Solving Algebraic Equations, Quizzes of Mathematics

Solutions to various algebraic equations and expressions. It covers topics such as simplifying fractions, working with exponents and roots, and solving for unknown variables. The solutions demonstrate step-by-step workings to help the reader understand the underlying concepts and techniques. Suitable for students studying algebra, mathematics, or related subjects at the high school or university level. It can be used as a reference or study guide to reinforce understanding and prepare for exams.

Typology: Quizzes

2023/2024

Available from 09/19/2024

rajjatt-sabhrwal
rajjatt-sabhrwal 🇮🇳

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Q1. Mark ck against the correct answer in the following:
By what number should (-8) be mulplied to get 10 ?
1.
2.
3.
4. None of these.
1 Mark
Ans: 3.
Soluon:
Required number = 10 ÷ (-8)
Q2.
1. 64
2. 16
3. 32
4. 4
1 Mark
Ans: 3. 32
Soluon:
Since,
Hence, the correct alternave is opon (c).
Q3. Mark ck against the correct answer in the following:
1.
2.
3.
4.
1 Mark
Ans: 3.
Soluon:
Q4.
If abc = 0, then find the value of
1 Mark
(
)
-1 -1
4
5
5
4
4
5
4
5
-1 -1
= ÷
( )
= ×
1
10 1
8 1
10 8
1
=4
5
{
(33)2 (31)2
}
5
7
{
(33)2 (31)2
}
5
7
= {1089 961} 5
7
= {128}5
7
= {27}5
7
= 27× 5
7[As,(xm)n= xmn]
= 25
= 32
(
)
( )
3÷
( )
8=?
1
51
5
(
)
5
1
5
( )
11
1
5
(5)5
( )
5
1
5
(5)5
( )
3÷
( )
8
1
51
5
=
(
)
38 =
(
)
5
1
51
5
= (5)5
{
(xa)b
}
c
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff
pf12
pf13

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Q1. Mark ck against the correct answer in the following:

By what number should (-8) be mulplied to get 10?

4. None of these.

1 Mark

Ans: 3.

Soluon:

Required number = 10 ÷ (-8)

Q2.

1 Mark

Ans: 3. 32

Soluon:

Since,

Hence, the correct alternave is opon (c).

Q3. Mark ck against the correct answer in the following:

1 Mark

Ans: 3.

Soluon:

Q4.

If abc = 0, then find the value of

1 Mark

= ÷ ( ) = ×

5 7

{(33)^2 − (31)^2 }

5 7

5 7

5 7

5 7

7× 57

[As, (xm)n^ = xmn]

÷ ( )

(−5)^5

÷ ( )

= (−5)^5

{(xa)b}

c

2. a

3. b

4. c

Ans: 1. 1

Soluon:

Since,

Hence, the correct alternave is opon (a).

Q5. What should be mulplied to 6 so that the product may be equal to 216?

1 Mark

Ans: 2. 6

Soluon:

Since,

Let 6 should be mulplied to 6

A.T.Q.

6 × 6 = 216

Comparing th exponent of both the sides, we get

-2 + m = 3

⇒ m = 3 + 2

m = 5

So, 6 should be mulplied.

Hence, the correct alternave is opon (b).

Q6. Which power of 8 is equal to 2?

1 Mark

Ans: 2. 2

Soluon:

Let power of 8 be x.

According to the queson,

Since, base equal, then by eqyang their exponents, we get

[dividing both sides by 3]

Hence, the power of 8 is 2, which is equal to 2

Q7. In standard form 72 crore is wrien as:

1. 72 × 10

2. 72 × 10

3. 7.2 × 10

4. 7.2 × 10

1 Mark

Ans: 3. 7.2 × 10

{(xa)b}

c

= (xa)bc^ [As, (xm)n^ = xmn]

= xabc^ [As, (xm)n^ = xmn]

= x^0 [As, abc = 0]

= 1 [As, x

= 1]

m -

-2 m

-2+m 3

x=2^6

⇒ (2)3x^ = 2

[ ∵ 8 = 2 × 2 × 2 = 2

]

3x

[ ∵ (a

m

n

= a

m×n

]

3x = 6

3x 3

⇒ x = 2

Hence, the correct alternave is opon (b).

Q11. Mark ck against the correct answer in the following:

Which of the following numbers is in standard form?

1. 21.56 × 10

2. 215.6 × 10

3. 2.156 × 10

4. None of these.

1 Mark

Ans: 3. 2.156 × 10

Soluon:

The number which is in standard form is 2.156 × 10

Q12. The standard form of the number 12345 is:

1. 1234.5 × 10

2. 123.45 × 10

3. 12.345 × 10

4. 1.2345 × 10

1 Mark

Ans: 4. 1.2345 × 10

Soluon:

A number in standard form is wrien as a × 10 , where a is a terminang decimal such that 1 ≤ a ≤ 10 and k is any integer.

So, 12345

= 1.2345 × 10

Q13. Mark ck against the correct answer in the following:

1 Mark

Ans: 3.

Soluon:

Q14. If then the value of K is:

1 Mark

Ans: 3. 3

Soluon:

Given,

So, the value of k is 3

Q15. (10 + 20 + 30) is equal to:

1 Mark

5 4 6 6 6 1 2 3 4 4 k 4

= ×

= K.

= K.

× 1 = K.

⇒ 2^1995 [2^3 − 2^2 − 2^1 + 1] = K.2^1995 [ ∵ am+n^ = am^ × an]

[8 − 4 − 2 + 1] = K.

K.2^1995

3 = K or K = 3

Ans: 3. 3

Soluon:

As we know, a = 1

Q16.

1 Mark

Ans: 4. 0

Soluon:

Since,

Hence, the correct alternave is opon is (d).

Q17.

1 Mark

Ans: 2. 4

Soluon:

Hence, the correct alternave is opon (b).

Q18. The number 2.35 × 10 in the usual form is wrien as:

1. 2.35 × 10

4. 235 × 10

1 Mark

Ans: 2. 23500

Soluon:

Since, 2.35 × 10 = 2.35 × 10000 = 23500

So, the number 2.35 × 10 in the usual form is wrien as 23500.

Hence, the correct alternave is opon (b).

Q19. If a = 3 - 3 and b = 3 - 3 , then

1 Mark

Ans: 1. 0

(−1)^301 + (−1)^302 + (−1)^303 + ⋯ + (−1)^400

(−1)^301 + (−1)^302 + (−1)^303 + ⋯ + (−1)^400

= (−1) + (1) + (−1) + ⋯ + (1) [As, (−1)odd^ = −1 and (−1)even^ = 1]

= −50 + 50 [As, there are50(−1)′s and 50 (1)

s]

1 2

1 2 32 −

1 2

1 2 32 −

(12^2 ) +(16^2 )

1 2

1 2 9−

(^12) 2× (^12)

7 [As, (x

m)n = xmn]

-3 3 3 -3 a − =

b

b a

2 × 2 × 2 × 2 × 2 > 5 × 5

32 > 25 (true)

Hence, opon (c) is not true.

Q22. Mark against the correct answer in the following:

1 Mark

Ans: 4.

Soluon:

Q23.

1 Mark

Ans: 3.

Soluon:

Since,

Hence, the correct alternave is opon (c).

Q24.

1 Mark

Ans: 3.

Soluon:

Hence, the correct alternave is opon (c).

Q25. x is a non-zero raonal number. Product of the square of x with the cube of x is equal to the:

1. Second power of x

2. Third power of x

3. Fih power of x

4. Sixth power of x

1 Mark

Ans: 3. Fih power of x

Soluon:

Square of x = x

Cube of x = x

Product of square with the cube of

−3^3

−3 [Since(^ )

−n

n

]

a b

b a

(−3)^3

4×4×

(−3)×(−3)×(−3)

64×−

−27×−

3 (As, x

x

× 5

)−1^ =

× 5

= ( × )

5 (As, x

x

(As, x−1^ = )

x

x = x × x = x [ a × a =a ]

i.e. fih power of x

Q26.

1 Mark

Ans: 4. 1

Soluon:

Hence, the correct alternave is opon (d).

Q27. Mark against the correct answer in the following:

4. None of these.

1 Mark

Ans: 1.

Soluon:

Q28. For non-zero numbers a and b, where m > n, is equal to:

1 Mark

Ans: 3.

Soluon:

We know that,

So,

Q29. Mark ck against the correct answer in the following:

4. None of these.

1 Mark

2 3 2+3 ∴ m n m+n

If abc = 0, then =

{(xa)b}

c

{(xb)c}

{(xa)b}

c

{(xb)c}

(xa)bc (xb)ac^

[As, (xm)n^ = xmn]

xabc xabc^

[As,(xm)n^ = xmn]

x^0 x^0

[As, abc = 0]

[As, x

= 1]

÷ ( )

−2^18

[Since a

m

÷ an^ = am−n]

÷ ( )

(−2)^2

m

÷ ( )

a n b

a b

mn a b

m+n a b

m-n a b

m

n a b

m-n a b

am^ + an^ = am-n(m > n)

n

m-n a b

a b

a b

Q33. Mark ck against the correct answer in the following:

1 Mark

Ans: 4.

Soluon:

Q34. Mark ck against the correct answer in the following:

1 Mark

Ans: 1.

Soluon:

Q35.

1 Mark

Ans: 1.

Soluon:

Hence, the correct alternave is opon (a).

Q36. a × a is equal to:

1. (a )

2. a

3. a

4. a

1 Mark

Ans: 3. a

Soluon:

We know that, if ‘a’ is a raonal number, m and n are natural numbers, then.

a × a = a

) × ( )

) × ( )

= 5 × × × =

)^2 =?

)^2 = ( − )

= × =

[{( − )}

]

[{( − )}

]

[{( − )

(−2)×(−1)

]

[As, (xm)n^ = xmn]

[As, (xm)n^ = xmn]

(−1)^4

[As, ( )

m

xy = ]

xm ym

m n

2 mn

m-n

m+n

mn

m+n

m n m+n

Q37. If a = 25, then

1 Mark

Ans: 2. 26

Soluon:

Hence, the correct alternave is opon (b).

Q38. Square of is:

1 Mark

Ans: 4.

Soluon:

Square of

So,

[ mulplicaon of two raonal number with same sign is always posive]

Q39.

4. None of these.

1 Mark

Ans: 3.

Soluon:

Hence, the correct alternave is opon (c).

Q40. Mark against the correct answer in the following:

1 Mark

Ans: 2.

Soluon:

Q41. Mark ck against the correct answer in the following: 1 Mark

a^25

0

+ a^0

25

a

+ a

= a^1 + a^0 (As, 25

= 1 and 0

= a + 1 (As, a^0 = 1)

is ( )

−2^2

) = ( ) × ( )

[As, (xm)n^ = xmn]

−5^1

−5 [Since(^ )

−n

n

]

a b

b a

= ( × ) =

Q45.

1 Mark

Ans: 2.

Soluon:

Hence, the correct alternave is opon (b).

Q46. Mark ck against the correct answer in the following:

1 Mark

Ans: 2.

Soluon:

Q47. In standard form, the number 72105.4 is wrien as 7.21054 × 10 where n is equal to:

1 Mark

Ans: 3. 4

Soluon:

We know that, if the given number is greater than or equal to 10, then the power of 10 (i.e. n) is a posive integer equal to the

number of places the decimal point has been shied.

Hence, 72105.

= 7.21054 × 10

Q48. Mark against the correct answer in the following:

Which of the following numbers is in standard form?

1. 32.63 × 10

2. 326.3 × 10

3. 3.263 × 10

4. None of these.

1 Mark

Ans: 3. 3.263 × 10

Soluon:

A given number is said to be in standarf form if it can be expressed as k × 10 , where k is a real number such that and n is

a posive integer.

For example: 3.263 × 10

)−1^ =

)−1^ =

(As, x−1^ = 1 )

x

(As, x−1^ = )

x

n

n 1 ≤ k < 10

Q49. Mark ck against the correct answer in the following:

1 Mark

Ans: 2.

Soluon:

Q50. Mark ck against the correct answer in the following:

1 Mark

Ans: 4.

Soluon:

Q51. Which of the following is not equal to?

1 Mark

Ans: 3.

Soluon:

We know that,

So,

or

or

Hence, opon (c) is not equal to 1

Q52. The number 4,70,394 is standard form is wrien as:

1. 4.70394 × 10

2. 4.70394 × 10

3. 47.0394 × 10

4. 4703.94 × 10

1 Mark

Ans: 1. 4.70394 × 10

Soluon:

Since, 4,70,394 = 4.70394 × 100000 = 4.70394 × 10

So, the number 4,70,394 in standard form is wrien as 4.70394 × 10

Hence, the correct alternave is opon (a).

Q53.

1 Mark

= (−2)^6

= (−2) × (−2) × (−2) × (−2) × (−2) × (−2)

)−1^ =?

−5^4

(−5)^4

−5^4

(4)^4

( − ) × ( − ) × ( − ) × ( − )

m

p q

pm qm

(−5)^4

(4)^4

(5)^4

(−4)^4

= ( ) × ( ) × ( )

1 2

Soluon:

Q58. Mark ck against the correct answer in the following:

1 Mark

Ans: 2.

Soluon:

Q59. If xyz = 0, then find the value of (a ) + (a ) + (a ) =

1 Mark

Ans: 1. 3

Soluon:

Since,

(a ) + (a ) + (a )

= a + a + a [As, (x ) = x ]

= a + a + a

= a + a + a

= 1 + 1 + 1 (As, x = 1)

Hence, the correct opon is (a).

Q60. If 3 = 6561, then 3 =

1 Mark

Ans: 2. 243

Soluon:

Comparing the exponent of both the sides, we get:

x = 8

Now, 3 = 3

Hence, the correct alternave is opon (b).

Q61. In standard form, the number 829030000 is wrien as K × 108 where K is equal to:

1 Mark

Ans: 4. 8.

Soluon:

÷ ( )

−2^5

= × =

= × × × ×

x yz y zx z xy

x yz y zx z xy

xyz yzx zxy m n mn

xyz xyz xyz

0 0 0

0

x x-

x

x 8

x-3 8-

5

We have, A number in a standard form is wrien as K x 10 , then K will be a terminang decimal such that 1 ≤ K ≤ 10

So, there is only one opon, where K

Q62. Mark ck against the correct answer in the following:

If then x =?

1 Mark

Ans: 3.

Soluon:

Comparing 8x = 6

Q63. Mark against the correct answer in the following:

4. None of these.

1 Mark

Ans: 3.

Soluon:

Q64.

If

1 Mark

Ans: 3.

Soluon:

Comparing the exponent of both the sides, we get:

Hence, the correct alternave is opon (c).

Q65. is equal to:

1 Mark

× ( )

8x

× ( )

8x

8x 5 3

8x 5 3

⇒ x = =

(a)

× ( )

8x

, then x =?

× ( )

8x 5 3

8x 5 3

3 (As, x

m×n = xm+n)

8x 5 3

8x = 6

⇒ x =

∴ x = 3

× ( )

( × )

( × )

( × )

( × )

1. x

2. x

3. x

4. x

Ans: 2. x

Soluon:

We know that, if ‘a’ is a raonal number, m and n are natural numbers such that m> n, then.

a ÷ a

= a

So,

Q70. Cube of is:

1 Mark

Ans: 4.

Soluon:

Cube of is

So,

Q71. Mark ck against the correct answer in the following:

4. None of these.

1 Mark

Ans: 3.

Soluon:

m n

m-n

x ÷ x^2 =

x^8 x^2 = x8−2^ = x^6

−1^3

= ( ) × ( ) × ( )

(−1)×(−1)×(−1)

4×4×

{ 6 −1^ + ( )

{ 6 −1^ + ( )

} = [( ) + ( )]