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Practice Algebra Questions and Answers

Find the value of 3/4 cot² 30° + cos² 30°-3cosec²60° + tan² 60°.
In a triangle ABC, a point D lies on AB and points E and F lie on BC such that DF is parallel to AC and DE is parallel to AF. If BE = 4 cm. EF = 6cm. then ...
If the seven-digit number 94x29y6 is divisible by 72, then what is the value of (2x+3y) for x ≠ y?
A certain number of students from school X appeared in an examination and 30% students failed. 150% more students than those from school X, appeared in the...
(√ (sec2 θ + cosec2 θ )) ((sinθ (1 + cosθ ))/(1 + cosθ - sin2 θ )) , 0˚ <&nb...
If x2 – xy + y2 = 16 and x4 + x2y2 + y4 = 320 then find x2 + xy + y2 = ?...
ABCD is a cyclic quadrilateral in which AB =16.5 cm. BC = x cm. CD= 11 cm. AD 19.8 cm, and BD is bisected by AC at O. What is the value of x?
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:

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