Explore topic-wise InterviewSolutions in Current Affairs.

The answer is: Tile 

Burglary is a theft committed by Breaking into or out of premises.

Correct answer is a. Tile 

Recycling and reuse of waste materials

Correct answer is d. Character

def filter (oldfile, newfile): 

fin = open(oldfile, "r") 

fout = open(newfile, 'w') 

while True: 

text = fin.readline() 

if len(text) == 0: 

break 

if text [0] = "@": 

continue

fout.write(text)

fin.close()

fout.close()

“Sum Insured” means the Monetary Amounts shown against item/s insured.

Correct answer is a. Template 

The return type of the input() function is string.

Correct answer is c. Alignment 

Correct answer is d. Percentage

The SUBTOTAL function in Excel allows users to create groups and then perform various other Excel functions such as SUM, COUNT, AVERAGE, PRODUCT, MAX,AVERAGE ,COUNTA ,MIN ,STDEV, STDEVP, VAR, VARP.

Correct answer is b. Style 

b) Style 

Style is the correct option because they are a group of formatting effects that can be added in a single step.

Inverse of matrix is \(A^{-1} = \begin{bmatrix}\frac1a&0&0\\0&\frac1b&0\\0&0&\frac1c\end{bmatrix}\)

If a transformer heats up, then the current will decrease across the transformer.

Fermentation is a metabolic process in which an organism converts a carbohydrate, such as starch or a sugar, into an alcohol or an acid. For example, yeast performs fermentation to obtain energy by converting sugar into alcohol. Bacteria perform fermentation, converting carbohydrates into lactic acid.

\(xy - 4 = 2x + y\)

⇒ \(y = \frac{4+2x}{x - 1}\)

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

\(=2\left(1 + \frac3{x - 1}\right)\)

\( = 2 + \frac6{x -1}\)

Hence, if x = 2, 3, 4 & 7 then y becomes natural numbers.

Hence, (x, y) pairs are (2, 8), (3, 5), (4, 4), (7, 3).

₀∫¹ (2 - 3x + x²) dx

\(=(2x-\frac{3x^2}2+\frac{x^3}3)^1_0\)

= 2 - 3/2 + 1/3 - 0

\(=\frac{12-9+2}6\) = 5/6.

Smallest 3 digit number which leaves remainder 4 when divided 7 is 102.

Largest 3 digit number which leaves remainder 4 when divided by 7 is 998.

102, 109, ....... 998 is A.P. of such numbers.

\(\therefore 998 = 102 + (n -1)7\)

⇒ \(n - 1 = \frac{998 - 102}{7} = \frac{896}{7} = 128\)

⇒ \(n = 129\)

Hence, total 129, 3 digit numbers give a remainder 4 when divided by 7.

Let v be speed of bus.

time=150/v

After speed is reduced,

^v₁=v-5

^{150/(v-5)​​​​}​​​​ -150/v = 1

solve to find v.

\(\begin{array}{c|c}2&32\\\hline2&16\\\hline 2&8\\\hline 2&2\\\hline&1\end{array}\)    \(\begin{array}{c|c} 2&54\\\hline3&27\\\hline3&9\\\hline3&3\\\hline &1\end{array}\)

Prime factorisation of 32 & 54 is 

32 = 2 x 2 x 2 x 2 x 2

54 = 2 x 3 x 3 x 3

∴ HCF(32, 54) = 2.

A rational number, in Mathematics, can be defined as any number which can be represented in the form of p/q where q ≠ 0. Also, we can say that any fraction fits under the category of rational numbers, where the denominator and numerator are integers and the denominator is not equal to zero. When the rational number (i.e., fraction) is divided, the result will be in decimal form, which may be either terminating decimal or the repeating decimal.

\(\begin{array}{c|c} 2 & 506 \\ \hline 11 & 253\\\hline23&23\\\hline &1 \end{array}\)    \(\begin{array}{c|c} 5 & 115 \\ \hline23&23\\\hline &1 \end{array}\) 

Prime Factorisation 506 & 115 are

506 = 2 x 11 x 23

115 = 5 x 23

∴ HCF(506, 115) = 23

LCM(506, 115) = 23 x 2 x 11 x 5 = 2530

fill in the blank 9,10

fill in the blank

9riekjieksjwjwmkjwjennenen

(-3)+(-12)+(-77)=_+(-12)+(-77)

-3-12-77=_+(12)-77

-92€-89

OR

-92€-65

(-3)+(-12)+(-77)€_+(-12)+(-77)

-3-12-77€_+(12)-77

-15€-12

OR

-15€12

(-3 + (-12)) + (-77) = ------- + ((-12) + (-77))

By associative property of addition , we know that

(a+b) + c = a + (b+c)

∴ (-3+ (-12)) + (-77) = -3 + ((-12) + (-77))

Hence , -3 is at blank.

(i) -3, -6, -9, -12 is given pattern

\(\Rightarrow\) -3, -5, -6, -7, -9, -10, -11, -12

(ii) 5, 10, 15, 20 is given pattern

\(\Rightarrow\) 5, 6, 7, 10, 12, 15, 18, 20 is pattern with four more rational numbers.

The coordinates of the centroid G of △ABC are

\((\frac{-1+0-5}3,\frac{3+4+2}3)\) i.e., (-2, 3)

Since G lies on the median x - 2y + k + 0. So, coordinates of G satisfy its equation.

∴ -2 - 6 + k = 0

⇒ k = 8.

An example of a simple random sample would be the names of 25 employees being chosen out of a hat from a company of 250 employees. In this case, the population is all 250 employees, and the sample is random because each employee has an equal chance of being chosen. Random sampling is used in science to conduct randomized control tests or for blinded experiments.

ANSWER:

1(42-54)-1(28-45)+24-30)

= -1

\(\vec T_1 = 2\hat i + 2\hat j - 3\hat k\)

\(\vec T_2 = -2\hat i + 2\hat j - 3\hat k\) 

\(|\vec T_1|=\sqrt{2^2+2^2+(-3)^2}\) = \(\sqrt{4+4+9}=\sqrt{17}\)

\(|\vec T_2|=\sqrt{-2^2+2^2+(-3)^2}\) = \(\sqrt{4+4+9}=\sqrt{17}\)

Let angle between T₁ and T₂ is θ.

\(\therefore\) θ = \(\frac{\vec T_1.\vec T_2}{|\vec T_1||\vec T_2|}\) = \(\frac{(2\hat i+2\hat j-3\hat k).(-2\hat i+2\hat j-3\hat k)}{\sqrt{17}{\sqrt{17}}}\)

\(=\theta = cos^{-1}\frac1{17}\)

Hence, angle between both tangents is cos^-1\(\frac9{17}\).

The correct option is (A)

 \(\vec T_1 = 2\hat i + 2\hat j - 3\hat k\)

\(\vec T_2 = -2\hat i + 2\hat j - 3\hat k\)

\(|\vec T_1|=\sqrt{2^2+2^2+(-3)^2}\) = \(\sqrt{4+4+9}=\sqrt{17}\)

\(|\vec T_2|=\sqrt{-2^2+2^2+(-3)^2}\) = \(\sqrt{4+4+9}=\sqrt{17}\)

Let angle between T₁ and T₂ is θ.

\(\therefore\) θ = \(\frac{\vec T_1.\vec T_2}{|\vec T_1||\vec T_2|}\) = \(\frac{(2\hat i+2\hat j-3\hat k).(-2\hat i+2\hat j-3\hat k)}{\sqrt{17}{\sqrt{17}}}\)

\(=\theta = cos^{-1}\frac1{17}\)

Hence, angle between both tangents is cos^-1\(\frac9{17}\).

Given:

Our given expression is 3(x + 2)2 + 5(x + 2) + 2

Calculation:

Our given expression is 3(x + 2)2 + 5(x + 2) + 2

Let (x + 2) be t, then our given equation becomes,

3t² + 5t + 2

⇒ 3t2 + 3t + 2t + 2

⇒ 3t(t + 1) + 2(t + 1)

⇒ (3t + 2)(t + 1)

Putting the value of t,

{3(x + 2) + 2}{(x + 2) + 1}

⇒ (3x + 6 + 2)(x + 3)

⇒ (3x + 8)(x + 3)

∴ The factor of the given expression is (3x + 8)(x + 3)

Given:

The given number = 3969

Concept:

Calculation skills trick

Calculation:

Step(1):

The unit digit in this number is 9, which can be a unit digit of its square root number such as 3 or 7. Because 3 x 3 is 9 and 7 x 7 is 49.

Step(2):

Now let us consider the first two digits that is 39 which comes between the squares of 6 and 7 because 36 < 39 < 49

Step(3):

We can assume that the ten’s digit of the square root of 3969 is the lowest among the two numbers i.e. 6

Step(4):

Now, we need to find among 63 and 67 which is the square root of 3969.

Step(5):

Since the ten’s digit is 6 and the next number is 7, we need to multiply both the numbers like 6 x 7 = 42 and since 42 is greater than 39.

Step(6):

Square root of 3969 will be the smaller number among 63 and 67 i.e. 63.

∴  √3969 = 63

Calculations :

2 : 3 = 2/3 = 0.67

3 : 5 = 3/5 = 0.60

4 : 7 = 4/7 = 0.57

5 : 8 = 5/8 = 0.625

So the biggest ratio will be 2 : 3.

∴ The correct choice will be option 4. 

Prime numbers are those numbers which have just two factors, 1 and itself.

(B) It is clear that C is the Brother of B but how B is related to C depends on the sex of B.

Given:

2365A is divisible by 9

Concept:

If the sum of all the digits is divisible by 9, then the number is also divisible by 9.

Calculation:

Sum of all the digits = 2 + 3 + 6 + 5 + A

⇒ 16 + A

As the number is divisible by 9, so 16 + A is also divisible by 9

Multiple of 9 nearest to 16 is 18

⇒ 16 + A = 18

⇒ A = 18 – 16

⇒ A = 2

∴ The value of A is 2.

Concept used:-

Trick for writing cube of a number.

Method & Calculation:-

• Write the cube of 3 & 2 in three digit form i.e. (027008)
• Now multiply all the digits within themselves i.e. (3 x 2) = 6
• Now multiply the result obtained from step (2) by 3 i.e. 6 x 3 = 18
• Now multiply 18 and 32 i.e. 18 x 32 = 576
• Now keep the unit digit vacant and add 027008 & 576 i.e. 027008 + 576_ = 32768

The given number = 6724

Concept:

Calculation skills trick

Calculation:

Step(1):

The unit digit in this number is 4, which can be a unit digit of its square root number such as 2 or 4. Because 2 x 2 is 4 and 8 x 8 is 64.

Step(2):

Now let us consider the first two digits that is 67 which comes between the squares of 8 and 9 because 64 < 67 < 81

Step(3):

We can assume that the ten’s digit of the square root of 6724 is the lowest among the two numbers i.e. 8

Step(4):

Now, we need to find among 82 and 84 which is the square root of 6724.

Step(5):

Since the ten’s digit is 8 and the next number is 9, we need to multiply both the numbers like 8 x 9 = 72 and since 72 is greater than 67.

Step(6):

Square root of 6724 will be the smaller number among 82 and 88 i.e. 82.

∴  √6724 = 82

9 * 4 * 22 * 14

9 × 4 – 22 = 14

Concept used:
a^x × a^y = a^{x + y}
If a, b and c are prime numbers, then the number of prime factors of ax × by × c^z is (x + y + z).

Calculation:
Prime factors of 30 = 2 × 3 × 5
Prime factors of 24 = 2 × 2 × 2 × 3
(30)5 × (24)5
⇒ (2 × 3 × 5)⁵ × (2 × 2 × 2 × 3)⁵
⇒ 2⁵ × 3⁵ × 5⁵ × 2⁵ × 2⁵ × 2⁵ × 3⁵
⇒ (2)^{5 + 5 + 5 + 5} × (3)^{5 + 5} × (5)⁵
⇒ (2)20 × (3)10 × (5)5
Number of prime factors = 20 + 10 + 5 = 35
∴ The number of prime factors in the product (30)5 × (24)5 are 35.