ALGEBRAIC IDENTITIES
1) The square root of a²+ 1/a²+ 2 is
a) a+ 1/a b) a- 1/a c) a²+ 1/a² d) a²- 1/a²
2) The square root of a+ 1/a - 2 is
a) a -1/a b) √a+ 1/√a c) ±(√a- 1/√a) d) a+ 1/a
3) The value of (a+ b)²/{(b -c)(c - a)} + (b + c)²/{(a - b)(c - a) + (c + a)²/{(a - b)(b - c)} is
a) -1 b) 0 c) 1 d) 2
4) The square root of the expression (1/abc) (a²+ b²+ c²) +2(1/a + 1/b+ 1/c) is
a) (a+ b+ c)/abc b) √a + √b + √c c) √(bc/a) + √(ca/b) + √(ab/c) d) √(a/bc)+ √(b/ca) + √c/ab)
5) The square root of x²/9 + 9/4x² - x/3 - 3/2x + 5/4 is
a) 2x/3 + 3/2x - 1/2 b) x/3 + 3/2x +1 c) 3/x + 2/3x - 1/2 d) x/3 + 3/2x - 1/2
6) The square root of the expression is (xy + xz - yz)² - 4xyz(x - y) is
a) xy + yz - 2xyz b) x + y - 2xyz c) xy + z - y d) xy + yz - xz
7) The square root of a²/4 + 1/a² - 1/a + a/2 - 3/4 is
a) a/2 - 1/a + 1/2 b) a/2 + 2/a - 1 c) a/2 + 1/a - 1/2 d) a/2 - 2/a - 1/2
8) The expression (4a + 5b+ 5c)² - (5a + 4b+ 4c)² + 9a² is a perfect square of the expression
a) √3(b + c) b) 3(a+ b + c) c) 3(b+ c) d) 3(-b + c - a)
9) The expression (3a + 2b+ 3c)² - (2a + 3b+ 2c)² + 5b² is a perfect square of the expression √(a + b+ c) b) √((a + b) c) √5(a +c) d) √5(a - b+ c)
10) If a/b + b/a =2, then (a/b)¹⁰ - (b/a)¹⁰ is equal to
a) (2¹⁰-1)/2¹⁰ b) 2 c) 0 d) (2²⁰+1)/2¹⁰
11) If ab c = 6 and a + b + 6 = 6, then 1/ac + 1/ab + 1/bc =
a) 2 b) 1 c) 3 d) 0
12) √{(a + b+ c)²+ (a + b- c)²+ 2(c² -b²- a²- 2ab) is equal to
a) 2c b) 2a c) 2b d) a + b+ c
13) If a/b + b/a = -1, then a³- b³=
a) 1 b) -1 c) 1/2 d) 0
14) If a+ b=8 and ab= 12, then a³+ b³=
a) 244 b) 224 c) 144 d) 284
15) If (a + 1/a +2)²=4, then a²+ 1/a²=
a) 12 b) 13 c) 14 d) -14
16) If x+ 1/x =7, then x³- 1/x³=
a) 9√5 b) 144√5 c) 135√5 d) √5
17) {(a - b)³ - (a + b)³}/2 + a(a²+ 3b²)=
a) a³- b³ b) (a + b)³ c) a³+ b³ d) (a - b)³
18) If x+ 1/x =5, then x²+ 1/x²=
a) 25 b) 10 c) 23 d) 27
19) If x+ 1/x =2, then x³ + 1/x³=
a) 64 b) 14 c) 8 d) 2
20) If x+ 1/x =4, then x⁴ + 1/x⁴=
a) 196 b) 194 c) 192 d) 190
21) If x+ 1/x =3, then x⁶ 1/x⁶=
a) 927 b) 414 c) 364 d) 322
22) If x² + 1/x² =102, then x- 1/x=
a) 8 b) 10 c) 12 d) 13
23) If x³+ 1/x³ =110, then x + 1/x =
a) 5 b) 10 c) 15 d) none
24) If x³- 1/x³ =14, then x- 1/x=
a) 5 b) 4 c) 3 d) 2
25) If a+ b+ c= 9 and ab+ bc+ ca= 23, then a²+ b²+ c²=
a) 35 b) 58 c) 127 d) none
26) (a - b)³+ (b - c)³+ (c - a)³=
a) (a+ b+ c)(a²+ b²+ c²- ab - bc - ca)
b) (a - b)(b - c)(c - a)
c) 3(a - b)(b - c)(c - a) d) none
27) a+ b= 3 and ab = 2, then a³+ b³=
a) 6 b) 4 c) 9 d) 12
28) If a- b =-8 auab = -12, then a³- b³=
a) -244 b) -240 c) -224 d) -260
29) if the volume of a cuboid is 3x²- 27, then its possible dimensions are
a) 3, x, -27x b) 3, x -3, x+3 c) 3, x², 27x d) 3,3,3
30) 75 x 75 +2 x 75 x 25+25 x 25 is equal to
a) 10000 b) 6250 c) 7500 d) 3750
31) (x - y)(x+ y)(x²+ y²)(x⁴+ y⁴) is equal to
a) x¹⁶- y¹⁶ b) x⁸- y⁸ c) x⁸+ y⁸ d) x¹⁶+ y¹⁶
32) If x⁴+ 1/x⁴ =623, then x + 1/x=
a) 27 b) 25 c) 3√3 d) -3√3
33) If x- 1/x = 15/4, then x + 1/x =
a) 4 b) 17/4 c) 13/4 d) 1/4
34) If 3x+ 2/x = 7, then 9x² - 4/x² =
a) 25 b) 35 c) 49 d) 30
35) If a²+ b²+ c²- ab - bc - ca = 0, then
a) a+ b = c b) b + c = a c) c + a= b d) a= b= c
36) If a+ b + c = 0, then a²/bc + b²/ca + c²/ab is
a) 0 b) 1 c) -1 d) 3
37) If a¹⁾³ + b¹⁾³ + c¹⁾³= 0, then
a) a+ b+ c= 0 b) (a+ b + c)³= 27abc c) a+ b + c = 3abc d) a³+ b³+ c³= 0
38) If a+ b + c = 9, then ab+ bc + ca =23, then a³+ b³+ c³- 3abc=
a) 108 b) 207 c) 669 d) 729
39) {(a² - b²)³+ (b²- c²)³+ (c²- a²)³}/{(a - b)+ (b - c)+(c - a)}=
a) 3(a + b) (b +c)(c +a) b) 3(a - b)(b - c)(c - a)} c) (a - b) (b - c)(c - a) d) (a + b) (b +c)(c+ a)
40) The product (a + b)(a - b)(a²- ab+ b²)(a²+ ab+ b²) =
a) a⁶+ b⁶ b) a⁶- b⁶ c) a³- b³ d) a³+ b³
41) The product (x²-1)(x⁴+ x²+1) is equal to
a) x⁸-1 b) x⁸+1 c) x⁶-1 d) x⁶+1
42) If a/b + b/a = 1, then a³+ b³=
a) 1 b) -1 c) 1/2 d) 0
43) If 49a²- b = (7a + 1/2)(7a - 1/2), then the value of b is
a) 0 b) 1/4 c) 1/√2 d) 1/2
44) One of the factors of (5x +1)² -(5x -1)² is
a) 5 + x b) 5- x c) 5x -1 d) 20x
45) If 9x² - b =(3x + 1/2)(3x - 1/2), then the value of b is
a) 0 b) 1/√2 c) 1/4 d) 1/2
46) The Coefficient of x in (x +3)³ is
a) 1 b) 9 c) 18 d) 27
47) The value of 249²- 248² is
a) 1 b) 477 c) 487 d) 497
48) Which of the following is a factor of (x + y)³-(x³+ y³)?
a) x²+ 2xy + y² b) x² - xy + y² c) xy² d) 3xy
49) If x/y + y/x = -1 (x,y ≠ 0), the value of x³- y³ is
a) 1 b) -1 c) 0 d) 1/2
50) If x + y=2 and xy = 1, then x⁴+ y⁴=
a) 6 b) 4 c) 8 d) 2
51) If x² + y²+ xy =1 and x + y = 2, then xy=
a) -3 b) 3 c) -3/2 d) 0
52) If a, b, c are natural numbers such that a²+ b²+ c²= 29 and ab + bc + ca = 26, and a+ b + c=
a) 9 b) 6 c) 7 d) 10
53) If 2x + y/3= 12 and xy = 30, then 8x³+ y³/27=
a) 1008 b) 168 c) 106 d) none
ASSERTION- REASON
Each of the following examples contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
a) Statement-1 and statement-2 are true; Statement-2 is a correct explanation for statement-1 .
b) Statement -1 and Statement-2 are true; Statement -2 is not a correct explanation for statement-1.
c) Statement -1 is true, statement -2 is false.
d) Statement -1 is False, Statement -2 is true.
1) Statement -1(A): √{(a+ b + c)+ (a - b + c)+2(b²- a²- c²- 2ac)}= 2b
Statement-2 (R): (x + y+ z)²= x²+ y²+ z²+ 2(xy + yz + zx). a
2) Statement -1(A): a³+ b³+ 3ab -1= (a+ b -1)(a²+ b²+ a+ b - ab +1)
Statement-2 (R): a³+ b³+ c³- 3abc= (a+ b + c)(a²+ b²+ c²+ ab + bc + ca). c
3) Statement -1(A): (a - b)³+(b - c)³+(c - a)³= 3(a - b)(b - c)(c - a)
Statement-2 (R): If a+ b + c = 0, then a³+ b³+ c³= 3abc. a
4) Statement -1(A): a²+ b²+ c²- ab - bc - ca = 0 if and only if a= b = c.
Statement-2 (R): (a+ b + c)²= a²+ b²+ c²+ 2ab + 2bc + 2ca. b
5) Statement -1(A): a+ b + c = 6 and 1/a + 1/b + 1/c = 3/2, then a/b + a/c + b/a + b/c + c/a + c/b = 6
Statement-2 (R): (a + b + c)²= a²+ b²+ c²+ 2(ab + bc + ca). b
6) Statement -1(A): if a+ b + c = 0, then a³+ b³+ c³= 3abc
Statement-2 (R): a³+ b³+ c³ - 3abc = (a + b + c)(a²+ b²+ c²-ab - bc - ca).
7) Statement -1(A): (a+ b + c)² = a²+ b²+ c²-2(ab+ bc + ca)
Statement-2 (R): a³+ b³+ c³ - 3abc = (a + b + c)(a²+ b²+ c²-ab - bc - ca).
8) Statement -1(A): a³ + 3ax/8 + cpx³/64 - 1/8 = (a + x/4 - 1/2)(a²+ x²/16 + 1/4 - ax/4 + x/8 + a/2)
Statement-2 (R): a³+ b³+ c³ + 3abc = (a + b + c)(a²+ b²+ c²+ ab + bc + ca).
9) Statement -1(A): If a+ b + c =0, ab + bc+ ca = 11, then a²+ b² + c²= 14
Statement-2 (R): (a+ b+ c)³ = a²+ b²+ c²+ 2(ab + bc + ca).
10) Statement -1(A): {(x²- y²)³+(y²- z²)³+(z³- x²)³}/{(x - y)³+(y - z)³+ (z - x)³}= (x + y)(y+ z)(z + x).
Statement-2 (R): If a + b + c= 0, then a³+ b³+ c³= 3abc.
11) Statement -1(A): (1/abc) (a²+ b² + c²)+ 2(1/a + 1/b+ 1/c) is √(a/bc) + √(b/ca) + √(c/ab).
Statement-2 (R): a³+ b³+ c³ - 3abc = (a + b + c)(a²+ b²+ c²-ab - bc - ca).
ALGEBRAIC EXPRESSIONS
1) (a - b)³+ (b - c)³+ (c - a)³ is equal to
a) 2a³+ 2b³+ 2c³
b) (a - b) (b - c)(c - a)
c) 0
d) 3(a - b)(b - c)(c - a)
2) If x + y=12 and xy = 27, then x³+ y³=
a) 765 b) 756 c) 657 d) 675
3) If x+ y= -4 then x³+ y²- 12xy +64=
a) -64 b) 128 c) 0 d) none
4) If x = 2y+6, then x³- 8y³- 36xy=
a) 216 b) -216 c) 36 d) -36
5) (a+ b+ c){(c - b)²+ (b - c)²+ (c - a)²}=
a) a³+ b³+ c³- 3abc b) a³+ b³+ c³ c) 2(a³+ b³+ c³- 3abc) d) 3abc
6) If a³+ b³= 5 and a+ b=1, then ab=
a) -4/3 b) 4/3 c) -3/4 d) 3/4
7) If a³+ (b - a)³ - b³ = k(a - b), then k=
a) ab b) 3ab c) -3ab d) 3
8) If a+ b+ c= 0, then a²/bc + b²/ca + c²/ab=
a) 1 b) 0 c) -1 d) 3
9) The factor of x³ - x²y - xy²+ y³, are
a) (x+y)(x²- xy+ y²)
b) (x+y)(x²+ xy+ y²)
c) (x+y)²(x- y)
d) (x-y)²(x + y)
10) The factor of x³ - 1 +y³ + 3xy, are
a) (x-1+y)(x²+1+ y²+ x + y - xy)
b) (x+1+y)(x²+1+ y²+ 1- x - y - xy)
c) (x-1+y)(x²-1- y²+ x + y - xy)
d) 3(x-1+y)(x²-1+ y²)
11) The factor of 8a³+ b³- 6ab +1 are
a) (2a+ b-1)(4a²+ b²+1- 3ab- 2a)
b) (2a- b+1)(4a²+ b²+1- 4ab- 2a+ b)
c) (2a+ b+1)(4a²+ b²+1- 2ab- b -2a)
d) (2a+ b-1)(4a²+1- 2ab- b- 4a)
12) (x + y)³ -(x - y)³ can be Factorized as
a) 2y(3x²+ y²) b) 2x(3x²+ y²) c) 2y(3y²+ x²) d) 2x(x²+ 3y²)
13) The expression (a - b)³ + (b - c)³+ (c - a)³ can be Factorized as
a) (a- b)(b - c)(c - a)
b) 3(a- b)(b - c)(c - a)
c) -3(a- b)(b - c)(c - a)
d) (a+ b+c)(a²+b² + c²- ab - bc - ca)
14) The value of {(2.3)³ - 0.027}/{(2.3)²+ 0.69+ 0.09}, is
a) 2 b) 3 c) 2.327 d) 2.273
15) The value of {(0.013)³ +(0.007)³}/{(0.013)² - 0.013 x 0.007+ (0.007)²} is
a) 0.006 b) 0.02 c) 0.0091 d) 0.00185
16) The factors of a² - 1 - 2x - x², are
a) (a - x +1)(a - x -1)
b) (a + x +1)(a - x +1)
c) (a + x +1)(a - x -1) d) none
17) The factors of x⁴+ x²+ 25, are
a) (x²+ 3x +5)(x²- 3x +5)
b) (x²+ 3x +5)(x²+ 3x -5)
c) (x²+ x +5)(x²- x +5) d) none
18) The factors of x²+ 4y²+ 4y - 4xy - 2x - 8, are
a) (x - 2y -4)(x - 2y +2)
b) (x - 2y +2)(x - 4y -4)
c) (x + 2y -4)(x + 2y +2) d) none
19) The factors of x³- 7x + 6, are
a) x(x -6)(x -1)
b) (x² -6)(x -1)
c) (x +1)(x +2)(x -3)
d) (x +3)(x -2)(x -1)
20) The expression x⁴+ 4 can be Factorized as
a) (x²+ 2x +2)(x²- 2x +2)
b) (x²+ 2x +2)(x²+ 2x -2)
c) (x²- 2x -2)(x²- 2x +2)
d) (x²+2)(x²- 2)
21) If 3x = a+ b + c, then the value of (x - a)³+ (x - b)³+(x - c)³ -3(x - a)(x - b)(x - c), is
a) a+ b + c b) (a - b)(b - c)(c - a) c) 0 d) none
22) If (x + y)³ - (x - y)³ - 6y(x²- y²)= ky³, then k=
a) 1 b) 2 c) 4 d) 8
23) If x³- 3x²+ 3x +7= (x +1)(ax²+ bx + c), then a+ b + c=
a) 4 b) 12 c) -10 d) 3
24) If x/y + y/x = -1 (x,y ≠ 0), then the value of x³- y³ is
a) 1 b) -1 c) 0 d) 1/2
25) Which of the following is a factor of (x + y)³ - (x + y³)?
a) x²+ y²+ 2xy
b) x²+ y²- xy
c) xy² d) 3xy
Assertion- Reason based
Each of the following examples contains STATEMENT-1(Assertion ) and STATEMENT-2( (Reason) and has following four choices (a), (b), (c) and (d ), only one of which is the correct choice.
a) Statement-1 and Statement -2 are True; statement-2 is a correct explanation for statement-1
b) Statement-1 and statement-2 are True ; Statement -2 is not a correct explanation for Statement-1.
c) Statement -1 is True , Statement -2 is False .
d) Statement -1 is False , Statement -2 is True .
1) Statement -1 (A): The value 1000³ - 900³ - 100³ is 270000000
Statement -2 (R): If a+ b + c= 0, then a³+ b³+ c³= 3abc.
2) Statement -1 (A): The value of (0.093³+ 0.007³)/(0093² - 0.093 x 0.007 + 0.007²) is 0.1.
Statement -2(R): a³+ b³= (a+ b)(a²- ab + b²).
3) Statement -1(A): a³(b - c)³+ b³(c - a)³+ c³(a - b)³= 3(a - b)(b - c)(c - a)
Statement -2(R): if a+ b + c = 0, then a³+ b³+ c³= 3abc.
4) Statement -1(A): (a+ b + c){(a - b)²+ (b - c)²+ (c - a)²}= 2(a³+ b³+ c³ - 3abc)
Statement -2(R) If a+ b + c = 0 then (a+ b)³+ (b + c)³+ (c + a)³= - 3abc.
5) Statement -1(A): The product of (x²+ 4y²+ z²+ 2xy + xyz - 2yz) and (-z + x - 2y) is x³- 8y³- z³ - 6xyz
Statement -2(R): a³+ b³+ c³ - 3abc = (a + b + c)(a²+ b²+ c² - ab - bc - ca).
Statement -1(A): a²+ b²+ c²- ab - bc - ca = 0 if and only if a= b= c.
Statement -2(R): a³+ b³+ c³ - 3abc = (a+ b + c)(a²+ b²+ c²- ab - bc - ca).
6) statement-1(A): (a - b)³+ (b - c)³+ (c - a)³= 3(a - b)(b - c)(c - a)
Statement -2:(R): if a+ b + c = 0, then a³+ b³+ c³= 3abc.
7) Statement-1(A): if 3x= a+ b + c, then (x - a)³+ (x - b)³+ (x - c)³= 3(x - a)(x - b)(x - c)
Statement -2(R): if a+ b + c= 0, then a³+ b³+ c³= 3abc.
8) Statement -1(A): if a+ b + c = 5 and ab + bc+ ca= 10, then a³+ b³+ c³ - 3abc = 25
Statement-2(R): a³+ b³+ c³ - 3abc = (a+ b + c){(a+ b + c)² -3(ab + bc+ ca)}.
9) Statement -1(A): If a,b,c are all non-zero such that a+ b + c = 0, then a²/bc + b²/ca + c²/ab = 3
Statement-2 (R): If a+ b + c = 9 and a²+ b² + c²= 35, then ab + bc+ ca= 23.
10) Statement -1(A): The value of (0.027³+ 0.023³)/(0.027²- 0.027 x 0.023 + 0.023²) is 0.05
Statement-2 (R): a³- b³= (a- b)(a²- ab + b²).
DIRECT & INVERSE PROPORTION
1) 15 man can dig a 20m long trench in one day. How many should be employed for digging 140 metres long tranch of the same type in one day ?
2) The shadow of Qutub Minar, which is 72m high is 80m at a particular time on a day. Find the height of an electric pole that cast a shadow of 10m under similar condition.
3) if 721 men construct a bridge in 48 days then in how many days 1442 men can do this work ?
4) Raman takes 20 minutes to reach his school at an average speed of 6 km/h. if he is required to reach school in 24 minutes, what should be his speed ?
5) In a military camp there is a food for 30 days for 50 soldiers. Assuming that average meal of every soldier is same. If 25 more soldiers join them, how many days this food will last ?
6) Mahesh goes 5 km with a speed of 10 km/hr. if he doubles his speed, find the time taken to cover the same distance.
7) Amar weaves 35 seats of chairs in 7 days. huow many days will he take to weave seat of chairs?
8) If a minute hand makes an angle of 30° in 5 minutes. Find the angle covered between 7:10 pm to 7:30 pm.
9) A train is running at a peed of 18 km/he. if it crosses a pole in 35 seconds , find the length of the train.
10) A vegetable vendor has Rs2000 to buy potatoes available at the rate of Rs8 per kg. If the price of potatoes increases by 25%, find how much potatoes he can purchase at the same amount.
11) If 14 kg of pulses cost Rs 441, what is the cost of 22 kg of pulses?
12) A car takes 2 hours to reach a destination by travelling at 60 km/h. How long will it take while traveling at 80 km/h ?
TEST PAPER
SECTION - A (8 x1 = 8)
1) CP of 360 books= SP of 270 books. Find profit %.
2) Find the single discount equivalent to two successive discounts of 20% and 10%.
3) If 14 kg of pulses cost Rs 441, what is the cost of 22 kg is a pulses ?
4) If x and y vary inversely and x= 40, find y when constant of variation=8
5) Complete (a+ b)² - (a - b)²= ?
a) 2ab b) 4ab c) (a+ b)² d) (a - b)²
6) Simplify x²- y²=? , when x =7 and y= 5.
a) 22 b) 23 c) 24 d) 25
7) Two cylinder have same base radius r. if their height are 5m and 15cm. What is the ratio of their volume ?
a) 3:1 b) 1:3 c) 2:1 d) 1:2
8) Lateral surface area of a cube is 100m², find the length of each edge.
a) 5m b) 6m c) 8m d) 10m
SECTION - B
(Any 10) (10x3=30)
9) P sells an articles to Q at 10% profit. Q sells it to R at 25% profit. if R pays Rs250 for it. What did P pay for it.
10) Ahmed buys a plot of land for Rs96000. He sales 2/5 of it loss of 6%. At what gain percent should he sale the remaining part of the plot to gain 10% on the whole ?
11) Whats should be the price marked on a washing machine whose cost is Rs14409, if the retailer wants to get a profit of 10% giving a discount of 12% ?
12) A factory requires 42 machines to produce a given number of articles in 56 days. How many machines would be required to produce the same articles in 48 days ?
13) A vegetable vendor has Rs2000 to buy potatoes available at the rate of Rs8 per kg. if the price of potatoes increases by 25%, find how much potatoes he can purchase at the same amount.
14) a) Factorise: a) 7x²+ 35x +42. b) x²/98 - y²/50 c) 9p⁴- 24p²q² + 16q²- 256r² d) x²y²- 6xyz + 9z²
15) If the side of a cube is increased by 12% by how much percent does it volume increase ?
16) Three solid cube of side 1cm, 6cm and 8cm are melted to form a new cube , find the surface area of the new cube thus formed .
17) 8) Numbers 1 to 10 are written on 10 separate slips and kept in a box and mixed up well. One slip is chosen from the box without looking into it. Find the probability of
a) getting a number 5
b) getting a number less than 8
c) getting a number greater than 7
d) getting a two digit number.
18) A letter is chosen from the word EQUATION. Find the probability that the letter is a constant
19) A bag contains 8 white balls. 5 green balls and 7 balls. They are mixed thoroughly and one ball is drawn random. Find the probability of getting
a) red ball
b) a green ball
c) a yellow ball
d) a white ball rolling
20) Read the table carefully and answer the following questions:
Marks. Students
10-20 7
20-30 12
30-40 19
40-50 11
50-60 21
60-70 10
70-80 8
80-90 02
90-100 10
If the passing marks in the test is 30, then
a) How many students have failed in the examination?
b) If A⁺ is awarded to students with 90 marks, how many students have achieved A⁺ marks?
c) How many students have passed the examination?
d) If student getting 60 or more is declared 1st division then find the number of students who have been put in 1st division.
21) The data shows India's total population (in millions) from 1951 to 2011. Represent the given data by bar graph.
Years. Population
1951 360
1961 432
1971 540
1981 684
1991 852
2001 1020
2011 1210
Test- Factorization
2) The value of (348)²- (347)² is
a) (1)² b) 685 c) 695 d) 705
3) The product of x/(1 -3y)(3y+ x/2)(x²/4 + 9y²).
4) If 49x²- y = (7x + 1/2)(7x - 1/2), then the value of y is
a) 0 b) 4 c) 1/√2 d) 1/2
5) If the area of a rectangle is 4x²+ 4x - 3, then find its possible dimensions.
6) Factorize: 1/2 - x²/50.
7) If x+ 1/x = 8, then the value of x²+ 1/x is
a) 62 b) 64 c) 66 d) 60
8) If 9x²- 36x + k is a perfect square then the value of k is
a) 25 b) 5 c) 36 d) 81
9) Factorize: a³- 2√2 b³.
10) 162x⁴- 50.
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