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This assessment will evaluate your knowledge in Mathematics, Science, and English based on CBSE 9th-10th curriculum.
Total questions: 50 | Time allotted: 60 minutes
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1. If the polynomial x³ - 6x² + 11x - 6 is divided by (x - 2), what is the remainder?
- A) 0
- B) 1
- C) 2
- D) -1
2. In a right triangle, if one acute angle is 35°, what is the other acute angle?
- A) 45°
- B) 55°
- C) 65°
- D) 145°
3. The area of a rhombus is 96 cm² and one diagonal is 12 cm. Find the other diagonal.
- A) 16 cm
- B) 14 cm
- C) 18 cm
- D) 20 cm
4. If sin θ = 3/5, then cos θ equals:
- A) 4/5
- B) 3/4
- C) 5/3
- D) 4/3
5. The coordinates of the point which divides the line segment joining A(2,3) and B(6,7) in the ratio 1:3 internally are:
- A) (3, 4)
- B) (4, 5)
- C) (2.5, 3.5)
- D) (3.5, 4.5)
6. If the sum of first n terms of an AP is 3n² + 2n, then the common difference is:
- A) 6
- B) 3
- C) 2
- D) 5
7. The volume of a cone is 1232 cm³ and its base radius is 7 cm. Find its height. (Use π = 22/7)
- A) 12 cm
- B) 15 cm
- C) 16 cm
- D) 18 cm
8. If α and β are zeros of the polynomial 2x² - 5x + 3, then α + β equals:
- A) 5/2
- B) 3/2
- C) -5/2
- D) 2/5
9. The probability of getting a sum of 9 when two dice are thrown is:
- A) 1/9
- B) 1/6
- C) 4/36
- D) 1/4
10. If tan A = 1/√3, then the value of sin A cos A is:
- A) 1/4
- B) √3/4
- C) 1/2
- D) √3/6
11. The median of the data: 5, 8, 12, x, 18, 20 is 11. Find x.
- A) 10
- B) 9
- C) 11
- D) 8
12. If the perimeter of a semicircle is 36 cm, find its radius. (Use π = 22/7)
- A) 7 cm
- B) 6 cm
- C) 8 cm
- D) 9 cm
13. Solve: √(x + 7) = x + 1
- A) x = 2
- B) x = 3
- C) x = 2 or x = -4
- D) x = 2 (only valid solution)
14. If the ratio of areas of two similar triangles is 16:25, then the ratio of their corresponding sides is:
- A) 16:25
- B) 4:5
- C) 8:10
- D) 2:3
15. The distance between points (3, -2) and (-1, 2) is:
- A) 4√2
- B) 6
- C) 5
- D) 3√2
16. If x + 1/x = 5, then x² + 1/x² equals:
- A) 23
- B) 25
- C) 27
- D) 21
17. The sum of first 20 terms of the series 7, 10, 13, 16,... is:
- A) 710
- B) 650
- C) 740
- D) 680
18. In triangle ABC, if ∠A = 90°, AB = 8 cm, BC = 10 cm, then AC equals:
- A) 6 cm
- B) 4 cm
- C) 5 cm
- D) 7 cm
19. If sec θ + tan θ = 2, then sec θ - tan θ equals:
- A) 1/2
- B) 2
- C) 1
- D) 1/4
20. The area of the sector of a circle with radius 14 cm and central angle 60° is: (Use π = 22/7)
- A) 102⅔ cm²
- B) 98 cm²
- C) 108 cm²
- D) 88 cm²
21. A car travels 60 km in the first hour, 80 km in the second hour, and 40 km in the third hour. What is its average speed?
- A) 60 km/h
- B) 50 km/h
- C) 70 km/h
- D) 55 km/h
22. A stone is dropped from a height of 45 m. How long does it take to reach the ground? (g = 10 m/s²)
- A) 3 seconds
- B) 4 seconds
- C) 2 seconds
- D) 5 seconds
23. The power of a lens is +2.5 D. What is its focal length?
- A) 0.4 m
- B) 0.25 m
- C) 2.5 m
- D) 0.5 m
24. A body weighs 60 N on Earth. What will be its weight on the moon? (g_moon = g_earth/6)
- A) 60 N
- B) 10 N
- C) 360 N
- D) 6 N
25. The resistance of a wire is 10 Ω. If it is stretched to double its length, what will be its new resistance?
- A) 20 Ω
- B) 40 Ω
- C) 5 Ω
- D) 10 Ω
26. A current of 2 A flows through a 5 Ω resistor for 10 seconds. How much heat is produced?
- A) 100 J
- B) 200 J
- C) 400 J
- D) 50 J
27. The frequency of a sound wave is 500 Hz and its wavelength is 0.68 m. What is the speed of sound?
- A) 340 m/s
- B) 320 m/s
- C) 360 m/s
- D) 300 m/s
28. An object is placed 30 cm from a concave mirror of focal length 20 cm. Where is the image formed?
- A) 60 cm from mirror
- B) 50 cm from mirror
- C) 40 cm from mirror
- D) 45 cm from mirror
29. A force of 20 N acts on a body of mass 4 kg. What is the acceleration produced?
- A) 5 m/s²
- B) 4 m/s²
- C) 80 m/s²
- D) 16 m/s²
30. The kinetic energy of a body of mass 2 kg moving with velocity 10 m/s is:
- A) 200 J
- B) 100 J
- C) 20 J
- D) 400 J
31. Two resistors of 4 Ω and 6 Ω are connected in parallel. Their equivalent resistance is:
- A) 10 Ω
- B) 2.4 Ω
- C) 5 Ω
- D) 1.2 Ω
32. The refractive index of glass is 1.5. What is the critical angle for total internal reflection?
- A) 42°
- B) 48°
- C) 30°
- D) 60°
33. What is the molecular formula of methane?
- A) CH₄
- B) C₂H₆
- C) C₃H₄
- D) CH₃OH
34. Which of the following is a reducing agent in the reaction: CuO + H₂ → Cu + H₂O?
- A) CuO
- B) H₂
- C) Cu
- D) H₂O
35. The pH of a neutral solution at 25°C is:
- A) 0
- B) 7
- C) 14
- D) 1
36. Which gas is evolved when zinc reacts with dilute hydrochloric acid?
- A) Oxygen
- B) Chlorine
- C) Hydrogen
- D) Carbon dioxide
37. Which tissue is responsible for the transport of water in plants?
- A) Phloem
- B) Xylem
- C) Cambium
- D) Parenchyma
38. The process by which green plants make their food is called:
- A) Respiration
- B) Photosynthesis
- C) Transpiration
- D) Excretion
39. Which part of the human brain controls balance and posture?
- A) Cerebrum
- B) Medulla
- C) Cerebellum
- D) Pons
40. The hormone insulin is produced by which organ?
- A) Liver
- B) Kidney
- C) Pancreas
- D) Thyroid
41. Choose the synonym of "Meticulous":
- A) Careless
- B) Careful
- C) Reckless
- D) Hasty
42. Fill in the blank: "She has been living here _____ five years."
- A) since
- B) from
- C) for
- D) by
43. Identify the correctly spelled word:
- A) Definately
- B) Definitely
- C) Definatly
- D) Definetely
44. Choose the correct sentence:
- A) Neither of the boys are present
- B) Neither of the boys is present
- C) Neither of the boy are present
- D) Neither of the boy is present
45. What is the antonym of "Abundant"?
- A) Plenty
- B) Scarce
- C) Sufficient
- D) Ample
46. Fill in the blank: "The meeting has been _____ until next week."
- A) postponed
- B) preponed
- C) advanced
- D) promoted
47. Choose the correct form: "I wish I _____ rich."
- A) am
- B) was
- C) were
- D) will be
48. Identify the part of speech of the underlined word: "He runs quickly."
- A) Noun
- B) Verb
- C) Adjective
- D) Adverb
49. Choose the correct preposition: "She is good _____ mathematics."
- A) in
- B) at
- C) on
- D) with
50. Fill in the blank with the correct article: "_____ Ganga is a sacred river."
- A) A
- B) An
- C) The
- D) No article needed
Test Results
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Solutions:
Mathematics Solutions:
1. Correct answer: A) 0 - Using remainder theorem, f(2) = (2)³ - 6(2)² + 11(2) - 6 = 8 - 24 + 22 - 6 = 0
2. Correct answer: B) 55° - Sum of angles in triangle = 180°. Right angle = 90°, so 90° + 35° + x = 180° → x = 55°
3. Correct answer: A) 16 cm - Area of rhombus = (d₁ × d₂)/2 → 96 = (12 × d₂)/2 → d₂ = 16 cm
4. Correct answer: A) 4/5 - Using identity sin²θ + cos²θ = 1, cosθ = √(1 - (3/5)²) = √(1 - 9/25) = √(16/25) = 4/5
5. Correct answer: A) (3, 4) - Using section formula, x = (1×6 + 3×2)/(1+3) = (6+6)/4 = 12/4 = 3, y = (1×7 + 3×3)/(1+3) = (7+9)/4 = 16/4 = 4
6. Correct answer: A) 6 - Sₙ = 3n² + 2n, S₁ = 3(1)² + 2(1) = 5, S₂ = 3(4) + 4 = 16, a₁ = 5, a₂ = S₂ - S₁ = 11, d = a₂ - a₁ = 6
7. Correct answer: C) 16 cm - Volume of cone = (1/3)πr²h → 1232 = (1/3)×(22/7)×7²×h → h = (1232×3×7)/(22×49) = 16 cm
8. Correct answer: A) 5/2 - For quadratic ax²+bx+c, sum of roots = -b/a = 5/2
9. Correct answer: A) 1/9 - Possible outcomes: (3,6), (4,5), (5,4), (6,3) → 4/36 = 1/9
10. Correct answer: A) 1/4 - tan A = 1/√3 → A = 30°, sin A cos A = (1/2)(√3/2) = √3/4
11. Correct answer: A) 10 - For even number of terms, median = average of (n/2)th and (n/2+1)th terms → (12+x)/2 = 11 → x = 10
12. Correct answer: A) 7 cm - Perimeter of semicircle = πr + 2r = r(π+2) = 36 → r(22/7+2) = 36 → r(36/7) = 36 → r = 7 cm
13. Correct answer: D) x = 2 (only valid solution) - Squaring both sides: x+7 = (x+1)² → x+7 = x²+2x+1 → x²+x-6=0 → (x+3)(x-2)=0 → x=-3 or x=2, but x=-3 is extraneous
14. Correct answer: B) 4:5 - Ratio of areas = (ratio of sides)² → 16:25 = (4:5)²
15. Correct answer: A) 4√2 - Distance = √[(3-(-1))² + (-2-2)²] = √[16+16] = √32 = 4√2
16. Correct answer: A) 23 - (x+1/x)² = x²+2+1/x² = 25 → x²+1/x² = 23
17. Correct answer: A) 710 - This is an AP with a=7, d=3, S₂₀ = (20/2)[2×7 + (20-1)×3] = 10[14+57] = 10×71 = 710
18. Correct answer: A) 6 cm - Using Pythagoras theorem: AC = √(BC² - AB²) = √(100-64) = √36 = 6 cm
19. Correct answer: A) 1/2 - sec²θ - tan²θ = 1 → (secθ+tanθ)(secθ-tanθ)=1 → 2×(secθ-tanθ)=1 → secθ-tanθ=1/2
20. Correct answer: A) 102⅔ cm² - Area of sector = (θ/360)×πr² = (60/360)×(22/7)×14² = (1/6)×(22/7)×196 = (1/6)×616 = 102.67 = 102⅔ cm²
Science Solutions:
Physics:
21. Correct answer: A) 60 km/h - Total distance = 60+80+40 = 180 km, total time = 3 hours, average speed = 180/3 = 60 km/h
22. Correct answer: A) 3 seconds - Using h = ½gt² → 45 = ½×10×t² → t² = 9 → t = 3 seconds
23. Correct answer: A) 0.4 m - Power = 1/f → f = 1/P = 1/2.5 = 0.4 m
24. Correct answer: B) 10 N - Weight on moon = (1/6)×weight on earth = (1/6)×60 = 10 N
25. Correct answer: B) 40 Ω - Resistance R ∝ L², so if length doubles, resistance becomes 4 times → 4×10 = 40 Ω
26. Correct answer: B) 200 J - Heat = I²Rt = (2)²×5×10 = 4×5×10 = 200 J
27. Correct answer: A) 340 m/s - Speed = frequency × wavelength = 500 × 0.68 = 340 m/s
28. Correct answer: A) 60 cm from mirror - Using mirror formula: 1/f = 1/v + 1/u → 1/20 = 1/v + 1/(-30) → 1/v = 1/20 + 1/30 = 5/60 → v = 60 cm
29. Correct answer: A) 5 m/s² - F = ma → a = F/m = 20/4 = 5 m/s²
30. Correct answer: B) 100 J - KE = ½mv² = ½×2×100 = 100 J
31. Correct answer: B) 2.4 Ω - 1/R = 1/4 + 1/6 = 5/12 → R = 12/5 = 2.4 Ω
32. Correct answer: A) 42° - Critical angle θ = sin⁻¹(1/μ) = sin⁻¹(1/1.5) = sin⁻¹(0.6667) ≈ 42°
Chemistry:
33. Correct answer: A) CH₄ - Methane is the simplest hydrocarbon with formula CH₄
34. Correct answer: B) H₂ - H₂ is the reducing agent as it reduces CuO to Cu
35. Correct answer: B) 7 - pH of neutral solution is always 7 at 25°C
36. Correct answer: C) Hydrogen - Zn + 2HCl → ZnCl₂ + H₂↑
Biology:
37. Correct answer: B) Xylem - Xylem tissue transports water and minerals in plants
38. Correct answer: B) Photosynthesis - Photosynthesis is the process by which plants make food using sunlight
39. Correct answer: C) Cerebellum - The cerebellum controls balance, coordination, and posture
40. Correct answer: C) Pancreas - Insulin is produced by the beta cells of the pancreas
English Solutions:
41. Correct answer: B) Careful - Meticulous means showing great attention to detail; very careful and precise.
42. Correct answer: C) for - "For" is used with a period of time, while "since" is used with a point in time.
43. Correct answer: B) Definitely - This is the correct spelling of the word meaning without doubt.
44. Correct answer: B) Neither of the boys is present - "Neither" is singular and takes a singular verb.
45. Correct answer: B) Scarce - Abundant means plentiful, so the antonym is scarce.
46. Correct answer: A) postponed - Postponed means to delay something to a later time.
47. Correct answer: C) were - "I wish I were" is the correct subjunctive form for hypothetical situations.
48. Correct answer: D) Adverb - "Quickly" modifies the verb "runs", so it's an adverb.
49. Correct answer: B) at - We use "good at" to indicate proficiency in a subject or activity.
50. Correct answer: C) The - We use "the" before the names of rivers.