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Correct option is C) sent

Correct option is B) lay

(a) I am determined that I shall never do it again. 

(b) He sat for some rest because he was tired. 

(c) We know it that she has come.

Given:

Selling price = ₹ 750

Festival Discount = 70%

Normal Discount = 30%

Formula used :

SP = MP × (100 - D)/100

Calculation:

Substituting the values in the formula

750 = MP × (100 - 70)/100

750 × 10/3 = MP     

Marked price = ₹ 2500       ----(i)

Substituting the (i) in the formula

SP on normal days = 2500 × (100 - 30)/100

SP on normal days = ₹ 1750

∴ Selling price on normal days is ₹ 1750

Correct option is D) questioned

Correct option is B) extends

(i) She asked me who I was. 

(ii) The teacher told his students that work is worship. 

(iii) He wished that God might save her life. 

(iv) Ram tells Mohan that he (Ram) has done his (Ram) home work.

Manju told Mohan that I was not so tall as you.

Correct option is D) was moving / are repairing

Correct option is C) signs

Given:

SP₁ = Rs.16,725

D₁ = 22%

SP₂ = Rs.15,685

D₂ = 15%

Formula used:

Marked Price = Sale Price × 100/(100- Discount %)

Calculation:

MP₁ = 16725 × 100/78 = 21,442.30

MP₂ = 15685 × 100/85 = 18452.94

Difference = MP₁ - MP₂ = 21442.30 - 18452.94 = 2989.36

∴ The difference between Marked Prices is 2989.

(a) She told me that she was learning English.

(b) He wished happy Christmas.

(c) I requested my friend to have a cup of tea.

Correct option is D) had been waiting

Correct option is B) yet

Correct option is B) has been closed

Given:

Investment amount ratio of A and B = 3 : 5

Profit of A is Rs.3450

Calculation:

Current Ratio = 3 : 5

Ratio of Next year = 3 × 110% : 5 × 88% = 3 : 4

A's Profit = Rs. 3450

Total Profit = 3450 × (7/3) = Rs.8050

∴ The total profit is Rs. 8050.

Correct option is C) have been waiting

Correct option is A) Had

Correct option is (c) 6.75

Given:

Ram and Sita invested capital in the ratio 4 : 5. The time Sita invested her money for was one year lesser than that invested by Ram. The ratio of their profits is is in the ratio 6 : 7.

Formula:

Ratio of Profit = ratios of product of Amount invested and time

Calculation:

Let the money invested by Rama and Sita be 4x and 5x respectively.

Let the time they invested for be t and t – 1 respectively.

Ratio of profit = 4xt/5x(t-1)

⇒ 4xt/{5x (t-1)} = 6/7

⇒ 4t/{5(t-1)} = 6/7

⇒ 28t = 30t – 30

⇒ 2t = 30

⇒ t = 15

Time Sita invested for = t – 1 = 15 – 1 = 14 years

∴ The time Sita invested the money for is 14 years.

A) at / in / at 

Correct option is B) Had

Given:

A invested 17800 for 12 months. B invested a certain amount for 6 months and further increased the amount by 500 for the next 6 months. The ratio of profit for A and B at the end of the year is 26/25..

Formula:

Ratio of Profit = ratios of product of Amount invested and time

Calculation:

ATQ,

Profit sharing ratio = investment × time

Let B invested Rs x initially

A/B= 17800 × 12/6x + (x + 500) × 6 = 26/25

213600/12x + 3000 = 26/25

5340000 = 26(12x + 3000)

x = 5262000/312 = 16865

Given:

A invested a certain amount in a business for 6 months. B invested 1000 more than that invested by A for six months. After 6 months, A decreased his capital by 1000. At the same time, B also decreased his investment by 1000. The ratio of their profit after one year is 37 : 39.

Formula:

Ratio of Profit = ratios of product of Amount invested and time

Calculation:

Let the amount invested by A each for six months be x and x – 1000.

Let the amount invested by B each for six months be x + 1000 and x.

(6x + 6(x - 1000))/(6(x + 1000) + 6x) = 37/39

(2x - 1000)/(2x + 1000) = 37/39

x = 19000

The amount B invested in the initial six months = x + 1000 = 19000 + 1000 = Rs. 20000

∴ The amount B invested in the initial six months  is Rs.20000.

\(tan\, t + 2cos \,t \; cosec \, t\)

\(= \frac {sin\,t}{cos\,t }+ \frac{2cos\,t}{sin\,t}\)

\(= \frac{sin^2t+ 2cos^2t}{sin\,t \;cos\,t}\)

\(= \frac{1+ cos^2t}{sin\,t \;cos\,t}\)    \((\because sin^2t + cos^2 t = 1)\)

\(= sec\,t . cosec\,t + \frac{cos\,t}{sin\,t}\)

\(= sec\, t . cosec.t + cot\,t\)

Hence Proved.

Correct option is C) private

Correct option is A) visit 

Correct option is D) with/at

Financial accounting is concerned with the preparation of the financial statements and provides financial information to various accounting users. It is performed according to the basic accounting concepts like Business Entity, Money Measurement, Consistency, Conservatism, etc. These concepts allow various alternatives to treat the same transaction. For example, there are a number of methods available for calculating stock and depreciation, which can be followed by various firms. This leads to wrong interpretation of financial results by external users due to the problem of inconsistency and incomparability of financial results among different business entities. In order to mitigate inconsistency and incomparability and to bring uniformity in preparation of the financial statements, accounting standards are being issued in India by the Institute of Chartered Accountant of India. Accounting standards help in removing ambiguities and inconsistencies. Hence, accounting standards and accounting concepts are referred as the essence of financial accounting.

Given:

X and Y invested a total of Rs. 65200 in their business for 4 months.

X then, decreased his amount by Rs. 10000 for the next 8 months.

Y increased his amount by Rs. 12000 for the next 8 months.

The ratio of their profit is 250/249.

Formula Used:

Ratio of Profit = ratios of product of Amount invested and time

Calculation:

Let X invested Rs. X and Y invested Rs. (65200 – x)

X                                                                    y

X [For 4 months]                                           (65200 – x) [For 4 months]

(x – 10000) [For next 8 months]                   (77200 – x) [For next 8 months]

⇒ {x × 4 + (x - 10000) × 8}/{4 × (65200 - x) + (77200 - x) × 8} = 250/249

⇒ (12x - 80000)/(878400 – 12x) = 250/249

⇒ x = 40000

∴ Initial amount invested by X was Rs. 40000

Given:

A invested Rs. 17000 for 6 months and 21000 for another 6 months. B invested 22000 for 5 months and 18000 for 7 months.

Formula:

Ratio of Profit = ratios of product of Amount invested and time

Calculation:

A invested Rs. 17000 for 6 months and 21000 for another 6 months.

B invested 22000 for 5 months and 18000 for 7 months

A                                          :            B

17000 × 6 + 21000 × 6        :            22000 × 5 + 18000 × 7

102000 + 126000                :            110000 + 126000

228000                                :             236000

Ratio of profit after one year = 228/236 = 57/59

Correct option is C) came 

\(cos^2(x + \frac\pi3) = sin^2(\frac{-\pi}3-x)\)

⇒ \(cos^2(x + \frac\pi3) = sin^2(x + \frac\pi3)\)   \((\because sin(-\theta)= -sin\theta)\)

⇒ \(cos^2(x + \frac\pi3)- sin^2(x + \frac \pi3) = 0\)

⇒ \(cos(2(x + \frac \pi3)) =0 = cos\frac\pi2\)   \((\because cos^2\theta -sin^2\theta = cos2\theta)\)

⇒ \(2(x + \frac\pi3) = 2n\pi \pm \frac \pi 2\)

⇒ \(x + \frac \pi3 = n\pi \pm \frac \pi 4\)

⇒ \(x= n\pi \pm \frac\pi4 - \frac\pi3\)

⇒ \(x = n\pi + \frac \pi 4 - \frac\pi3 \; or\; n\pi - \frac\pi4 - \frac\pi3\)

⇒ \(x = n\pi - \frac \pi{12} \;or\; n\pi - \frac{7\pi}{12}, n\in Z\).

Correct option is C) and 

Let y = sin²x & z = e^cosx

\(\therefore\frac{dy}{dx}\) = 2 sin x cos x

& \(\frac{dz}{dx}=-e^{cosx}\) sin x

\(\frac{d(sin^2x)}{de^{cos x}}\) = \(\cfrac{\frac{dsin^2x}{dx}}{\frac{de^{cos x}}{dx}}\) = \(\cfrac{\frac{dy}{dx}}{\frac{dz}{dx}}\) = \(\frac{2sin xcos x}{-e^{cos x}sin x}\)

If ABC is a triangle 

Then \(A + B + C = \pi\)

\(\therefore cos \left(\frac{A + B}2\right) cos \left(\frac{B +C}2\right) cos\left(\frac{C +A}2\right)\)

\(= cos \left(\frac{\pi - C}2\right) cos \left(\frac{\pi - A}2\right) cos\left(\frac{\pi - B}2\right)\)

\(= cos \left(\frac\pi2 - \frac C2\right) cos \left(\frac\pi2 - \frac A2\right) cos\left(\frac\pi2 - \frac B2\right)\)

\(= sin\left(\frac C2\right) sin\left(\frac A2\right) sin\left(\frac B2\right)\)

a. Duvet Cover: These are quilt covers usually made of varied fabrics and embellished with placement prints, embroideries etc. 

b. Bedcover: These are placed over the bedsheet for decorative purposes. 

c. Throws: These are long rectangular sheet-like products that adorn the couches or beds. They can be woven or knitted. 

d. Quilts: These are padded and stitched bedsheet sized fabrics filled with cotton or poly fil. In order to keep the filling in place, the quilts are stitched by hand or machine.

Creativity process continually improves ideas and solutions by making gradual alterations and refinements.

\(u = tan^{-1} (x + \sqrt {1 + x^2})\)

\(v = \frac {tan^{-1}x}{1 + \sqrt{1 + x^2}}\)

\(\frac{d u}{d x} = \frac{1}{1 + (x + \sqrt{1 + x^2})^2} \;\frac {d}{dx} (x + \sqrt{1+ x^2})\)

\(= \frac{1}{2(x^2 + 1) + 2x\sqrt{1 + x^2}} \times \left(1 + \frac{2x}{2\sqrt{1 + x^2}}\right)\)

\(= \frac 1{2\sqrt{x^2 + 1} .(\sqrt{x^2 + 1}+x)} \times \frac {x + \sqrt{1 +x^2}}{\sqrt {1 +x^2}}\)

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

\(\frac{d v}{d x} = \cfrac{(1 + \sqrt {1 +x^2})\times \frac 1{1+x^2} - tan^{-1}x \times\frac{2x}{2\sqrt{1 + x^2}}}{(1+ \sqrt{1 +x^2})^2}\)

\(=\cfrac {\frac{1 + \sqrt{1 +x^2}}{1 + x^2} - \frac{xtan^{-1}x}{\sqrt{1 + x^2}}}{( 1 + \sqrt{1 + x^2})^2}\)

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

\(\cfrac{d\,tan^{-1} (x + \sqrt{ 1+ x^2})}{d\left(\frac{tan^{-1}x}{1 + \sqrt{1 + x^2}}\right)} = \frac {du}{dv} = \cfrac{\frac{du}{dx}}{\frac{d v}{d x}}\)

\(= \cfrac{\frac1{2( 1 + x^2)}}{\frac{1+ \sqrt{1+ x^2} (1- x\,tan^{-1}x)}{(1+x^2) (1+ \sqrt{1+ x^2})^2}} \)

\(= \frac{(1 +\sqrt{1 +x^2})^2}{2(1 + \sqrt{ +x^2}( 1 - x \, tan^{-1}x))}\)

The origin of the energy bandgap in the solid matter can be explained in terms of the interaction between the moving charged particles on the background ionized periodic arrangement of atoms/molecules. This interaction imposes restrictions on allowed and not allowed energy levels.

Correct option is (c) Both 1 and 2 

Given:

The word is ASSASSIN containing 3 vowels and 5 consonants.

Calculation:

If vowels come together, we can assume the three vowels as one single letter.

In that case, number of letters in the word = 5 + 1 = 6

Number of ways that can be arranged = 6! / 4! [It contains 4 ‘S’s]

Number of ways the vowels can be arranged between themselves = 3! / 2! [It has 2 ‘A’s]

Required number of ways = 6! / 4! × 3! / 2! = 90 ways

The total number of ways in which the letters of the word PROBABILITY are arranged is 11!/2! 2!

If two B's are together, it can be considered as one object.

So, total number of ways in which the letters of the word PROBABILITY are arranged such that two B's are together is 10!/2!

The probability that two B-s are together is, 10!/2!/11!/2! 2! = 2/11