Practice Algebra Questions and Answers

• If the sum of three numbers is zero, then which of the options below will always be equal to the value of the sum of the cubes of those numbers?
• In a best-of-two chess match between Player X and Player Y, the probability that Player X wins a game is (5/9), and the probability that Player Y loses a g...
• What is the average of the first 20 multiples of 12?
• If 112 ÷28 x 22 –12 x 6 ÷ 3 +12 = z, then find the value of z.
• Find the number in place of ? 6, 14, 26, ?, 106, 214
• If there are a total of 1000 students in the school, how many students prefer Mathematics and science?
• A dishonest dealer claims to sell goods at cost price but uses a false weight of 900g instead of 1kg. What is his profit percentage?
• A company’s expenditure on three departments over four years is as follows (in thousands): What is the total percentage increase in expenditure on R&D f...
• The mean age of 30 students was calculated as 15 years. However, it was later discovered that one student's age was mistakenly entered as 15 years instead ...
• 47.98 × 4.16 + √325 × 12.91 + ? = 79.93 × 5.91
• If p3 + 9p2 + 8p + 13 = 6p2 + 5p + 12, then find the value of {(p4 + 1/p2)}/(p2 + 3p + 1)....
• If x + 1/x = 3, find the value of x³ + 1/x³.
• Find the largest 5-digit number that is divisible by 12, 15, 18, and 24. Also, what is the remainder when this number is divided by 11?
• If 2x + y = 10 and 3x - 2y = 5, find the value of x + y.
• If x² + px + q = 0 has roots 4 and -3, find the values of p and q.
• Find the values of 'a' and 'b', so that the polynomial x3 − ax2 − 13x + b has (x−1) and (x+3) as factors:
• If x2 - 3x + 2 is a factor of, x4 - px2 + q, then (p, q) =
• If (x – 12)3 + (x – 5)3 + (x – 7)3 = 3(x – 12)(x – 5)(x – 7) then find the value of (x2 + 5x + 12) ...
• If x + y + z = 9 and (x2 + y2 + z2) = 21, then find the value of (xy + yz + zx)
• If (a + b)2 = 18 + c2, (b + c)2 = 22 + a2 and (c + a)2 = 24 + b2, then find the value of (a + b + c)....
• Consider a function f(x) = x4 + x3 + x2 + x + 1, where x is a positive integer greater than 1. What will be the remainder if f(x5) is divided by f(x) ?...
• If 2x + (1/9x) = 5, then find the value of 81x2 + (1/4x2) - (1785/4)
• If (3x - y) = 3, xy = (2/3), then find the value of {x3 - (y3/27)}
• Solve for x in the equation: 3(x + 2) + 2(2x - 5) = 5x + 9
• A number is increased by 20%, and the resulting number is decreased by 20%. If the initial number is ₹x, the final number is ₹2880. What is the value o...
• Simplify the following expression:  (8x - 6y - 5z)  2
• If 8x3 - 125y3 = (2x - Ay) X (Bx2 + 25y2 + Cxy), then find the value of 3 X (2A + 6B) - 2C.
• (p + q) = 8 and (p2 + q2 - 6) = 28. If p < q, then determine the value of (p/q).
• Ravi marked an item at 125% above its cost price and then sold it after applying three successive discounts of 20%, 20%, and 25%. Calculate the profit or l...
• In a college, the proportion of boys to girls is 7:9, and the proportion of graduate students to postgraduate students is 4:5. Determine the total number o...
• The roots of the quadratic equation x² + px + q = 0 are in the ratio 3:4. If the sum and product of the roots are 7 and 12, respectively, find the values ...
• You are provided with three sequences below. Determine the values of P, Q, and R, and then identify the relationship among them. (i) 840, P, 584, 456, 520,...
• If (p/q) = (7/8) and (q/r) = (3/11), then the find the value of {(r – p)/(p + q)}.
• If x2 - 7x + 1 = 0, then determine the value of: ...
• Given that (3a + 7b = 54) and (ab = 24), determine the value of (9a2 + 49b2).
• Calculate the value of the expression: {2 X (P3 - Q3) - 30 X P X Q} if (P - Q) = 6 and (P2 + Q2) = 80
• If x + y + xy = 118, such that x < y and both 'x' and 'y' are positive integers, then find minimum value of (x + y) .
• Find the common factor of (x2 - 4x - 12) and (x2 - 14x - 32).
• If x2 = 15x + 1, then find the value of {x3 - (1/x3) }.