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Q1. What is the value of log₄(16)?
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Q2. The scalar product of vector 'a' and unit vector 'j' is:
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Q3. If A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]], what is det(A)?
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Q4. If $x = 2$, $y = -1$, $z = -1$, then the value of $x^3+y^3+z^3-3xyz$ is:
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Q5. Simplify 2⁵.
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Q6. The scalar product of two non-zero vectors is zero if and only if the vectors are:
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Q7. What is the sum of the first 5 terms of the GP 1, 2, 4, 8, ...?
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Q8. Find the missing number in the series 1, 4, 7, 10, ?
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Q9. For a homogeneous system of linear equations Ax = 0, where A is an n x n matrix, a non-trivial solution exists if and only if:
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Q10. If f(x) = 2^x, then f⁻¹(x) is:
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Q11. What is the modulus of z = 2 + 2i?
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Q12. If $2^x = 4$, $4^y = 8$, $8^z = 16$, then the value of $xyz$ is:
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Q13. The sum of the first n terms of an arithmetic progression is given by S_n = 3n^2 + 2n. If the 10th term of the series is 32, what is the common difference?
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Q14. The sum of an infinite geometric series is 18. If the first term is 6, what is the common ratio?
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Q15. If f(x) = 2x, what is f(f(3))?
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Q16. What is the common difference of the arithmetic progression: 10, 7, 4, 1, ...?
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Q17. If a, b, c are in Harmonic Progression, then which of the following is always true?
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Q18. If $x-a$ is a factor of $x^2 - 5x + 6$ and $x-b$ is a factor of $x^2 - 7x + 12$, and $a < b$, what is the value of $a+b$?
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Q19. What is the domain of the function f(x) = 5?
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Q20. A car travels from city A to city B at a speed of 60 km/hr and returns from city B to city A at a speed of 40 km/hr. What is the average speed for the entire journey?
