is not the correct explanation of A.
C) A is true but R is false.
D) A is false but R is true.

4. The far point of a myopic person is 80 cm in front of the eye. What is the power of the lens required to enable him to see far objects clearly?

A) -1.25 D
B) 1.25 D
C) -0.8 D
D) 0.8 D

5. The resistivity of a material depends on:

A) Length
B) Area of Cross-section
C) Temperature
D) All of the above

6. A wire of resistance R is stretched to double its length. The new resistance is:

A) R/4
B) R/2
C) 2R
D) 4R

7. The magnetic field inside a long straight solenoid carrying current:

A) Is zero
B) Decreases as we move towards its end
C) Increases as we move towards its end
D) Is the same at all points

8. Which of the following is not a renewable source of energy?

A) Solar energy
B) Wind energy
C) Nuclear energy
D) Hydroelectric energy

9. The splitting of white light into its component colors is called:

A) Reflection
B) Refraction
C) Dispersion
D) Interference

10. The human eye forms the image of an object at its:

A) Cornea
B) Iris
C) Pupil
D) Retina

11. The SI unit of electric potential difference is:

A) Ampere
B) Coulomb
C) Volt
D) Ohm

12. Case-Based: A student is studying the refraction of light through a rectangular glass slab.

(i) What is the angle between the incident ray and the normal at the point of incidence called?
(ii) What is the angle between the refracted ray and the normal inside the glass slab called?
(iii) What happens to the speed of light as it enters the glass slab?
(iv) What is the lateral displacement of the emergent ray?

A) (i) Angle of incidence, (ii) Angle of refraction, (iii) Decreases, (iv) Perpendicular distance between incident and emergent ray
B) (i) Angle of deviation, (ii) Angle of refraction, (iii) Increases, (iv) Refracted distance
C) (i) Angle of incidence, (ii) Reflected angle, (iii) Remains same, (iv) No displacement
D) (i) Angle of refraction, (ii) Angle of incidence, (iii) Increases, (iv) Opposite to incident ray

13. Case-Based: An electric circuit consists of a battery, a resistor, and an ammeter.

(i) What is the function of the ammeter?
(ii) How is the ammeter connected in the circuit?
(iii) What is the relationship between potential difference and current in the resistor?
(iv) If the resistance is doubled, what happens to the current?

A) (i) Measures current, (ii) Series, (iii) V = IR, (iv) Halves
B) (i) Measures voltage, (ii) Parallel, (iii) V = IR, (iv) Doubles
C) (i) Controls current, (ii) Series, (iii) I = VR, (iv) Same
D) (i) Produces current, (ii) Parallel, (iii) V = I/R, (iv) Zero

14. Case-Based: A student uses a concave mirror to form an image of a distant object.

(i) Where should the object be placed to get a real and inverted image of the same size?
(ii) Where should the object be placed to get a highly enlarged virtual image?
(iii) What is the focal length of the mirror if the radius of curvature is 40 cm?
(iv) What is the nature of the image formed when the object is placed between the pole and the focus?

A) (i) At 2F, (ii) Between pole and focus, (iii) 20 cm, (iv) Virtual and magnified
B) (i) At F, (ii) At C, (iii) 40 cm, (iv) Real and inverted
C) (i) At C, (ii) At F, (iii) 10 cm, (iv) Virtual and diminished
D) (i) Between F and C, (ii) Beyond C, (iii) 25 cm, (iv) Real and magnified

15. Case-Based: A current-carrying conductor is placed in a magnetic field.

(i) What is the force experienced by the conductor?
(ii) State Fleming's left-hand rule.
(iii) What happens to the force if the current is reversed?
(iv) What happens to the force if the magnetic field is doubled?

A) (i) F = BILsinθ, (ii) Fleming’s left-hand rule, (iii) Direction reverses, (iv) Doubles
B) (i) F = ILB, (ii) Fleming’s right-hand rule, (iii) No effect, (iv) Halves
C) (i) F = qvB, (ii) Right-hand thumb rule, (iii) Becomes zero, (iv) Remains same
D) (i) F = BIL, (ii) Left-hand rule, (iii) Direction remains, (iv) Triples

🧪 Chemistry

1. Case-Based: A student adds zinc granules to dilute hydrochloric acid and observes a reaction.

(i) Write the balanced chemical equation for the reaction.
(ii) What gas is evolved?
(iii) What is observed when a burning splint is brought near the mouth of the test tube?
(iv) What is the nature of this reaction?

A) (i) Zn + 2HCl → ZnCl₂ + H₂, (ii) Hydrogen, (iii) Pop sound with burning splint, (iv) Exothermic
B) (i) Zn + HCl → ZnHCl₂, (ii) Oxygen, (iii) White smoke, (iv) Endothermic
C) (i) Zn + 2HCl → ZnCl₂ + H₂, (ii) Oxygen, (iii) Color change, (iv) Displacement
D) (i) Zn + Cl₂ → ZnCl₂, (ii) Hydrogen, (iii) Pop sound, (iv) Neutralization

2. Case-Based: Reactions of ethanoic acid were performed in the laboratory.

(i) What is the IUPAC name of CH₃COOH?
(ii) What is the reaction with sodium carbonate?
(iii) Which functional group is present in ethanoic acid?
(iv) What is the esterification reaction involving CH₃COOH?

A) (i) Ethanoic acid (CH₃COOH), (ii) 2CH₃COOH + Na₂CO₃ → 2CH₃COONa + H₂O + CO₂, (iii) Carboxylic acid (-COOH), (iv) CH₃COOH + C₂H₅OH → CH₃COOC₂H₅ + H₂O
B) (i) Formic acid, (ii) CH₃COOH + Na → CH₃COONa + H₂, (iii) Hydroxyl, (iv) CH₃COOH + NaCl → CH₃COONa + HCl
C) (i) Acetic acid, (ii) CH₃COOH + Na₂CO₃ → CH₃COONa + CO₂, (iii) Aldehyde, (iv) CH₃COOH + CH₃OH → CH₃COOCH₃ + H₂O
D) (i) Ethanoic acid, (ii) CH₃COOH + Na₂O → CH₃COONa + H₂O, (iii) Carbonyl, (iv) CH₃COOH + CH₃CH₂OH → CH₃COOHCH₃CH₂ + H₂O

3. Case-Based: The periodic table groups elements based on recurring trends in properties.

(i) What did Mendeleev state about the periodicity of elements?
(ii) What happens to atomic size across a period?
(iii) What happens to atomic size down a group?
(iv) Which element has the smallest size among the halogens?

A) (i) The physical and chemical properties of elements are the periodic functions of their atomic numbers, (ii) decreases, (iii) increases, (iv) Fluorine (F)
B) (i) Atomic masses determine the periodicity, (ii) increases, (iii) decreases, (iv) Iodine (I)
C) (i) Properties repeat after every 8 elements, (ii) remains constant, (iii) decreases, (iv) Bromine (Br)
D) (i) Periodic function of atomic weight, (ii) decreases, (iii) decreases, (iv) Chlorine (Cl)

4. Case-Based: Reactions of metals with oxygen and water are studied.

(i) Which metal reacts vigorously with oxygen and water?
(ii) What is the product of the reaction of sodium with oxygen?
(iii) What is the product when sodium oxide reacts with water?
(iv) What is the nature of the solution formed?

A) (i) Sodium (Any alkali or alkaline earth metal or Al), (ii) 2Na + O₂ → Na₂O, (iii) Na₂O + H₂O → 2NaOH, (iv) Alkaline solution or base
B) (i) Calcium, (ii) Ca + O₂ → CaO, (iii) CaO + H₂O → Ca(OH)₂, (iv) Neutral solution
C) (i) Potassium, (ii) 4K + O₂ → 2K₂O, (iii) K₂O + H₂O → 2KOH, (iv) Acidic solution
D) (i) Zinc, (ii) Zn + O₂ → ZnO, (iii) ZnO + H₂O → Zn(OH)₂, (iv) Amphoteric solution

5. Which of the following is not a physical change?

A) Boiling of water
B) Melting of ice
C) Burning of candle
D) Dissolving sugar in water

6. Which of the following is not a chemical change?

A) Burning of magnesium ribbon
B) Rusting of iron
C) Boiling of water
D) Cooking of food

7. The number of protons in the nucleus of an atom is called:

A) Atomic number
B) Mass number
C) Neutron number
D) Valency

8. The modern periodic law states that:

A) Properties of elements are periodic functions of atomic number
B) Properties of elements are periodic functions of atomic mass
C) Elements are arranged in groups of 7
D) Atomic size increases across the period

9. The valency of an element is determined by:

A) Number of protons
B) Number of electrons in the outermost shell
C) Atomic mass
D) Number of neutrons

10. Which of the following metals will displace hydrogen from dilute acids?

A) Copper
B) Silver
C) Gold
D) Zinc

11. Which gas is evolved when sodium carbonate reacts with dilute hydrochloric acid?

A) Hydrogen
B) Oxygen
C) Carbon dioxide
D) Chlorine

12. What happens when a magnesium ribbon is burnt in air?

A) It catches fire with red flame and forms MgO
B) It burns with a dazzling white flame and forms MgO
C) It turns black
D) It remains unchanged

13. The chemical formula of washing soda is:

A) Na₂CO₃.10H₂O
B) NaHCO₃
C) Na₂CO₃
D) NaCl

14. Which of the following is used in the preparation of soap?

A) Ethanol
B) Sodium hydroxide
C) Acetic acid
D) Carbon dioxide

15. Which of the following is a saturated hydrocarbon?

A) Ethene
B) Ethyne
C) Ethanol
D) Ethane

Your Results

🧮 Mathematics

0 / 15

🔬 Physics

0 / 15

⚗️ Chemistry

0 / 15

Total Score

0 / 45

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