Explore topic-wise InterviewSolutions in Current Affairs.

Vector quantity: Impulse.

3 red  4 blue, 4 green  add them up and it is 11  the first three times you might pull out all red so u have one color so your down to blue and green the next for times you pull out all blues so that is a total of 7 Tries add 1 there is only green in your pocket now so it is  8  it can be 9 also it matters what the first color is

Given:

The efficiency of A = 5 × the efficiency of B

Then ratio of efficiency of A to the efficiency of B = 5 : 1

A can complete a work in 60 days less than B.

Concept used:

Days is inversely proportional to efficiency

If A does a work in x days and B does a work in y days, the ratio of days = x : y and

The ratio of efficiency = y : x

If a person does a work in ‘n’ days then one day work by a person will be 1/n part of total work

Calculation:

Let the efficiency of A and B be 5x and x respectively.

Then the number of days taken by A and B for a work will be x and 5x respectively

A takes less time than B = 5x – x

⇒ A – B = 4x days

According to question, A – B = 60 days

⇒ 4x = 60

⇒ x = 60/4

⇒ x = 15

Then A takes days to complete a work = x

⇒ 15 days

Now one day work by A = 1/15

B takes days to complete a work = 5x

⇒ 5 × 15

⇒ 75 days

Now one day work by B = 1/75

One day work when both work together = one day work by A + one day work by B

⇒ 1/15 + 1/75

⇒ (5 + 1)/75

⇒ 6/75

⇒ 2/25

⇒ 1/12.5

Now, one work completed by both A and B = 12.5 days

∴ The work would be completed by both in 12.5 days

They are in GP 

Answer (B)  for two numbers a and b

A= (a+b)/2

G²= a.b

H= 2a.b/(a+b)

Thus A.H= a.b = G²

^{Shows A, G,H are in GP}

The pattern of the given series can be explained as:

2³ + 1 = 9

4³ + 2 = 66 ≠ 65

6³ + 3 = 219

8³ + 4 = 516

10³ + 5 = 1005

∴ The wrong number is 65.

Phasor Diagrams are a graphical way of representing the magnitude and directional relationship between two or more alternating quantities. Sinusoidal waveforms of the same frequency can have a Phase Difference between themselves which represents the angular difference of the two sinusoidal waveforms.

• When a lawn mower is pushed, the mower moves along the grassy ground but the force is applied at an angle to the direction in which the mower moves.
• Opening or close a tap, or for that matter where a turning moment is produced, are examples of the cross product of two vectors.
• Opening/closing a tap, we apply equal and opposite forces at the two diametrically opposite ends of the tap. These force produce a turning couple which turns the tap.
• The turning moment of the couple is equal to r × f, where r= diametet of the tap head, at two ends of which force f is applied.
• Same is true of when we put or take out a screw.
• When a door is opened/closed the angular momentum it has is equal to r × p, where p is the linear momentum of the free end of the door being opened/closed, and r is the perpendicular distance from the hinges on which the door rotates and the free end of the door.

Correct answer is: (a) intersecting

Lines x=a is a line parallel to y axis and y=b is a line parallel to x axis. So they will intersect.

Correct answer is: (c) 2,5

Since it has a terminating decimal expansion,

so prime factors of the denominator will be 2,5

We know 2⁴ = 16

The reminder when 2⁴ is divided by 17 is – 12²⁰¹³ = (2⁴)⁵⁰³. 2¹

∴ The remainder when 2²⁰¹³ is

divided by 17 is (–1)⁵⁰³. 2

= (–1)² = – 2.

The given word contains 6 letters in which one C, one H, 3E's and one S.

Since no two E's come together, first arrange the remaining 3 letters in 3! ways. Then we can find 4 gaps between them. The 3E's can be arranged in these 4 gaps in ⁴P₃/3! = 4 ways.

∴ The number of required arrangements = 3! × 4 = 24

The number of ways of selecting

4 English books out of 7 books = ⁷C₄

3 Telugu books out of 6 books = ⁶C₃

2 Hindi books out of 5 books = ⁵C₂

Hence, the number of required ways

⁷C₄ × ⁶C₃ × ⁵C₂ = 35 × 20 × 10 = 7000.

Given equation is x³ + 3x² + 2 = 0

Put y = x³ so that x = y^1/3

∴ y + 3y^2/3 + 2 = 0

3y^2/3 = – (y + 2)

Cubing on both sides, 27y² = – (y + 2)³

= – (y³ + 6y² + 12y + 8)

∴ y³ + 6y² + 12y + 8 = 0

⇒ y³ + 33y² + 12y + 8 = 0

Required equation is x³ + 33x² +12x +8= 0

We have x = \(\frac{a}{b-c},\) y = \(\frac{b}{c-a},\) z = \(\frac{c}{z-b}\)

Now, \(\begin{vmatrix}1&-x&x\\1&1&-y\\1&z&1\end{vmatrix}\) = \(\begin{vmatrix}1&-x&x\\0&1+x&-(x+y)\\0&x+z&1-x\end{vmatrix}\) (By applying R₂ - 1 R₂ - R₁ and R₃ - 1, R₃ - R₂)

 = (1 + x) (1 - x) + (x + y)(x + z) (By expanding determinant along C₁)

 = 1 - x² + x² + xy + xz + yz

 = 1 + \(\frac{a}{b-c}\times\frac{b}{c-a}\) + \(\frac{a}{b-c}\times\frac{c}{a-b}\) + \(\frac{b}{c-a}\times\frac{c}{a-b}\) 

 = 1 + \(\frac{ab(a-b)+ac(c-a)+bc(b-c)}{(a-b)(b-c)(c-a)}\) 

 = 1 + \(\frac{a^2b-ab^2+ac^2-a^2c+b^2c-b^2c}{(a-b)(b-c)(c-a)}\) 

 = \(\frac{(a-b)(b-c)(c-a)+a^2b-ab^2+ac^2-a^2c+b^2c-bc^2}{(a-b)(b-c)(c-a)}\) 

 = \(\frac{(-a^2b-ac^2+a^2c-b^2c+ab^2+bc^2)+(a^2b-ab^2+ac^2-a^2c+b^2c-bc^2)}{(a-b)(b-c)(c-a)}\) 

 = \(\frac{0}{(a-c)(b-c)(c-a)}\)

 = 0

\(\begin{vmatrix}a+b+c&-c&-b\\-c&a+b+c&-a\\-b&-a&a+b+c\end{vmatrix}\)

Applying C₁→ C₁ + C₂ & C₂ → C₂ + C₃

\(=\begin{vmatrix}a+b&-(b+c)&-b\\a+b&b+c&-a\\-(a+b)&b+c&a+b+c\end{vmatrix}\)

Applying C₁ → \(\frac{C_1}{a+b}\) & C₂ → \(\frac{C_2}{b+c}\)

= (a + b)(b + c)\(\begin{vmatrix}1&-1&-b\\1&1&-a\\-1&1&a+b+c\end{vmatrix}\)

Applying R₁ → R₂  - R₁, & R₃ → R₃ + R₁

 = (a + b)(b + c)\(\begin{vmatrix}1&-1&-b\\0&2&-a+b\\0&0&a+c\end{vmatrix}\)

= 2(a + b) (b + c) (c + a) (Expand determinant along C₁)

 \(\begin{vmatrix}x&y&z\\x^2&y^2&z^2\\x^3&y^3&z^3\end{vmatrix}\)

Applying C₁ → \(\frac{C_1}x\), C₂ → \(\frac{C_2}y\) & C₃ → \(\frac{C_3}z\)

\(=xyz\begin{vmatrix}1&1&1\\x&y&z\\x^2&y^2&z^2\end{vmatrix}\)

Applying C₁ → C₁ - C₂  and C₂ → C₂ - C₃

\(=xyz\begin{vmatrix}0&0&1\\x-y&y-z&z\\x^2-y^2&y^2-z^2&z^2\end{vmatrix}\)

\(=xyz\begin{vmatrix}0&0&1\\x-y&y-z&z\\(x-y)(x+y)&(y+z)(y-z)&z^2\end{vmatrix}\)

Applying C₁ → \(\frac{C_1}{x-y}\) and C₂ → \(\frac{C_2}{y-z}\)

= xyz(x - y)(y - z)\(\begin{vmatrix}0&0&1\\1&1&z\\x+y&y+z&z^2\end{vmatrix}\)

= xyz(x - y)(y - z)\(\begin{vmatrix}1&1\\x+y&y+z\end{vmatrix}\) (By Expanding determinant along R₁)

= xyz(x - y) (y - z) (y + z - (x + y))

= xyz(x - y) (y - z) (z - x)

The number of common roots = H.C.F of {15, 25} = 5

Given z = 2− i√7

⇒ z – 2 = − i√7

⇒ (z – 2)² = (− i√7)²

⇒ z² – 4z + 4 = 7i²

⇒ z² – 4z + 4 = – 7

⇒ z² – 4z + 11 = 0

3z³ –4z² + z + 88 = 3z(z² – 4z + 11) + 8z² – 32z + 88

= 3z(0) + 8(z² – 4z + 11) = 0 + 8(0) = 0

∴ 3z³ – 4z² + z + 88 = 0

\(\frac{ax}{b} - \frac{by}{a} = a + b\)   ....(1)

\(ax - by = 2ab\)      ....(2)

From (2), we get

\(\frac{ax - by}{a} = 2b\)

⇒ \(x - \frac ba y = 2b\)     .....(3)

Subtract equation (3) from (1), we obtain

\(\left(\frac ab -1\right)x = a - b\)

⇒ \(\left(\frac {a-b}b\right)x = a - b\)

⇒ x = b

∴ From (3), we get 

\(b - \frac ba y = 2b\)

⇒ \( \frac ba y = b-2b\)

⇒ \( \frac ba y = -b\)

⇒ y = -a

Hence, x = b, y = -a be solution of given system of equations.

Given:

Numbers are 3 and 5

Final ratio = 2 : 3

Calculation:

Let x is added in both the terms.

(3 + x)/(5 + x) = 2/3

⇒ 3(3 + x) = 2(5 + x)

⇒ 9 + 3x = 10 + 2x

⇒ x = 1

∴ The number to be added is 1

Concept used:

The numerator is the upper part and denominator is the lower part of any fraction

Calculation:

Let the numerator of the rational number be x then its denominator be x + 6

Rational number = Numerator/Denominator

The original rational number = x/(x + 6)

Now, A/Q

(x + 4)/(x + 6 – 8) = 5/3

⇒ (x + 4)/(x – 2) = 5/3

⇒ 3(x + 4) = 5(x – 2)

⇒ 3x + 12 = 5x – 10

⇒ 2x = 22

⇒ x = 11

Numerator = x and Denominator = 11 + 6 = 17

∴ The original rational number is 11/17

P₁ = 6.5 g/cm³

P₂ = 2.7 g/cm³

H₂ = 40 mm

H₁= ?

We know that

P₁H₁ = P₂H₂

6.5 x H₁ = 2.7 x 40

H₁ = 108/6.5

H₁ = 16.61 mm

It determines the rate of respiration in living beings. Measuring BOD gives the COD or Chemical Oxygen Demand of inorganic substances. It indicates the polluting potential of water. BOD is used in the medical and pharmaceutical industries to measure the oxygen consumption of cell cultures.

Major enzymes involved in photosynthesis:

ATP synthase- synthesis of ATP

RUB is CO-captures carbon dioxide from the atmosphere

PEP carboxylase- fix carbon dioxide in the cells of the mesophyll

Carbonic anhydrase- releases CO from the dissolved hydrocarbonate ions

Oxygenase - catalyses the oxygenation reactions.

Dialysis is not complete treatment because dialysis does some of the work of healthy kidneys, but it does not cure your kidney disease. You will need to have dialysis treatments for your whole life unless you are able to get a kidney transplant.

Management as a Science- Science means a systematic body of knowledge pertaining to a specific field of study. It contains general principles and facts which explains a phenomenon. These principles establish cause-and-effect relationship between two or more factors. Scientific methods of observations and experiments are used to develop principles of science.

Herbarium and Botanical garden may be used as tools for the plant taxonomy. Museum, Taxonomical keys and Zoological parks are classical tools for animal studies. Field visits, survey, identification, classification, preservation and documentation are the important components of taxonomical tools.

Correct option is D) went

Taxonomy is the science of classifying organism. Taxonomy is the basis for all meaningful studies on biodiversity, pest management, medicine, bioprospecting, fisheries, quarantine, defense etc. Taxonomy provides basic understanding about the components of biodiversity which is necessary for effective decision-making about conservation and sustainable use.In short, taxonomy provides the basic foundations of conservation practice and sustainable management of the world remaining resources.