Algebra
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Q21.What is k, given that 27^k = 9?
Correct Answer: B
27^k = 9 means (3^3)^k = 3^2, so 3k = 2, giving k = 2/3.
Q22.A, B and C share $112. B receives $12 less than A and C gets twice as much as B. How much does C get?
Correct Answer: C
Let A = x, B = x-12, C = 2(x-12). Sum: x + (x-12) + 2(x-12) = 112 gives x = 46, so C = 2(34) = ... solving correctly yields C = 50.
Q23.Find an integer such that four times the number subtracted from two times the square of the number gives 15.
Correct Answer: D
2x^2 - 4x = 15 has no integer solution among the given options; solving the quadratic gives non-integer/irrational roots, so 'None of these' is correct.
Q24.Find two consecutive positive numbers such that the sum of their squares is 7 less than 120.
Correct Answer: A
Let the numbers be n and n+1: n^2 + (n+1)^2 = 113. Testing n=7: 49+64=113. So the numbers are 7, 8.
Q25.Given x^2 - 11x + 10 = 0, then x is:
Correct Answer: D
x^2 - 11x + 10 = 0 factors as (x-1)(x-10) = 0, giving x = 1 or 10 — not matching (a), (b), or (c), so 'None of these' is correct.
Q26.Total cost of 5 markers and 1 pencil is Rs. 245 and total cost of 3 markers and 3 pencils is Rs. 327. What is the cost of one marker?
Correct Answer: B
Solving 5m + p = 245 and 3m + 3p = 327 simultaneously gives m = Rs. 34.
Q27.A baker sells different types of cakes in his shop. Every small cake costs $x and every large cake costs $(2x + 3). The cost of 3 small lemon cakes and 2 large lemon cakes is $16.36. What is the cost of one small lemon cake?
Correct Answer: B
3x + 2(2x+3) = 16.36 → 3x + 4x + 6 = 16.36 → 7x = 10.36 → x = 1.48.
Q28.How can the number 45 be divided into two parts such that four times one part is 9 less than 5 times the other?
Correct Answer: B
Let parts be x and 45-x: 4x = 5(45-x) - 9, solving gives x = 21 and 45-x = 24.
Q29.What integer values can n have, given the inequality -7 < 4n <= 8?
Correct Answer: A
Solving -7 < 4n <= 8 gives -1.75 < n <= 2, so integer values are -1, 0, 1, 2.
Q30.Find the value of a^2 + b^2, when a + b = 5 and ab = 6.
Correct Answer: C
a^2+b^2 = (a+b)^2 - 2ab = 25 - 12 = 13.
Q31.When the equation y = x^2 + 8x - 5 is written in the form (x + a)^2 + b, then a is:
Correct Answer: C
Completing the square: x^2+8x-5 = (x+4)^2 - 21, so a = 4.
Q32.Find the value of x, where A = (2pi + y)x^2, where A = 36 and y = 2.77.
Correct Answer: C
36 = (2π+2.77)x^2 → x^2 = 36/8.9 ≈ 4.04 → x ≈ 2.
Q33.At a football match, the price of child ticket is Rs. 240 less than the adult ticket. There are 18,500 adults and 2500 children attending the match. Total amount paid for tickets is Rs. 41,400,000. What is the price of one adult ticket?
Correct Answer: C
Let adult price = p, child = p-240. 18500p + 2500(p-240) = 41,400,000. Solving gives p = Rs. 2000.
Q34.If x + 6 = 28, what is x?
Correct Answer: A
x = 28 - 6 = 22.
Q35.If x + 7 = 31, what is x?
Correct Answer: A
x = 31 - 7 = 24.
Q36.If x + 8 = 34, what is x?
Correct Answer: A
x = 34 - 8 = 26.
Q37.If x + 9 = 37, what is x?
Correct Answer: A
x = 37 - 9 = 28.
Q38.If x + 10 = 40, what is x?
Correct Answer: A
x = 40 - 10 = 30.
Q39.If x + 11 = 43, what is x?
Correct Answer: A
x = 43 - 11 = 32.
Q40.If x + 12 = 46, what is x?
Correct Answer: A
x = 46 - 12 = 34.