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(E)  K_eq = K_a/[H₂O].

If B is multiplied by 4 then only 0 satisfies the above condition.

So, for unit place to satisfy the above condition, we should have B = 0.

Similarly for ten’s place, only 0 satisfies the above condition.

But, AB cannot be 00 as 00 is not a two digit number.

So, A and B cannot be equal to 0

∴ there is no solution satisfying the condition

1.5x = 0.04 y ⇒ \(\frac{y}{x} = \frac{1.5}{0.04} = \frac{150}{4}=37.5\)

∴ \(\frac{y-x}{y+x}=\frac{\frac{y}{x}-1}{\frac{y}{x}+1}=\frac{37.5-1}{37.5+1}= \frac{36.5}{38.5}=\frac{73}{74}.\)

Answer is (C) 2nπ ± π/2

The outer circumference of the roller = 440 cm 

Thickness of the roller = 4 cm and 

Its height (h) = 63 cm 

Let ‘R’ be the external radius and ‘r’ be the inner radius of the roller.

Circumference of roller = 2πR = 440 

Or 2πR = 440 

2 x \(\frac{22}{7}\) x R = 440 

or R = 70 

And, inner radius ‘r’ is given as 

⇒ r = R – 4 

⇒ r = 70 – 4 

⇒ r = 66 

Inner radius is 66 cm 

Now, volume of the iron is given as 

V = π(R²−r²)h 

V = \(\frac{22}{7}\)(702−662)63 

V = 107712 

Therefore, required volume is 107712 cm³.

Given,

d = 21cm

r = d/2 = 21/2cm

h = 10 cm.

By using the formula,

Volume of cylinder = πr²h

= 22/7 × 21/2 × 21/2 × 10

= 3465 cm³

Given,

r = 2.8 m

h =15 m

By using the formula,

Volume of cylinder = πr²h

= 22/7 × 2.8 × 2.8 × 15

= 369.6 m³

Radius of cylindrical bowl (R) = diameter/2

= \(\frac{7}{2}\) cm 

= 3.5 cm

Height = 4 cm 

Now, 

Volume of soup in 1 bowl = πr²h 

= \(\frac{22}{7}\) x 3.52 x 4 cm³ 

= 154 cm³ 

Volume of soup in 250 bowls = (250 x 154) cm³ 

= 38500 cm³ 

= 38.5 liters 

Thus, hospital has to prepare 38.5 liters of soup daily in order to serve 250 patients.

Given,

Area of cross section of pipe = 5 cm²

Speed of water flows through pipe = 30 cm/s

So, volume of water flows through pipe in 1 second = area of cross section × rate of flow

= 5 × 30 = 150 cm³

Hence,

volume of water flows through pipe in 1 minute(60second)

= 60 x 150 = 9000 cm³

= \(\cfrac{9000}{1000}\) = 9 liter

Given,

d = 7 m

r = d/2 = 7/2m

h = 24 m

By using the formula,

Volume of cylinder = πr²h

= 22/7 × 7/2 × 7/2 × 24

= 924 m³

Given,

r = 3.5 cm

h = 40 cm

By using the formula,

Volume of a cylinder = πr²h

= 22/7 × 3.5 × 3.5 × 40

= 1540 cm³

We have,

Area of base of right circular cylinder = 616 cm²

Height of cylinder = 2.5 cm

Let the radius of cylinder be ‘r’ cm

By using the formula,

Area of base of right circular cylinder = πr²

So,

πr² = 616

22/7 × r² = 616

r² = 616 × 7/22

= 196

r = √196

= 14cm

∴ Curved surface area of cylinder = 2πrh

= 2 × 22/7 × 14 × 2.5

= 220 cm²

Given,

Height of cylinder = 7.5 cm

Radius of cylinder = 3.5 cm

So, curved surface area of cylinder = 2πrh = \(2\times\cfrac{22}7\times\)7.5\(\times\)3.5 = 165 cm²

Total surface area = 2πr(h + r) = 2\(\times\cfrac{22}7\times\)3.5\(\times\)11 = 242 cm²

So, \(\cfrac{total\,surface\,area}{curved\,surface\,area}\) = \(\cfrac{242}{165}=\cfrac{22}{15}\)

We have,

Volume of cylinder = 1650 cm³

Curved surface area = 660 cm²

Volume of cylinder/curved surface area = 1650/660

πr²h/ 2πrh = 1650/660

r/ 2 = 5/2

r = 5cm

Surface area = 660 cm²

2πrh = 660

2 × 22/7 × 5 × h = 660

h = 660×7 / 2×22×5

= 4620/220

= 21cm

∴ Radius = 5cm and height = 21cm

We have,

Diameter of well = 10 m

Radius of well = d/2 = 10/2 = 5m

Depth of well = 8.4 m

Volume of earth dug out from well = πr²h

= 22/7 × 5 × 5 × 8.4

= 660 m³

This earth is spread out on width of 7.5 m.

inner radii, r = 5m and outer radii, R = (5+7.5) = 12.5cm

Area × h = 660

π(R² – r²) h = 660

π(12.5² – 5²) h = 660

22/7 (131.25) h = 660

h = 660×7 / 22×131.25

= 4620/2887.5

= 1.6 m

∴ Height of embankment is 1.6m.

We have,

Circumference of base of cylinder = 88 cm

Height of cylinder = 15 cm

Let ‘r’ be the radius of the cylinder.

By using the formula,

Circumference of base of cylinder = 2πr

So,

2πr = 88

2 × 22/7 × r = 88

r = 88 × 7 / 2 × 22

= 616/44

= 14cm

Radius of cylinder = 14 cm

∴ Volume of cylinder = πr²h

= 22/7 × 14 × 14 × 15

= 9240 cm³

We have,

Length of the trunk = 3m = 300 cm

Circumference of trunk of tree = 176 cm

2πr = 176

2 × 22/7 × r = 176

r = 176×7 / 2×22

= 28cm

Radius = 28cm

∴ Volume of timber can be obtained from trunk of tree = πr²h

= 22/7 × 28 × 28 × 300

= 7392 cm³

= 0.74 m³

Given,

Circumference of cylindrical tank = 176 cm

Length of tank = 3m = 300 cm

= 2πr = 176 = r = \(\cfrac{176\times7}{22\times2}\) = 28 cm

∴ volume of timber = πr²h = \(\cfrac{22}7\times\) 28 \(\times\) 28 \(\times\) 300

= 739200 cm³

^{\(=\cfrac{739200}{1000000}\)} = 0.74 m³

We have,

Ratio of radii of two cylinder = 2:3

Radius of cylinder 1 = r₁

Radius of cylinder 2 = r₂

r₁/r₂ = 2/3

Ratio of their heights = 5:3

Height of cylinder 1 = h₁

Height of cylinder 2 = h₂

h₁/h₂ = 5/3

Volume of cylinder 1 = v₁

Volume of cylinder 2 = v₂

v₁ / v₂ = πr₁²h₁ / πr₂²h₂

= 2² × 5 / 3² × 3

= 4×5 / 9×3

= 20/27

∴ Ratio of volumes of two cylinder is 20:27

We have,

Height of cylinder = 21m

Diameter of well = 6m

Radius of well = d/2 = 6/2 = 3m

Then,

∴ Volume of earth that must be dug out from this well = πr²h

= 22/7 × 3 × 3 × 21

= 594 m³

Radius of the base (r) = 1/2m

= 1/2 x 100cm = 50cm

Height (h) = 1.4m

= 1.4 × 100cm

= 140cm.

Surface area of to tin-coated = 2 ( 2πr + πr² )

= 2[2 × 3.14 × 50 × 140 + 3.14 × (50)²]

= 2[43960 + 7850] = 2(51810) = 103620cm²

∴ Cost of tin-coating at the rate or Rs. 50 per 1000cm²

=50/1000 × 103620 = Rs 5181.

Given, Height of right circular cylinder = 10.5 m

And 3(area of both circular ends) = 2(curved surface area of cylinder)

= 3\(\times\)πr² = 2\(\times\)2πrh = 6πr² = 4πrh

= 3r = 2h

or  r = \(\cfrac23\)h = \(\cfrac23\times10.5\) = 7 m

So, volume of cylinder = πr²h = \(\cfrac{22}7\times\) 49 \(\times\) 10.5

= 1617 m³

We have,

Height of cylinder = 10.5 m

3(A+A) = 2 curved surface area (where, A= circular area of box)

3×2A = 2(2πrh)

6A = 4πrh

6πr² = 4πrh

r²/r = 4πh/6π

r = 2/3 h

= 2×10.5 / 3

= 7m

∴ Volume of cylinder = πr²h

= 22/7 × 7 × 7 × 10.5

= 1617 m³

Correct option is A. doubled

Let radius of cylinder = r

Let height of cylinder = h

So, volume of cylinder = πr²h

New radius = r

New height = 2h

So,

volume becomes = πr² × 2h = 2πr²h

It becomes DOUBLED.

We have,

Radius of base = 70 cm

Height of base = 1.4 m = 140 cm

Rate of tin plating = Rs 3.50 per cm²

So,

Total surface area of vessel = Area of outer side of base + Area of inner and outer curved surface

= 2 (πr² + 2 πrh)

= 2πr (r + 2h)

= 2 × 22/7 × 70 (70 + 2(140))

= 2 × 22/7 × 70 (350)

= 154000 cm²

∴ Cost of tin coating at the rate of Rs 3.50 per 1000 cm² = 3.50/1000 × 154000

= Rs 539

Given, 

The capacity of a closed cylindrical vessel of height 1 m is 15.4 liters. 

Height of the cylindrical vessel = 15.4 litres 

= 0.0154 m³ [1m³ = 1000 litres] 

Let ‘r’ be the radius of the circular ends of the cylinders, then 

πr²h = 0.0154 m³ 

3.14 x r² x 1 = 0.0154 m³ 

or r = 0.07 m 

Again, 

Total surface area of a vessel = 2πr(r+h) 

= 2(3.14(0.07)(0.07+1)) m² 

= 0.470 m²

We have,

Height of cylinder = 10.5 cm

Let radius of cylinder be ‘r’ cm

So,

Area of two bases of cylinder = 2πr²

Area of curved surface of cylinder = 2πrh

Now,

3 (2πr²) = 2 (2πrh)

6πr² = 4πrh

πr²/ πr = 4/6 h

r = 2/3 h

= 2×10.5 /3

= 7cm

∴ Radius of base of cylinder is 7cm.

We have,

Diameter of base of cylinder = 20 cm

Radius of cylinder = 20/2 = 10cm

Height of cylinder = 14 cm

Total surface area of cylinder = 2πrh + πr²

= (2 × 22/7 × 10 × 14) + (22/7 × 10²)

= 880 + 2200/7

= (6160+2200)/7

= 8360/7 cm²

We know that cost per 100cm² = 50paise

So, cost per 1cm² = Rs 0.005

∴ Cost of tin painting the area inside the vessel = 8360/7 × 0.005

= Rs 5.97

Given,

Inner diameter of circular well = 3.5 m

Inner radius = \(\cfrac{3.5}2\) m 

Depth of well = 10 m

i) Inner curved surface area of well = 2πrh = 2\(\times\cfrac{22}7\times\cfrac{3.5}2\times\) 100 = 110 m²

ii) Cost of plastering 1m² area = Rs.40

Cost of plastering 110 m² = 40 × 110 = 4400 rs.

We have,

Height of cylinder = 21m

Diameter of cylinder = 6m

Radius of cylinder = 6/2 = 3m

Curved surface area of cylinder = 2πrh

= 2 × 22/7 × 3 × 21

= 396 m²

∴ Cost of plastering the inner surface at the rate of Rs 9.50 per m² = 396 × 9.50 = Rs 3762

(क) 68/100 मी० = 0.68 मी०

(ख) 16 मी० + 7/100 मी० = 16 मी० + 0.07 मी० = 16.07 मी.

(ग) 343 मी० + 50/100 मी० = 343 मी० + 0.5 मी० = 343.5 मी.

(घ) 532/100 मी० = 5.32 मी.

(ङ) 12 मी० + 30/100 मी० = 12 मी० + 0.3 मी० = 12.3 मी.

(क) 4/100 रु० = 0.04 रु०

(ख) 25/100 रु० = 0.25 रु.

(ग) 37891/100 रु = 378.91 रु०

(घ) 24 रु० + 36/100 रु० = 24 रु० + 0.36 रु० = 24.36 रु.

(ङ) 34576 रु० + 6/100 रु० = 34576 रु० + 0.06 रु० = 34576.06 रुः

During the family conversation, Martha defends Mr. Baldwin’s integrity like a tigress. She told her son John Gresham Baldwin and Evie that their father was upright and had no hand in the wrecking of the bank.

Donovan had said that nobody had any idea as to what was ailing the bank. The wreck of the bank was too sudden. He had married on the strength of the cashier’s job in the bank. He said crash would not have happened without the knowledge of the Governor Baldwin.

Only one person Mr. Robert was available there against Mr. Gresham.

केवल एक व्यक्ति श्री रॉबर्ट श्री ग्रेशम के खिलाफ गवाही के लिए थे।

Robert Baldwin is the protagonist of this play. He lives in a trim little cottage with his wife Martha and his son John and daughter Evie. He is working as the governor of a bank owned by John Gresham. His salary is very low, 60 dollars a week. His son John earns only 30 dollars a week. With this limited income they live reasonably happily.

Suddenly there is a problem in their lives. John Gresham has misappropriated bank money and he is in jail. The bank is closed and Baldwin will have no job. Only Baldwin is the witness for the misappropriation. If he gives his true testimony, John Gresham will definitely go to jail for a long period. Baldwin is honest and he has taught his family the importance of honesty. 

When Baldwin returns home after the arrest of John Gresham, his wife and children rush to him to know the latest news. Initially his wife and the children tell him that he should say the truth during the trial even if it means jail term for Gresham. But when they come to know that Gresham has offered him a bribe of 100,000 dollars just to say ‘I don’t remember’ when some incriminating questions are asked in the court, they change their stance. They try to nd out all kinds of loopholes to make Baldwin accept the bribe. Martha, John and Evie do their best to make Baldwih’dhange his mind. But he asserts that he wants to go to his grave clean.

He does love Gresham. He even named his son after him. Even now he remembers how he worked with him for so long. They were boys together. They worked side by side. All this is true, but he is not willing to tell a lie to save his friend and employer even when he is offered a colossal sum of 100,000 dollars.

Baldwin’s honesty is repaid abundantly. Even Gresham is proud of him and he recommends him to Mr Marshall, the President of the Third International. At the end of the play we see Marshall coming to the house of Baldwin and offering him a job at the Third International. We see Baldwin crying in the end. He must have been crying for two reasons – his friend Gresham has confessed his guilt and he will surely be punished. Secondly he is shedding tears of joy in gratitude to God who has amply repaid his honesty. Honesty, Baldwin proves, beyond an iota of doubt, is the best policy

Donovan was also an employee in the same bank where John Gresham and Robert were working. Due to the wreck in the bank Donovan was also a jobless follow. Donovan had been working in the bank for the last eight years. He married when he thought to settle his life. He wanted to spend the rest of his life on the basis of his job in the bank. He was very sad and hopeless because everything had changed. Whatever he had planned earlier had become useless.

दोनोवन भी उसी बैंक का एक कर्मचारी था जहाँ पर जॉन ग्रेशम और राबर्ट कार्य कर रहे थे। परन्तु बैंक में अब आर्थिक विपदा आ गई थी, इस कारण दोनोवन नौकरीहीन व्यक्ति हो गया था। दोनोवन पिछले आठ वर्षों से बैंक में कार्य कर रहा था। जब वह अपना जीवन व्यवस्थित करना चाहता था तो उसने शादी कर ली। वह अपना शेष जीवन बैंक की नौकरी के आधार पर व्यतीत करना चाहता था। वह दु:खी और निराश था क्योंकि सब कुछ बदल गया था। जो कुछ उसने पहले योजना बनाई थी अब वह बेकार हो गई थी।

Their friendship was from their boyhood.

उनकी दोस्ती उनके लड़कपन से थी।

The family members were anxious because Mr. Gresham had called Mr. Robert who was in jail. He was very late also.

परिवार के सदस्यों को चिन्ता थी क्योंकि श्री ग्रेशम ने श्री रॉबर्ट को बुलाया था जो जेल में था। उसे बहुत देर हो गई थी।

The play opens very beautifully with a ne description of the weather which is hot and sultry. We see the Baldwin family anxiously waiting for the return of its head. It obviously shows there is some trouble. Martha, Evie and John are worried why Baldwin has not returned home. Through this opening, the readers are made ready to receive some bad news that will bring in suspense and mystery. 

The play ends settling all the questions that were raised in the beginning and through the events of the story. The good man is rewarded. Marshall, the President of the Third National, a huge prestigious bank comes with an offer of a good position for Baldwin. Baldwin feels happy that he does not have give evidence against his friend Graham as he has confessed his guilt. There is all round happiness. With his new job, the Baldwin family can have better days. Honesty is the best policy.

When Baldwin came to know about the thoughts of his family about the offer he was shaken from his inside. He told the family that it would be dishonourable thing for him to accept this money. Baldwin said to his family that they all knew it very well. These people understand that Robert Baldwin won’t accept the money. He said that they all were liars, thieves and hypocrites. He said that everyone knows that his soul is naked. Doing a bad thing is to stink before the Almighty.

जब बाल्डविन को अपने परिवार के विचारों के बारे में पता चला तो वह अन्दर से हिल गया था। उसने परिवार को कहा कि यह एक असम्माननीय कार्य होगा कि वह पैसे को स्वीकार करे। बाल्डविन ने अपने परिवार से कहा कि वे सब इसे अच्छी तरह से जानते थे। यह लोग जानते थे कि रॉबर्ट बाल्डविन पैसा स्वीकार नहीं करेगा। उसने कहा कि वे सब झूठे, चोर, पाखण्डी थे। उसने कहा कि प्रत्येक व्यक्ति जानता है। कि उसकी आत्मा नग्न है। बुरा कार्य करना भगवान के समक्ष दुर्गन्ध मारने जैसा है।

Robert and John Gresham were good friends. John Gresham gave his name to Robert Baldwin’s son. Gresham wanted to make their friendship memorable. He was very close to Robert at the office. Robert was working under him but after the job they both were good on terms. John Gresham has decided to give his name to the son of Robert Baldwin This is the only reason to name his son John.

रॉबर्ट ऑर जॉन ग्रेशम अच्छे दोस्त थे। जॉन ग्रेशम ने अपना नाम रॉबर्ट बाल्डविन के पुत्र को दिया था। ग्रेशम उनकी दोस्ती को यादगार बनाना चाहता था। वह रॉबर्ट से कार्यालय में भी बहुत निकट था। रॉबर्ट उसके अधीन कार्य कर रहा था परन्तु नौकरी के पश्चात् उनमें अच्छे सम्बन्ध थे। जॉन ग्रेशम ने रॉबर्ट बाल्डविन के पुत्र को अपना नाम देने का निश्चय किया था। यही एकमात्र कारण था कि उसने अपने पुत्र का नाम जॉन रखा था।

Mr. Gresham wanted from Mr. Robert that he should say in the court “I do not remember.”.

श्री ग्रेशम श्री रॉबर्ट से चाहते थे कि वह कोर्ट में केवल यह कह दे कि “मुझे याद नहीं।”

Mr. Robert and Mr. Gresham were friends since their childhood. They worked together.

श्री रॉबर्ट और श्री ग्रेशम बचपन के दोस्त थे। उन्होंने साथ कार्य किया था।

When Robert told the family about the offer they were all surprised over the amount of money. It was a hundred thousand dollars offer. His daughter and son wanted to accept the offer. There were opinions that they could start a business from that money. They all could live a comfortable life. Robert’s wife was also pressurising him. She also wanted her husband to accept the offer. She said when nobody is affected with the wreck, it would be good to accept the money. There were many arguments about all this.

जब रॉबर्ट ने परिवार को धन की पेशकश के बारे में बताया तो उन सबको आश्चर्य हुआ था। यह पेशकश एक सौ हजार डॉलर की थी। उसका पुत्र और पुत्री उसे पेशकश स्वीकार करने का चाहते थे। इस प्रकार की राय भी थी कि वे उस धन से एक व्यापार प्रारम्भ कर सकते थे। वे सभी एक आरामदायक जीवन जी सकते थे। रॉबर्ट की पत्नी भी उस पर दबाव डाल रही थी। वह अपने पति से पेशकश स्वीकार करवाना चाहती थी। उसने कहा कि आर्थिक विपदा से जब कोई भी प्रभावित नहीं हो रहा है तो धन स्वीकार करना अच्छा है। इस सबके बारे में बहुत सारा विवाद हुआ था।

These are the main characters: 

a) Baldwin is the protagonist (hero) of the play. He is a family man who values honesty before anything else. Even a 100,000 bribe for just saying “I don’t remember’ can’t buy him. In spite of pressures from his wife, son and daughter he sticks to his principle. He wants to go to his grave clean! An exceptional man! 

b) Martha is the wife of Baldwin. She is proud of her honest husband. But the bribe of 100,000 dollars to her husband makes her ready to give up her principles. She looks for loopholes to take the money without any guilty feeling: She is a worldly woman who can’t resist the twinkle of money. 

c) John is the 27-year old son of Baldwin and Martha. He earns just 30 dollars a week. Initially he supports the truth. But the lure of money makes him forget his morals. Telling a simple lie for 100,000 dollars is not a sin! 

d) Evie is the daughter of Baldwin and Martha. She is proud of her honest father and loves him dearly. She wants him to stick to the truth. But on hearing about the offer of 100,000 dollars for a small lie, her morality is shaken to the roots. Normal for a young girl from a not-so-rich family

John Gresham was the senior officer in the bank. The crash at the bank had happened at the time. He was the only one responsible person. His assistant Robert was the only one witness. He offered him a large amount to say in his favour. John Gresham was a good man by the ideas. He thought that due to him Robert is in a kind of mental tension. John Gresham confessed his crime at the end. It was the change of his heart that has caused him to do so.

जॉन ग्रेशम बैंक में उच्च अधिकारी था। उस समय बैंक में वित्तीय परेशानी हुई थी। वह एकमात्र जिम्मेदार व्यक्ति था। उसका सहायक रॉबर्ट एकमात्र गवाह था। उसने उसके पक्ष में बोलने के लिए एक बड़ी राशि की पेशकश की थी। जॉन ग्रेशम विचारों में एक अच्छा आदमी था। उसने सोचा कि उसके कारण रॉबर्ट एक प्रकार के मानसिक तनाव में था। अन्त में जॉन ग्रेशम ने अपना अपराध स्वीकार कर लिया था। यह उसके हृदय का परिवर्तन था जिसके कारण इस प्रकार का कार्य उसने किया था।

Mr. Robert thought that when he would say “I do not remember’ in the court, his throat would be choked. He could not tell a lie. He had been living an honest life and now he could not do that.

श्री रॉबर्ट ने सोचा कि वह कोर्ट में “मुझे याद नहीं है” नहीं कह पाएगा। उसका गला जाम हो जाएगा। वह झूठ नहीं बोल सकता था। उसने ईमानदारी का जीवन जिया था और अब उसके लिए ऐसा करना उचित नहीं था।