Practice Algebra Questions and Answers

• A solid metallic sphere of radius 15 cm is melted and recast into spherical balls of radius 3 cm each. What is the ratio of the surface area of the origina...
• Given that x8-34x4+1=0, x>0. What is the value of (x3+ x-3)?
• In an orchard, the ratio of the number of mango and lichi trees is 9:10, respectively. Also, there are few apple trees in the orchard which is 50% more tha...
• A man running at the speed of 6 kmph was over taken by the train moving with the speed of 78 kmph in 20 seconds. Find the length of train.
• The speed of a car is 25% more than that of a bike. Both of them start from a same point. After travelling for 4 hours, the speed of the bike is increased ...
• In an A.P 41st term is 50, then the sum of 81 terms of that A.P is:
• If (x2 + y2) = 9 and (xy)2 = 3, then find the value of (x4 + y4). 
• If (x + y + z) = 68, (x/z) = (3/4) and (z/y) = (2/5), then find the value of ‘y’.
• If a + (1/a) = 2, then find the value of (a5 + a3 + 6)/(7a – 5). 
• If x + y + z = 4, xyz = 6 & x2 + y2 + z2 = 8 then find the value of x3 + y3 + z3.
• If 4x + 1/3x = 12 then find the value of 9x2 +1/16x2. 
• If √x + 1/√x = 2 then find the value of 3x2 + 1/3x2.
• If x = (√13 + √12)/ (√13 - √12) and y = (√13 - √12)/(√13 + √12), then find the value of 4x2 – xy + 4y2....
• If x4 + x - 4 = 47 then find the value of (x + x-1). 
• If (a + b) = 1 and (1/a) – 2b = 5/a then find the value of a2 + b2.
• If 0.125x3 +0.216y3 = 210 and 0.25x2 + 0.36y2 = 10.30 then find the value of 0.5x + 0.6y.
• Find the value x2 + y2, if xy = 13 and x + y = 7.
• Evaluate (998)3 without multiplying directly.
• If (5x + 2)3 + (x – 1)3 + 8(3x – 7)3 = 6(5x + 2) × (x – 1) × (3x – 7), then the value of (5x + 3) is ...
• If (x + y) = 6 and (x2 + y2) = 20, then the value of (x – y)2 is equal to:
• If a – b – c = 0, then the value of (a2 + b2 + c2)/(b + ac) is: 
• If a3 + b3 = 6240 and a + b = 30, then find the value of {(a + b)2 – 3ab}
• If x2 – 8√2x + 1 = 0, then what is the value of x3 + 1/x3.
• If A = (7)1/3 + (7) -1/3, then the value of {3A3 – 9A} will be:
• If 9x2 + 16y2 = 24xy, then find the ratio of ‘x’ and ‘y’, respectively.
• If x2 – 5x + 1 = 0, then find the value of {x2 + (1/x2)}.
• If a + b + c = 12 and ab + bc + ca = 50, then find the value of a2 + b2 + c2.
• If x + y = 4 and (1/x) + (1/y) = 24/7, then the value of (x3 + y3).
• In a class of 70 students and 25 teachers, each student got gifts that were 20% of total number of students and each teacher got gifts that were 10% of tot...
• 125 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. H...
• A train can cross a pole, a bridge of 720 meter long and platform of 640 meter long in 9 seconds, _____ seconds and 25 seconds, respectively. The value giv...
• If x + y = 2 and 1/x + 1/y = 18/15, then find the value of (x3 + y3)?
• If [8(x + y)3 – 27(x – y)3] ÷ (5y – x) = Ax2 + Bxy + Cy2, then the value of (A2 - 2B + 3C) is:...
• If polynomial P(x) = x3 - 3x2 + 5x-3 is divided by polynomial G (x) = x2 - 2, the quotient and remainder are:
• Out of total number of people in an office, 40% are males. Ratio of number of married to that of unmarried people in the office is 3:2 while ratio of numbe...
• Before servicing, a car runs at a speed of 25 km/hr while after servicing, it runs at a speed of 50 km/h. After servicing the car covers a certain distance...
• If (x + y) = 35, then find the value of (x - 10)6 + (y - 25)6.
• A shopkeeper marked his article 25% above its cost price and offered a discount of 30%. If cost price of the article is Rs. 560, then find profit or loss o...