Maths and Science test by Abhinav Sir

Math & Science Quiz

Welcome to the Math & Science Quiz! This quiz tests your knowledge in algebra, factorization, and fossil fuels. You have 1 hour to complete 20 questions. Each question has four options. Select the correct answer, and upon submission, correct answers will turn green, and incorrect ones will turn red. Your score, rank, and detailed explanations will be displayed at the end. Good luck!

Time Left: 60:00

1. Simplify \((ax + by)^2 + (bx - ay)^2\):

\((a^2 + b^2)(x^2 + y^2)\) \((a^2 - b^2)(x^2 - y^2)\) \((ax + by)(bx - ay)\) \(a^2x^2 + b^2y^2\)

2. If \(x + \frac{1}{x} = 5\), find \(x^2 + \frac{1}{x^2}\):

23 25 27 21

3. If \(a + b = 12\) and \(ab = 14\), find \(a^2 + b^2\):

116 144 172 28

4. Factorize \(ab(x^2 + y^2) - xy(a^2 + b^2)\):

\((ax - by)(bx + ay)\) \((ax + by)(bx - ay)\) \((ax - by)(bx - ay)\) \((ax + by)(bx + ay)\)

5. Factorize \(y^2 + 2y - 3\):

\((y + 3)(y - 1)\) \((y + 1)(y - 3)\) \((y + 2)(y - 1)\) \((y - 2)(y + 3)\)

6. Factorize \(40 + 3x - x^2\):

\((x + 8)(5 - x)\) \((x - 8)(5 + x)\) \((x + 5)(8 - x)\) \((x - 5)(8 + x)\)

7. Factorize \(3 + 23y - 8y^2\):

\((8y + 3)(y - 1)\) \((8y - 3)(y + 1)\) \((8y + 1)(3 - y)\) \((3 - y)(8y - 1)\)

8. Divide \(a^3 - b^3\) by \((a - b)\). What is the quotient?

\(a^2 + ab + b^2\) \(a^2 - ab + b^2\) \(a^2 + ab - b^2\) \(a^2 - ab - b^2\)

9. Which is the correct formula for \(a^3 - b^3\)?

\((a - b)(a^2 + ab + b^2)\) \((a + b)(a^2 - ab + b^2)\) \((a - b)(a^2 - ab + b^2)\) \((a + b)(a^2 + ab + b^2)\)

10. Find the smallest number that should multiply 4000 to make it a perfect cube:

5 25 50 125

11. Find the number that should multiply 125 to make it a perfect square:

5 25 125 625

12. Which of the following is used as a reducing agent in the extraction of iron metal?

Coal Bitumen Charcoal Coke

13. The slow process by which large land plants and trees buried deep under the earth have become coal is called:

Carbonation Carburetion Carbonization Carbocation

14. Which is the major component of CNG?

Ethane Propane Methane Butane

15. Which one of the following is not a fossil fuel?

Petrol Coke Charcoal Coal

16. Which of the following is being used as a source of hydrogen gas needed to manufacture fertilizers?

Biogas Natural gas Coal gas Petroleum gas

17. The various compounds present in coal tar are separated by the process of:

Simple distillation Destructive distillation Fractional distillation Fractional crystallization

18. The substance W is a fossil fuel found deep below the ground. Another fossil fuel X is trapped above W. When W is subjected to process Y, a special grade of product Z is used as aviation fuel. What is Z?

Petrol Diesel Kerosene Bitumen

19. Fossil fuel P is formed by the decomposition of vegetable matter under water by anaerobic bacteria. Its major component is Q. P is used to produce gas R for nitrogenous fertilizers and as fuel S in vehicles. What is S?

LPG CNG Petrol Diesel

20. Which of the following is a fossil fuel?

Wood Coal Charcoal Biomass

Results

Score: /20

Rank:

Analysis

Correct Answers:

Incorrect Answers:

Explanations