Explore topic-wise InterviewSolutions in Current Affairs.

False.

From the question it is given that,

One number = x

Other number = 40 –x

Let us assume (40 – x) > x

So, 40 – x + 8 = 3 (x + 8)

48 – x = 3x + 24

– x – 3x = 24 -48

– 4x = -24

X = -24 × (-1/4)

X = 6

∴One number is x = 6

Other number is = 40 – x

= 40 – 6

= 34

Difference between numbers = 34 – 6 = 28

R is reflexive and symmetric, but not transitive since for (1, 0) ∈ R and (0, 3) ∈ R whereas (1, 3) ∉ R.

Since A = {0, 1, 2, 3}

R : A → A

Since,  0, 1, 2, 3 \(\in\) A

and (0, 0), (1, 1), (2, 2) (3, 3) \(\in\) R

Hence, for each a \(\in\) A

(a, a) \(\in\) R

∴ R is a reflexive relation.

Since, (0, 1) ∈ R Then (1, 0) ∈ R

(0, 3) ∈ R Then (3, 0) ∈ R

Hence, if (a, b) ∈ R Then (b, a) ∈ R

∴ Relation R is symmetric relation.

Since, (1, 0) ∈ R, (0, 3) ∈ R but (1, 3) \(\notin\) R

∴ Relation R is not transitive.

(a) \(\frac{radius}{2}\)

V = πr²h and Curved surface area = 2πrh

∴ V = \(\frac{2πrh}{2}\times{r }= CSA\times\frac{r}{2}\)

Correct option is  D) x + 3 = 7

Correct option is  D) – 9

Correct option is (D) –9

3x + 7 = –20

\(\Rightarrow\) 3x = -20 - 7 = -27

\(\Rightarrow\) x = \(\frac{-27}3\) = -9.

Correct option is  C) 9x = 9

Correct option is (C) 9x = 9

(A) 8x – 3 = 4 \(\Rightarrow\) 8x = 4+3 \(\Rightarrow\) x = \(\frac78\) is not a natural number.

(B) 2x = 1 \(\Rightarrow\) x = \(\frac12\) which is not a natural number.

(C) 9x = 9 \(\Rightarrow\) x = \(\frac99=1\) which is a natural number.

(D) 3x + 1 = 0 \(\Rightarrow\) 3x  = -1 \(\Rightarrow\) x = \(\frac{-1}3\) which is not a natural number.

Correct option is  C) 2/3

Correct option is (C) 2/3

3z – 1 = 1

\(\Rightarrow\) 3z = 1+1 = 2

\(\Rightarrow\) z = \(\frac23.\)

Let the age of the girl = x years.

So, the age of her younger sister = (x – 4) years.

Thus, the age of the brother = (x – 4 – 4) years = (x – 8) years.

According to question:

⇒ (x – 4) + (x – 8) = 16

⇒ x + x – 4 – 8 = 16

⇒ 2x – 12 = 16

Adding 12 to both sides, we get

⇒ 2x – 12 + 12 = 16 + 12

⇒ 2x = 28

Dividing both sides by 2, we get

⇒ 2x/2 = 28/2

⇒ x = 14

Thus, the age of the girl = x = 14 years,

The age of the younger sister = x – 4 = 14 – 4 = 10 years,

The age of the younger brother = x – 8 = 14 – 8 = 6 years.

Let the present age of the son = x years.

Therefore, the present age of his father = 4x years.

So, after 16 years,

Son’s age = (x + 16) and father’s age = (4x + 16) years

According to question:

⇒ 4x + 16 = 2(x + 16)

⇒ 4x + 16 = 2x + 32

Transposing 2x to LHS and 16 to RHS, we get

⇒ 4x – 2x = 32 – 16

⇒ 2x = 16

Dividing both sides by 2, we get

⇒ 2x/2 = 16/2

⇒ x = 8

So, the present age of the son = x = 8 years,

And the present age of the father = 4x = 4(8) = 32 years.

Correct option is  D) 0

Correct option is (D) 0

3x – x = 0

\(\Rightarrow\) 2x = 0

\(\Rightarrow\) x = \(\frac02\) = 0.

After 18 years, Swarnim will be 4 times as old as he is now. His present age is 6 years.

Let us assume swarnim’s parent age be x year.

Then, after 18 year, Swarnim’s age = (x + 18) year

According to the question,

x + 18 = 4x

x – 4x = -18

– 3x = -18

– 3x/3 = (-18/3)

x = 6

Therefore, swarnim’s present age is 6 year.

MPN = MOST PROBABLE NUMBER : सार्वप्रायिक संख्या |

Correct option is  A) 11

Correct option is (A) 11

\(6-\frac{x-1}{2}=\frac{x-2}{3}+\frac{3-x}{4}\)

\(\Rightarrow\) \(\frac{x-2}{3}+\frac{3-x}{4}+\frac{x-1}{2}=6\)

\(\Rightarrow\) \(\frac{4(x-2)+3(3-x)+6(x-1)}{12}=6\)

\(\Rightarrow\) 4x-8+9-3x+6x-6 = 72

\(\Rightarrow\) 7x - 5 = 72

\(\Rightarrow\) 7x = 72+5 = 77

\(\Rightarrow\) x = \(\frac{77}7\) = 11.

Correct option is D) none

Correct option is (D) none

\(\frac{6}{7}-\frac{5}{4}-\frac{1}{3}\)x + 2x = 0

\(\Rightarrow\) \(2x-\frac x3=\frac{5}{4}-\frac67\)

\(\Rightarrow\) \(\frac{6x-x}3=\frac{5\times7-6\times4}{4\times7}\)

\(\Rightarrow\) \(\frac{5x}3=\frac{35-24}{28}=\frac{11}{28}\)

\(\Rightarrow\) \(x=\frac{11}{28}\times\frac35=\frac{33}{28\times5}=\frac{33}{140}.\)

(c) 4x + 7 = x + 2

Transposing 7 to RHS and it becomes -7 and x to LHS it becomes -x

4x – x = 2 – 7

3x = – 5

X = -5/3

So, -5/3 is neither a fraction nor an integer.

(c) 5

Given, 3x – 4 = 2x + 1

Transposing -4 to RHS and it becomes 4 and 2x to LHS it becomes -2x.

3x – 2x = 1 + 4

x = 5

(c) Linear equation in one variable has only one variable with power 1.

e.g. 3x + 1 = 0,2y – 3 = 7 and z + 9 = – 2 are the linear equations in one variable.

(a) positive

Let a = 3, b = 4

Then, ax = b

3x = 4

x = 4/3

5 more than the number = x + 5

3 less than the number = x – 3

Half of the number = 1/2 x

1 less half of the number = 1/2 x - 7

4 more than one third of the number = 1/3 x + 4

6 more than triple of the number = 3x + 6

3 less than 5 times of the number = 5x – 3

True

The root of 3x = 20/7 – x is 5/7.

True

The root of 2x + 3 = 2(x – 4) does not exist.

The correct option is (c) 5/2.

False

The root of z ÷ 4 = – 8 is 32.

1. \(\frac{2x}{x + 6} = 1\)

By cross multiplication

2x = x + 6

⇒ 2x – x = 6 | On transposing x

⇒ x = 6

2. 10 = x + 3

⇒ 10 – 3 = x | On transposing 3

⇒ 7 = x

⇒ x = 7

3. 16 = 7x – 9

⇒ 16 + 9 = 7x | On transposing – 9

⇒ 25 = 7x

⇒ 7x = 25

⇒ 7x/7 = 25/7

On dividing by 7 on both sides

x = 25/7

4. \(\frac{x + 5}x = 2 \frac{2}{3}\)

\(\frac{x + 5}x = \frac{8}{3}\)

By cross multiplication

⇒ 3(x + 5) = 8x

⇒ 3x + 15 = 8x

⇒ 3x – 8x = – 15

On transposing 8x and 15

⇒ – 5x = – 15

⇒ -5x/-5 = -15/-5 | On dividing by – 5 on both sides

x = 3

The solution of x – 4 = 5 is 5 + 4.

The correct option is (a) 1.

(c) x/2 + x/3 = 1/4

(c) any real number

x + 7 - 8x/3 = 17/6 - 5x/2

L.C.M. of the denominators, 2, 3, and 6, is 6.

Multiplying both sides by 6, we obtain

6x + 42 - 16x = 17 - 15x

⇒ 6x - 16x + 15x = 17 - 42

⇒ 5x = -25

⇒ x = -25/5

⇒ x= -5

1. ‘=’

2. transposed

3. linear

4. solution, root.

The solution of the equation 3x – 4 = 1 – 2 x is 1.

3x – 4 = 1 – 2

3x – 4 = – 1

3x = -1 + 4

x = 3/3

x = 1

2x – 3 = x + 2

⇒ 2x – x = 2 + 3

⇒ x = 5

2x – 3 = 7

⇒ 2x = 7 + 3

⇒ 2x = 10

⇒ x = 10/2 = 5

The solution of the equation 2y = 5y – 18 5 is (6/5).

2y = 5y – (18/5)

(18/5) = 5y – 2y

(18/5) = 3y

y = (18/5) × (1/3)

y = (6/5) × (1/1)

y = 6/5

बैटरी का कुल आन्तरिक प्रतिरोध = बाह्य परिपथ का प्रतिरोध।

Correct option is  A) 3/2

Correct option is (A) 7/5

\(p-\frac{p-1}{2}=1-\frac{p-2}{3}\)

\(\Rightarrow\) \(p-\frac{p-1}{2}+\frac{p-2}{3}=1\)

\(\Rightarrow\) \(\frac{6p-3(p-1)+2(p-2)}{6}=1\)

\(\Rightarrow\) 6p - 3p + 3 + 2p - 4 = 6

\(\Rightarrow\) 5p = 6 - 3 + 4 = 7

\(\Rightarrow\) \(p=\frac75.\)

Correct option is  A) 7/5

Correct option is  D) – 1

Correct option is (D) -1

3x – 4 = 5x – 2

\(\Rightarrow\) 5x - 3x = -4 - (-2) = -4+2

\(\Rightarrow\) 2x = -2

\(\Rightarrow\) x = \(-\frac22\) = -1.

Correct option is  A) 5

Correct option is (A) 5

\(\frac{x+2}{x-2}=\frac{7}{3}\)

\(\Rightarrow\) 3(x+2) = 7(x-2)

\(\Rightarrow\) 3x+6 = 7x - 14

\(\Rightarrow\) 7x - 3x = 6+14

\(\Rightarrow\) 4x = 20

\(\Rightarrow\) \(x=\frac{20}4=5.\)

Alternative \(\frac{x+2}{x-2}=\frac{7}{3}\)

\(\Rightarrow\) \(\frac{(x+2)+(x-2)}{(x+2)-(x-2)}=\frac{7+3}{7-3}\)

\(\Rightarrow\) \(\frac{2x}4=\frac{10}4\)

\(\Rightarrow\) 2x = 10

\(\Rightarrow\) \(x=\frac{10}2=5.\)

Correct option is  D) 1

Correct option is (D) 1

\(\frac{1}{2}\)p = \(\frac{1}{2}\)

\(\Rightarrow\) \(p=\cfrac{\frac{1}{2}}{\frac{1}{2}}=1.\)

e.g. x + 2 = 3 => x = 3-2 = 1 [transposing 2 to RHS]

Hence, x = 1 satisfies the equation and it is a solution of the equation.

4x +15 = 39

To convert the given statement into an equation, first x is multiplied by 4 and then 15 is added to get the result 39. i.e. 4x + 15 = 39.

Correct option is  B) 3.8

Correct option is (B) 3.8

0.18 (5x – 4) = 0.5x + 0.8

\(\Rightarrow\) 0.9x - 0.72 = 0.5x + 0.8

\(\Rightarrow\) 0.9x - 0.5x = 0.8+0.72 = 1.52

\(\Rightarrow\) 0.4x = 1.52

\(\Rightarrow\) \(x=\frac{1.52}{0.4}=\frac{15.2}{4}=3.8\)

9x – 3 = –21 has the solution (–2)

In the question it is given that, x = -2

Then, let us assume the missing number be y

(9 × (-2)) – y = -21

-18 – y = -21

– y = -21 + 18

– y = – 3

y = 3

Three consecutive numbers whose sum is 12 are 3, 4 and 5.

3 + 4 + 5 = 12

Correct option is (D) ₹ 680

Let cost price of radio be Rs x.

\(\therefore\) Selling price = x + 10% of x

= x + \(\frac{10x}{100}\) = x + \(\frac{x}{10}\) \(=\frac{11x}{10}.\)

Given that selling price = Rs 748

\(\therefore\) \(\frac{11x}{10}=748\)

\(\Rightarrow\) \(x=\frac{748}{11}\times10=680\)

\(\therefore\) Cost price of that radio is Rs 680.

Correct option is   D) ₹ 680

(i) 5x < 20 

⇒ x ……… 4 

As, 5x < 20 

Then, 

Dividing both the sides by 5 

\(\frac{X}{5} <\frac{20}{5}\)

x < 4 

Therefore, 

5x < 20 

⇒ x < 4 

(ii) -3x > 9 

⇒ x ……… -3 

As, -3x > 9 

Then, Dividing both the sides by 

\(\frac{X}{3}> - \big(\frac{9}{3}\big)\)

x > -3

Therefore, 

-3x > 9 ⇒ x > -3 

(iii) 4x > -16 ⇒ x ……… -4 As, 

4x > -16 

Then, Dividing both the sides by 4

\(\frac{X}{4} > - \big(\frac{16}{4}\big)\)

x > -4 

Therefore, 

4x > -16 

⇒ x > -4 

(iv) -6x ≤ -18 

⇒ x ……… 3 

As -6x ≤ -18 

Then, Dividing both the sides by 6

\(\frac{-X}{6} \le \big(\frac{-18}{6}\big)\)

-x \(\le\) -3

Now multiplying by -1 on both sides 

-x(-1) ≤ -3(-1) 

x ≥ 3 (inequality sign reversed) 

Therefore, 

-6x ≤ -18 ⇒ x ≥ 3 

Correct option is  A) -4

Correct option is (A) -4

2x – 3 = 4x + 5

\(\Rightarrow\) 4x - 2x = -3 - 5 = -8

\(\Rightarrow\) 2x = -8

\(\Rightarrow\) x = \(-\frac82\) = -4.

Correct option is  A) 3/4

Correct option is (A) 3/4

\(\frac{4x}{4}=\frac{3}{4}\)

\(\Rightarrow\) \(x=\frac34.\)