8/2/25
Expansion
1) Expand
a) (x/2 + 2y/3)²
b) (2a + 3b + 4c)².
c) (4a - 3b)²
d) (3a - 2b + 5c)².
2)) If x + 1/x = 4, find the value of
a) x²+ 1/x².
b) x⁴+ 1/x⁴.
3) If (x - 1/2x) =3, find the values of
a) (x²+ 1/4x²) b) (x⁴+ 1/16x⁴).
4) If (a²+ 1/a²)= 14, find the values of
a) (a+ 1/a) b) (a - 1/a) c) (a²- 1/a²).
5) Without multiplying, evaluate
a) (107)².
b) (20.6)².
c) (996)².
d) (9.7)².
6) Using the formula (a+ b)(a- b)= (a²- b²), evaluate (124 x 116).
7) Complete each of the following expressions, making it a perfect square:
a) 25a²+ 9b²+ _____.
b) 16a²- 8ab+ ____.
8) If (a²+ b²+ c²)= 125 and (ab+ bc+ ca)= 50, find the value of (a+ b + c).
9) Find the products by inspection
a) (x +5)(x+3).
b) (x -7)(x+2).
c) (2- x)(6- x).
d) (5x -3)(3x -2).
Factorisation
1) x²+ y - xy - x.
2) ab+ bc+ ax+ cx .
3) a²+ 4a + a+ 4.
4) 6ab - b²+ 12ac - 2bc .
5) (ax + by)²+ (bx - ay )².
6) (x²+ 2x)² - 3(x²+ 2x) - y(x²+ 2x)+ 3y.
7) x²+ 1/x²+2-2x - 2/x.
8) 25a²- 9b².
9) 1- (b - c)².
10) 2x³- 50x.
11) 16a³- 4a.
12) 3x⁵-48x.
13) x³-3x²- x +3.
14) x²-2y + xy -4.
15) a(a -1) - b(b -1).
16) a²+ b²- c²- 2ab.
17) 16x²- y²+ 4yz - 4z².
18) (x²+ y²- z²)² - 4x²y².
19) 2(ab+ CD) - a² - b² + c² + d².
20) (1- x²)(1- y²)+ 4xy.
21) x⁴+ y⁴- 11x²y².
22) Evaluate
a) {(968)²- (32)²}.
b) {(98.7)² - (1.3)²}.
23) x²+ 11x +30.
24) (x²+6x -27).
25) x²-5x -24.
26) 3x²+ 14x +8.
27) 2x²- 9x -26.
28) 7 - 12x - 4x².
29) 3x²- xy - 14y².
30) 2x³+ 5x²y - 12xy².
31) 3(a - 2b)² - 2(a - 2b) -8.
_____________________________
a) x b) y c) xy d) x+ y
2) At what rate of interest compounded annually will ₹625 amount to ₹784 in 2 years?
a) 12% b) 10% c) 15% d) 11%
3) If x and y vary inversely and x= 40, find y when constant of variation= 8.
a) 4 b) 6 c) 8 d) none
4) If a tank is emptied in x hours then in 1 hour ____ part will be emptied.
a) 1/x b) x/2 c) x d) none
5) Value of (a²+ b²+ 2ab)(a+ b)+ 6ab is
a) a b) b c) a²+ b² c) none
6) Factorize: x²- 14xy + 49y²
a) (x+7y)² b) (x-7y)² c) (x-7y)(x+7y) d) (x-7y)(x7y)
7) If (4x +8)/(5x +8)= 5/6 then x=?
a) 4 b) 6 c) 8 d) 12
8) Half of a number when decreased by 10 gives 14, what is the number?
a) 24 b) 84 c) 48 d) 74
9)
a) 90 b) 110 c) 180 d) none
10) The sum of all interior angle of a polygon is 1080, what is the measure of each interior angle?
a) 125 b) 130 c) 135 d) 140
11) How much soil is required to fill a triangular flower bed, where base is 35m and height is 8m ?
a) 140m² b) 141 m² c) 142 m² d) 143m²
12) Find the volume of a cubical tank of side 2cm.
a) 8cm² b) 8cm³ c) 7cm³ d) 6cm²
13) Three coins are tossed simultaneously. What are the possible outcomes ?
a) 7 b) 8 c) 9 d) 10
14) Empty set is a____ set.
a) finite set b) infinite set c) null set d) none
15) Simplify (³√2197 x ³√1728)/³√1331
a) 152/10 b) 150/12 c) 155/11 d) 156/11
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