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Practice Algebra Questions and Answers

In ∆ ABC, MN ‖ BC, the area of quadrilateral MBCN=130 sqcm. If AN : NC = 4 : 5, then the area of ∆ MAN is: ...
If x −y =4and xy =45,thenthevalueof x 3 −y3is:
If the length of a rectangle is increased by 40%, and the breadth is decreased by 20%,then the area of the rectangle increases by x%. Then the value of x i...
The area of △ ABC is 44 cm2 . If D is the midpoint of BC and E is the midpoint of AB, then the area of △ BDE is
A, B and C are three points on a circle such that the angles subtended by the chord AB and AC at the centre O are 110° and 130°, respectively. Then the v...
If x2a = y2b =z2c ≠ 0 and x2 = yz, then the value of (ab + bc + ca) /bc is :
If 27 (x+y)³ − 8(x−y)³ = (x + 5y) (Ax² + By² + Cxy), then what is the value of (A+B-C)?
If a + b + c = 6, a³ + b³ + c³-3abc = 342, then what is the value of ab + bc + ca
The average of three numbers a, b and c is 2 more than c. The average of a and b is 48. If d is 10 less than c, then the average of c and d is:
The graphs of the equations 3x-20y-2=0 and 11x-5y +61=0 intersect at P(a,b). What is the value of (a² + b² − ab)/(a² − b² +...
The area (in sq, units) of the triangle formed by the graphs of 8x + 3y = 24, 2x+8 = y and the x – axis is:
If (10 a³ + 4b³): (11a³ — 15b³) = 7:5, then (3a + 5b): (9a - 2b) = ?
When positive numbers x, y and z are divided by 31, the remainders are 17, 24 and 27, respectively. When (4x - 2y + 3z) is divided by 31, the remainder wil...
If 9x² + y² = 37 and xy=2, x, y>0, then the value of (27x³ + y³) is:
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 ...

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