Class 12th

The passage below is accompanied by a set of questions. Choose the best answer to each question.

The work by Corry Gellatly, a research scientist at the university, has shown that men inherit a tendency to have more sons or more daughters from their parents. This means that a man with many brothers is more likely to have sons, while a man with many sisters is more likely to have daughters.
In many of the countries that fought in the World Wars, there was a sudden increase in the number of boys born afterwards. The year after World War I ended, an extra two boys were born for every 100 girls in the UK, compared to the year before the war

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Raj Pandey

Contributor-Level 9

Propensity is the closest in meaning to the word tendency.

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New answer posted

a year ago

If the line y = mx bisects the area enclosed by the lines x = 0, y = 0, $x = \frac{3}{2}$ and the curve y = 1 + 4x – x², then 12 m is equal to _________.

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Vishal Baghel

Contributor-Level 10

$\frac{1}{2} \int_{0}^{3 / 2} (1 + 4 x - x^{2}) d x$

$= \frac{1}{2} {[x + 2 x^{2} - \frac{x^{3}}{3}]}_{0}^{3 / 2} = \frac{39}{8}$

$\int_{0}^{3 / 2} m x = \frac{9 m}{8}$

(as per question)

$\Rightarrow \frac{39}{8} = \frac{9 m}{4}$

$m = \frac{39}{18}$

12m = 26

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New answer posted

a year ago

The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.

I learned that unhappy minds tend to wander into the past, while happy minds often ponder the future. I also became convinced that wandering among our memories is crucial to helping prepare us for what is yet to come. Though some kinds of mind wandering, such as dwelling on problems that cannot be fixed, may be associated with depression, I now believe mind wandering is rarely a waste of time.

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Contributor-Level 10

Last sentence uses all the relevant key words and state the given paragraph briefly keeping the real lesson intact.

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New answer posted

a year ago

If $\int \frac{s i n x}{s i n^{3} x + c o s^{3} x} d x = α l o g_{e} | 1 + t a n x | + β l o g_{e} | 1 - t a n x + t a n^{2} x | + γ t a n^{- 1} (\frac{2 t a n x - 1}{\sqrt[]{3}}) + C,$ when C is constant of integration, then the value of 18 $(α + β + γ^{2})$ is _________.

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Vishal Baghel

Contributor-Level 10

$\int \frac{s i n x}{s i n^{3} x + c o s^{3} x} d x$

$I = \int \frac{t a n x s e c^{2} x}{t a n^{3} x + 1} d x$

Let, tan x = t

sec² xdx = dt

$\int \frac{t d t}{t^{3} + 1} = \int \frac{t}{(t + 1) (t^{2} - t + 1)} d t$

$\frac{t}{(t + 1) (t^{2} - t + 1)} = \frac{A}{(t + 1)} + \frac{B t + c}{t^{2} - t + 1}$

$l = \frac{- 1}{3} \int \frac{1}{t + 1} d t + \frac{1}{3} \int \frac{t + 1}{t^{2} - t + 1} d t$

The value of 18 $(α + β + γ^{2})$ is equal to 3.

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New answer posted

a year ago

The passage below is accompanied by a set of questions. Choose the best answer to each question.

In many of the countries that fought in the World Wars, there was a sudden increase in the number of boys born afterwards. The year after World War I ended, an extra two boys were born for every 100 girls in the UK, compared to the year before the wa

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Raj Pandey

Contributor-Level 9

The given fact can be found in the penultimate paragraph of the passage.

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New answer posted

a year ago

Fill in the blanks with the most appropriate option.

I now know that workplaces ____________ better when colleagues have good relationships with one another.

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Contributor-Level 10

As we are talking about workplace and colleagues here, the best option is function.

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New answer posted

a year ago

Let f(x) be a cubic polynomial with f(1) = -10, f(-1) = 6, and has a local, minima at x = 1, and f'(x) has a local minima at x = -1. Then f(3) is equal to _______.

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Vishal Baghel

Contributor-Level 10

$f (x) = a x^{3} + b x^{2} + c x + d$

$f' (x) = 3 a x^{2} + 2 b x + c$

$f'' (x) = 6 a x + 2 b$

$f'' (- 1) = 0$

-6a + 2b = 0

=> b = 3a

$f' (1) = 0$

-5 + d = -10 . (i)

f (-1) = 6

11a + d = 6 . (ii)

$a = 1, d = - 5, b = 3, c = - 9$

$f (3) = 27 + 27 - 27 - 5 = 22$

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New answer posted

a year ago

Fill in the blanks with the most appropriate option.

Depletion of the ozone layer, which was first _______ in the 1980s, allows free passage of UV rays into the inhabited _________ of the atmosphere.

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Contributor-Level 10

Observed is the correct word as per the context and there are layers of atmosphere.

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New answer posted

a year ago

The function f(x), that satisfies the condition f(x) = x + $\int_{0}^{\frac{π}{2}} s i n x . c o s y f (y) d y$ is :

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alok kumar singh

Contributor-Level 10

f (x) = x + a sin x

$w h e r e a = \int_{0}^{\frac{π}{2}} c o s y f (y) d y$

$a = \int_{0}^{\frac{π}{2}} c o s y (y + a s i n y) d y$

-> a = p - 2

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New answer posted

a year ago

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide in which blank (option 1, 2, 3, or 4) the following sentence would best fit.

Sentence: Choosing between tap water or bottled water is therefore not as straightforward as one may think.

(1)____________. As per its definition, tap water is delivered through public water systems, whereas bottled water is delivered in sealed containers that are filled in bottling facilities under controlled conditions. (2)__________. This fundamental difference and the specific circumstances under which it occurs for different brands and tap water systems is the ca

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