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Practice Algebra Questions and Answers

In Δ ABC, ∠ B= 68° and ∠ C 32°. Sides AB and AC are produced to points D and E, respectively. The bisectors of ∠ DBC and &...
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If 2x+1, x+2, 2 and 5 are in proportion, then what is the mean proportional between 3.5(1-x) and 8(1+x)?
In △ ABC, ∠ A = 90°. M is the midpoint of BC and D is a point on BC such that AD Ʇ BC. If AB = 7 cm and AC = 24 cm. then AD: AM is equa...
In △ ABC, AB = AC. A circle drawn through B touches AC at D and intersect AB at P. If D is the midpoint of AC and AP = 2.5 cm, then AB is equal to:
If a + b + c = 11, ab + bc + ca = 3 and abc = -135, then what is the value of a³ + b³ + c³ ?
When 732 is divided by a positive integer x, the remainder is 12. How many values of x are there?
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If x ,y,z are three integers such that x +y = 8,y +z =13 and z +x =17,then the value of x2 /yz is:
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 ...

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