1/8/21
** Simplify:
1) (256/576)¹⁾⁴ (64/27)⁻¹⁾³ (216/8)⁻¹. 1/18√6
2) (l⁴m⁶/n⁸). (m⁸n⁴/l⁻⁶).(n⁶l⁶/m⁴)². l¹²/(m⁶n²⁰)
Solve:
3)a) ³√(5/4)ˣ⁺²= 4096/15625. -20
b) 3²ˣ+ 2.3ˣ - 99= 0. 2
c) 3ˣ⁺³ - 3ˣ⁻³= 6552 then find x². 25
4) Find the value of z in terms of x and y if 3ˣ = 2ʸ = 6ᶻ, and x,y,z are not equal ? xy/(x+y)
5) xʸ = yᶻ= zˣ find the value of k? (xyz)ˣʸᶻ⁽ˣʸ⁺ ʸᶻ⁺ᶻˣ⁾
6) ³√x/392= 98/x then find x²⁾³. 196
7) If [(a³)ˣ]³= 8³. 8³ find a, b. 2,2
8) {(2ᵃ)ᵃ. (2ᵇ)ᵇ.(2ᶜ)ᶜ}/{(4ᵃ)⁻ᵇ.(4ᵇ)⁻ᶜ . (4ᶜ)⁻ᵃ}. -√3
9) If x= ³√2 +³√4, what is value of x³ - 6x ? 6
10) If 5ˣ =(0.125)ʸ = 10³ᶻ, then what is the relation between x,y and z, given that they are non-zero real numbers? 3/x= 1/y + 1/z
11) ((₈₁)4a)a ((₂₇)8b)b.((₂₄₃ (₉2)b². ₃(4a+3b)²
12) y²ʸ= 65536, xˣ⁾³= 20736, then find the value of x+y. 16
13) Solve for x,y:
3.5ˣ+ 2ʸ⁺²= 107, 5ˣ⁺¹ +8.2ʸ. 2,3
14) (729/1728)⁻²⁾³.(1024/9)¹⁾³ ÷(24/324). 256
15) (a⁴b³/c²)².(b⁴c³/a²)³.(c⁴a³/b²)⁴.
a¹⁴b¹⁰c²¹
16) 9/(6²⁾³- 18¹⁾³+ 3²⁾³) =
A) (6¹⁾³+ 3¹⁾³) B) 1/3(6¹⁾³+ 3¹⁾³)
C) (6¹⁾³- 3¹⁾³) D) 1/9(6¹⁾³+ 3¹⁾³)
17) ᵧp/(p+q+r). ᵧq/(p+q+r) ᵧr/(p+q+r).
A) y B) 1 C) 1/y D) y²
18) If a= ₂3² and b= ₃2², which is greater.
A) a B) b C) both are equal
19) Value of x: ₃xˣ = 81?
A) 2 B) 3 C) 4 D) √2
20) If 3ˣ. 7ʸ= 441 where x and y are integers, what is the value of x-y ?
A) 0 B) 1 C) 2 D) cannot determined
21) if 5¹⁾². 5³⁾². 5⁵⁾². 5⁷⁾².5⁹⁾² = 25ˣ. Find x
A) 12.5 B) 6.25 C) 25 D) 10
** Solve:::
22) √(5/7)ˣ⁺¹= 125/343. 8
23) 625ˣ⁻² = 25ˣ⁺². 6
24) (2491)ˣ⁻⁴= 49²ˣ⁻⁶. 2
25) 5²ˣ = 625.
A) 1 B) 2. C) -1 D) 0
26) Arrange the following in ascending order: 625⁶, 125⁷, 25¹⁰.
27) {(2ᵃ)ᵃ. (2ᵇ)ᵇ.(2ᶜ)ᶜ}/{(4ᵃ)⁻ᵇ.(4ᵇ)⁻ᶜ . (4ᶜ)⁻ᵃ}= 8, which of the following is a possible value of a+b+c ?
A) -√3 B) 1 C) 2 D) -√2 E) √2
28) If (5√7)⁵ˣ⁻⁴= (35)⁴(25)³⁾².
A)2. B) 5/4 C) 7/2 D) 3 E) 4/5
29) 3 5ˣ+ 2ʸ⁺²= 107, 5ˣ⁺¹+8. 2ʸ = 189
A) 3,2 B)5,7 C) 7,5 C) 7,3 E) 2,3
30) If [(a³)ᵇ]³= 8³. 8³, which of the following could be the possible values of a and b ?
A) 2,2 B) 3,2 C) 2,3 D) 4,2 E) 2,4
31) Solve: 3²ˣ+ 2.3ˣ - 99= 0.
A) 4 B) 3 C) 0 D) 1 E) 2
32) Solve: (a/b)ˣ (c/b)ˣ= 225/16, given a,b,c are prime numbers.
A) 4 B) 3 C) 2 D) 1 E) 5
33) Evaluate:1/(1+ mˣʸ⁻ ʸᶻ+ mˣʸ⁻ ᶻˣ) + 1/(1+ mʸᶻ ⁻ᶻˣ+ mʸᶻ⁻ ˣʸ) + 1/(1+mᶻˣ⁻ ˣʸ+ m ᶻˣ⁻ ʸᶻ)
A) 1/3 B) 1/2 C) 1 D) 2 E) -1/3
33) What is the value of z in terms of x and y. If 3ˣ= 2ʸ= 6ᶻ, and x,y z are not equal?
A) z=(x+y)/4xy. B)z= xy/(x+y)
C) z=(x+y)/2. D) z=(x²+y²)/xy
34) ³√x/392 = 98/x, then x²⁾3.
A) 14 B) 144 C) 16 D) 256 E) 196
35) If 3ˣ⁺³ - 3 ˣ⁻³ = 6552, then find x².
A) 5 B) 25 C) 3 D) 9 E) 4
36) If 5ˣ= (0.125)ʸ = 10³ᶻ, then what is the relation between x,y and z, given that they are non-zero real numbers?
A) 1/x +1/y +1/z=1 B)3/x = 1/y + 1/z C) 1/z - 1/y - 1/x =1 D) xyz=1 E) 2/x = 1/y + 1/z
37) If a.5²= 2020.20, what is the value of 10⁻³a/10⁴
38) 5ˣ⁺³ - 5 ˣ⁻³ =78120, find x.
A) 4 B) 3 C) 5 D) 6 E) 7
39) If x= 2⁵⁵, y= 17¹⁴ and z= 31¹¹, then which of the following is the correct ascending order of the values of x,y and z?
A) zyx B) zxy C) yxz D) xyz E) xzy
39) If aˣ = bʸ = cᶻ where a>1, b >1, c > 1, then the value of (abc)ˣʸᶻ/ˣʸ⁺ ʸᶻ⁺ᶻˣ is
A) aˣ+ bʸ+ cᶻ B) (abc)ˣʸᶻ
C) (a¹⁾ˣ+ b ¹⁾ʸ + c¹⁾ᶻ)/3 D) abc E) aˣ
40) If a and b are integers such that aᵃ + bᵇ= 1025, find the value of a+b.
A)12 B) 129 C) 1025/2 D) 11 E) n
41) {(81ᵃ)ᵃ (81ᵇ)ᵇ (82ᶜ)ᶜ}/{(6561ᵇ)⁻ᶜ (6561ᶜ)⁻ ᵃ (6561ᵃ)⁻ᵇ= 3 then a+b+c could be..
A) 2 B) 1/3 C) -1/2 D) -1/3 E) -2
8/7/21
1) If 3²ˣ = 81, then find 3⁻ˣ. 1/9
2) Simplify: (3ᵐ⁺² . 3²ᵐ⁻ⁿ)/(6ᵐ. 3 ᵐ⁻ⁿ⁻¹). 3ᵐ⁺³/2ᵐ
3) If x¹⁾ᵃ = y¹⁾ᵇ = z¹⁾ᶜ and a+b+c= 0, show that xyz = 1
4) If aˣ = b, bʸ= c, cᶻ= a, show that, xyz = 1. (a,b,c positive numbers)
5) If aˣ = bʸ and bˣ= aʸ (ab=1), prove that, a= b.
7/7/21
1) (a+b)⁻¹. (a⁻¹ + b⁻¹). a+b
2) (a⁻¹. b⁻¹) ÷(a⁻¹ + b⁻¹). a⁵
3) Express 3.146 as a vulgar fraction. 3143/999
4) 6x + 5y=7x +3y+1=2(x+6y-1). 3,2
5) Find the area of a triangle whose base is 15cm and the corresponding height is 9.6cm. 72
6/7/21
1) Insert three rational numbers between -1,1
2) 2³(6⁰+ 3²ˣ)= 204/27. Find x. -3/2
3) {(27)²ⁿ⁾³ x(8)⁻ⁿ⁾⁶}/(18)⁻ⁿ⁾². 3³ⁿ
4) 2x+3y= 0, 7x +y= 23. 3, -2
5) solve: 5x-8y= -4; 2x-7y= 6. -4,-2
6) A room is half as long again as it is broad. The cost of carpeting the room at ₹18 per m² is ₹972 and the cost of white washing the four walls at ₹6 per m² is ₹1080. Find the dimensions of the room. 9,6,6
5/7/21
1) Insert three rational numbers between 4 and 5.
* Simplify:
2) (1/4)⁻² - 3x 8²⁾³x 5⁰ + (9/16)⁻¹⁾²
3) (3ⁿ x 9ⁿ⁺¹)/(3ⁿ⁻¹ x 9ⁿ⁻¹).
4) Solve: x-y= 9/10; 11/{2(x+y)}=1
5) The base of an isosceles triangle is 24cm and it's area is 192 cm². Find its perimeter. 64
4/6/21
1) 4x -18= 3y, 6x+7y-4= 0. 3,-2
2) The wheel of a cart making 5 revolutions per second. if the diameter of the wheel be 84cm find its speed in km/hr. give your answer, correct to nearest km. 48
3) (64/125)⁻²⁾³ + 4⁰ x 9⁵⁾² x 3⁻⁴ - √25/³√(64) x (1/3)⁻¹ 13/16
4) Insert three rational numbers between 3 and 4. 13/4,7/2,15/4
5) Find the volume, the surface area and the diagonal of a cuboid 12cm long, 4cm wide and 3cm high. 144, 192,13
1) Area of a concentric circle ⭕ is 346.5 cm². The circumference of the inner circle is 88cm. Find the radius of the outer circle. 17.5
2) A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77cm. given that the bucket ascends in 1 minute 28 seconds with a uniform speed of 1.1m/s. calculate the number of complete revolutions the wheel makes in raising the bucket. Take π to be 22/7. 40
3) Simplify: (81)³⁾⁴ - (1/32)⁻²⁾⁵ +(8)²⁾³x (1/2)⁻¹ x 3⁰ - (1/81)⁻¹⁾² 22
4) 37x+ 41y= 70, 41x+37y= 86. 3,-1
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