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Q1. The x-intercept of a graph is the point where:
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Q2. If the origin is the centroid of the triangle with vertices (x, 2, 3), (4, y, 5), and (6, 7, z), find the value of x + y + z.
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Q3. What is the sum of the first 10 terms of the AP 10, 20, 30, 40,...?
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Q4. If f(x) = 4x - 1 and g(x) = x/4, what is f(g(8))?
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Q5. What is the first term of an arithmetic progression if the 5th term is 15 and the common difference is 2?
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Q6. In an AP, the sum of p terms is equal to the sum of q terms. Then the sum of the first (p+q) terms is:
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Q7. If log₃(x) = 3, then x = ?
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Q8. The cost of 2 kg of apples and 1 kg of grapes is Rs. 160. The cost of 4 kg of apples and 3 kg of grapes is Rs. 280. Find the cost of 1 kg of grapes.
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Q9. If the harmonic mean of three numbers is 6, and two of the numbers are 3 and 4, what is the third number?
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Q10. The sum of the diagonal elements of a square matrix is called its:
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Q11. If 12x = 144, what is x?
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Q12. If $a+b+c = 6$, $a^2+b^2+c^2 = 14$, and $a^3+b^3+c^3 = 36$, then the value of $abc$ is:
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Q13. If h(x) = 4x - 3, what is the solution to h(x) <= 9?
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Q14. If the arithmetic mean of two numbers is 15 and their harmonic mean is 9, what is their geometric mean?
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Q15. If f(x) = 2x + 1 and g(x) = 5x - 2, what is the solution to f(x) > g(x)?
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Q16. If $a-b=2$ and $a^2+b^2=20$, then the value of $a^3-b^3$ is:
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Q17. If x/a = y/b = z/c, then (x+y+z)/(a+b+c) is equal to:
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Q18. If $P(x) = x^3 - 3x^2 + 4$, then $(x-1)$ is:
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Q19. Find the equation of the plane passing through (1, 2, 3) and perpendicular to both the x-axis and y-axis.
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Q20. The geometric mean of two numbers is the square root of their sum.
