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वह फल नींबू था।

तिलक के अच्छे कार्यों और विचारों के कारण इनके नाम के साथ लोकमान्य शब्द जुड़ा।

हाँ, अदिति फल को खोज पाई।

स्वतन्त्रता आंदोलन गांधी जी के नेतृत्व में चलाया गया था।

पिता ने सलाह दी कि कोई ऐसा कार्य नहीं करना चाहिए, जिसके कारण लोगों से छिपना पड़े।

महान उद्देश्य की पूर्ति के लिए एक ऐसा महत्त्वपूर्ण समय आता है, जब साधारण पुरुष वीर और स्त्रियाँ वीरांगनाएँ बन जाती हैं।

Yes, Sachin was sorry for his action.

He dug a hole in the ground, put a coin there and covered the hole with soil.

Rohit was in the garden one morning.

कुछ लोग वस्तु के आकार-प्रकार को देखकर उसका मूल्य ऑकते हैं। वास्तव में वस्तु का महत्त्व उसके कद पर निर्भर नहीं होता। रहीमजी हमें यही समझाना चाहते हैं कि बड़ों को देखकर छोटों की अनदेखी नहीं करनी चाहिए। तलवार का आकार बड़ा है। वह युद्ध में बहुत उपयोगी है। उसकी तुलना में सुई बहुत छोटी होती है, फिर भी सुई का काम तलवार नहीं कर सकती। इसलिए हमें छोटों को भी बड़ों के समान ही महत्त्व देना चाहिए ।

We can keep our houses clean by observing the following ways:

• Throwing garbage into the dustbin.
• Washing the floors regularly.
• Keeping the things at the proper places.

1. We should put peel in the dustbin.
2. Meetu was hurt when she fell on the road.
3. Her mother was sad.

बुरी संगत का प्रभाव अच्छे स्वभाव वाले लोगों पर नहीं पड़ता है।

पेड़ फल देकर और नदी पानी बहाकर सबका भला करते हैं। इसी प्रकार सज्जन भी परोपकार करते हैं; अतः पेड़ और नदी से सज्जनों की तुलना की गई है।

मीरा ने कृष्ण के सुंदर रूप का वर्णन किया है।

बार-बार बाल बनाने और गूंथने से श्रीकृष्ण की चोटी नागिन की तरह लंबी और मोटी हो जाएगी।

लोग प्रायः बड़ों को महत्त्व देते हैं। समाज में धनीमानी लोगों को आदर-सम्मान दिया जाता है। गरीबों को लोग उपेक्षा की दृष्टि से देखते हैं। उपयोगिता की दृष्टि में देखें तो गरीब लोगों का काम भी कम महत्त्व का नहीं होता। किसान, मजदूर तथा छोटे काम करनेवाले जो देश की बहुमूल्य सेवा करते हैं, वह ऊंचे तबकेवाले नहीं कर सकते। इसलिए हमें बड़े लोगों को मान देते समय निम्नस्तर के लोगों की उपेक्षा नहीं करनी चाहिए।

रहीम जी कहते हैं कि किसी बड़े व्यक्ति अथवा वस्तु को देखकर हमें छोटे व्यक्ति अथवा वस्तु को छोड़ नहीं देना चाहिए अथवा उसका तिरस्कार नहीं करना चाहिए क्योंकि आवश्यकता के समय जहाँ सुई काम आती है, वहाँ तलवार किसी काम नहीं आती।

सौ बार रूठने पर भी सज्जनों को उसी तरह मना लेना चाहिए, जिस तरह, टूटे हुए हार के मोतियों को बार-बार पिरो लिया जाता है।

रावण के साथ महाशक्ति को देखकर राम को युद्ध में अपनी जीत का भरोसा नहीं रहा था।

बिहारी ने सोने में धतूरे से भी अधिक मादकता बताई है।

The given equations are 

6(ax + by) = 3a + 2b 

⇒6ax + 6by = 3a + 2b ………(i) 

and 6(bx – ay) = 3b – 2a 

⇒6bx – 6ay = 3b – 2a ………(ii) 

On multiplying (i) by a and (ii) by b, we get 

6a²x + 6aby = 3a² + 2ab ……….(iii) 

6b²x - 6aby = 3b² - 2ab ……….(iv) 

On adding (iii) and (iv), we get 

6(a² + b²)x = 3(a² + b²)

x = 3(a²+ b²)/6(a²+b²) = 1/2

On substituting x = 1/2 in (i), we get: 

6a × 1/2 + 6by = 3a + 2b 

6by = 2b 

y = 2b/6b = 1/3 

Hence, the required solution is x = 1/2 and y = 1/3.

As the formula states CP = (100 / (100 – Loss %)) × SP= (100/ (100-4)) × 657.60

= (100/96) × 657.60

=658

∴ The cost price is 658

As the formula states CP = (100 / (100+ Gain %)) × SP= (100/ (100+ (15/2))) × 34.40

= (100/ (215/2)) × 34.40

= (200/215) × 34.40

=32

∴ The cost price is 32

Total Cost of an Iron Safe = Purchase Cost + Transportation

= 12160 + 340

= 12500

Cost Price (CP) of Iron Safe = Rs.12500

Selling Price (SP) of an Iron Safe = Rs.12875

Gain on Sell = SP – CP

= 12875 - 12500 

= 375

Gain Percent = \(Gain\%=\frac{Gain\times100}{CP}\)

\(=\frac{375\times100}{12500}\)

= 3%

So, Gain Percent on Iron Safe is 3%.

Lets solve by using, the total cost of iron safe = purchase cost + transportation

= 12160 + 340 = 12500

CP of iron safe = 12500

SP of iron safe = 12875

Since, SP is more than CP so it’s a gain.

Gain = SP – CP = 12875 – 12500 = 375

Gain % = (Gain × 100) / CP

= (375 × 100) / 12500

= 3%

∴ The Gain percent is 3%

Given Mr. Virmani spent to purchase the house = Rs. 365000

Amount he spent on repair = Rs. 135000

Total amount he spent on the house (CP) = Rs. (365000 + 135000)

= Rs. 500000

Given SP of the house = Rs. 550000

Gain = SP – CP

= Rs. (550000 – 500000)

= Rs. 50000

Gain % = (Gain/CP) x 100

= (50000/500000) x 100

= 5000000/500000

Gain = 10%

From the question,

Sudhir bought an almirah for = ₹ 13600 = cost price

Transportation cost = ₹ 400

The total cost price of almirah = ₹ (13600 + 400)

= ₹ 14000

He sold it for = ₹ 16800 = Selling price

By comparing SP and CP = SP > CP, so there is a gain

Gain = SP – CP

= 16800 – 14000

= ₹ 2800

Gain % = {(gain/CP) × 100}

= {(2800/14000) × 100}

= {2800/140}

= 20%

93x = 12 – 15y 

⇒ 93x + 15y -12 = 0 

⇒ 93x + 15y + (- 12) = 0 

Here a = 93, b = 15 and c = – 12

The given system of equations is: 

x/3 + y/2 = 3 

⇒ 2x+3y/6 = 3 

2x + 3y = 18 

⇒ 2x + 3y – 18 = 0 ….(i)

and 

x – 2y = 2 

x – 2y – 2 = 0 …..(ii) 

These equations are of the forms: 

a₁x+b₁y+c₁ = 0 and a₂x+b₂y+c₂ = 0 

where, a₁ = 2, b₁= 3, c₁ = -18 and a₂ = 1, b₂ = -2, c₂ = -2 

For a unique solution, we must have: 

a₁/a₂ ≠ b₁/b₂ , i.e., 2/1 ≠ 3/−2 

Hence, the given system of equations has a unique solution. 

Again, the given equations are: 

2x + 3y – 18 = 0 …..(iii) 

x – 2y – 2 = 0 …..(iv) 

On multiplying (i) by 2 and (ii) by 3, we get: 

4x + 6y – 36 = 0 …….(v) 

3x - 6y – 6 = 0 ……(vi) 

On adding (v) from (vi), we get: 

7x = 42 

⇒x = 6 

On substituting x = 6 in (iii), we get:

2(6) + 3y = 18 

⇒3y = (18 - 12) = 6 

⇒y = 2 

Hence, x = 6 and y = 2 is the required solution.

8x + 5y – 3 = 0 

⇒ 8x + 5y + (- 3) = 0 

Here a = 8, b = 5 and c = – 3

\(\frac x3 + \frac y4 = 7\)

⇒\(\frac x3 + \frac y4 -7=0\)

 ⇒\(\frac {4x+3y-84}{12} = 0\)

⇒ 4x + 3y – 84 = 0 

Here a = 4, b = 3 and c = – 84

3x + 5y = 12

⇒ 3x + 5y + (- 12) = 0 

Here a = 3, b = 5 and c = – 12

9x- 5y = 10 

⇒ 9x- 5y – 10 = 0 

Here a = 9, b = -5, c = -10

2x = y 

⇒ 2x – y = 0 

Here a = 2, b = – 1 and c = 0

\(\frac x2 - \frac y3-5 =0\)

\(\frac {3x-2y-30}{6} = 0\)

⇒ 3x – 2y – 30 = 0 

Here a = 3, b = – 2 and c = – 30

Appropriate fraction is 0.00001

Appropriate fraction is 500

Correct answer is 1/7

Crrect answer is Greater than

3x + 2y = 9 

⇒ 3x + 2y – 9 = 0 

Here a = 3, b = 2, c = -9

Option : (D)

Distance between the graph of the equations x = -3 and x=2 is 

= 2 – (-3) = 5 units

Option : (B) 

Given, 

(2k - 1,k) is a solution of the equation 10x - 9y = 12 

⇒ 20x – 10 – 9k = 12 

⇒ 11k = 22 

⇒ k = 2

Given that (0, a) and (b, 0) are the solutions of 

3x = 7y – 21 

⇒ 3x – 7y = – 21 

∴ 3(0) – 7(a) = -21 and 3(b) – 7(0) = -21 

⇒ a = -21/-7 and b = -21/3

⇒ a = 3 and b = -7

Appripriate fraction is 3/2

(i) Given equation, 2x = -3 

The above equation can be written in two variables as, 

2x + 0y + 3 = 0 

(ii) Given equation, y = 3 

The above equation can be written in two variables as, 

0x + y – 3 = 0 

(iii) Given equation, 5x = 7/2 

The above equation can be written in two variables as,

5x + 0y – 7/2 = 0 

or 10x + 0y – 7 = 0 

(iv) Given equation, y = 3/2 x 

The above equation can be written in two variables as, 

2y = 3x 

3x – 2y = 0 

3x – 2y + 0 = 0

(i) We have

-2x +3y = 12

-2x +3y -12 = 0

On comparing this equation with ax +by +c = 0 we obtain a = -2, b =3 and c = -12.

(ii) Given that

x - y/2 -5 = 0

1x - y/2 -5 = 0

On comparing this equation with ax +by +c = 0 we obtain a =1, b = 1/2 and c = -5

(iii) Given that

2x + 3y = 9.35 bar

2x +3y - 9.35 bar = 0

On comparing this equation with ax +by +c = 0 we get a = 2, b =3 and c = -9.35 bar

(iv) 3x = -7y

3x +7y +0 = 0

On comparing this equation with ax +by +c = 0 we get a =3, b =7 and c = 0

(v) We have

2x +3 = 0

2x + 0(y) +3 =0

On comparing this equation with ax + by + c = 0 we get a =2, b=0, and c =3

(vi) Given that

y -5 = 0

0x + 1y -5 = 0

On comparing this equation with ax + by +c = 0 we get a =0, b =1 and c = -5

(vii) We have

4 = x

-3x + 0.y +4 = 0

On comparing the equation with ax + by +c = 0 we get a = -3, b = 0 and c =4

(viii) Given that,

y = x/2

2y = x

x -2y +0 =0

On comparing this equation with ax +by +c = 0 we get a =1, b =-2 and c= 0

(i) Given equation, -2x + 3y = 12 

Or – 2x + 3y – 12 = 0 

Comparing the given equation with ax + by + c = 0 

We get, a = – 2; b = 3; c = -12 

(ii) Given equation, x – y/2 – 5 = 0

Comparing the given equation with ax + by + c = 0,

We get, a = 1; b = -1/2, c = -5 

(iii) Given equation, 2x + 3y = 9.35 

or 2x + 3y – 9.35 = 0 

Comparing the given equation with ax + by + c = 0 

We get, a = 2 ; b = 3 ; c = -9.35 

(iv) Given equation, 3x = -7y 

or 3x + 7y = 0

Comparing the given equation with ax+ by + c = 0, 

We get, a = 3 ; b = 7 ; c = 0

(v) Given equation, 2x + 3 = 0 

or 2x + 0y + 3 = 0 

Comparing the given equation with ax + by + c = 0, 

We get, a = 2 ; b = 0 ; c = 3 

(vi) Given equation, y – 5 = 0 

or 0x + y – 5 = 0

Comparing the given equation with ax + by+ c = 0, 

We get, a = 0; b = 1; c = -5 

(vii) Given equation, 4 = 3x 

or 3x + 0y – 4 = 0 

Comparing the given equation with ax + by + c = 0, 

We get, a = 3; b = 0; c = -4 

(viii) Given equation, y = x/2 

Or x – 2y = 0 

Or x – 2y + 0 = 0 

Comparing the given equation with ax + by + c = 0, 

We get, a = 1; b = -2; c = 0

(i) x = 3y

1x − 3y + 0 = 0

Comparing this equation with ax + by + c = 0,

a = 1, b = −3, c = 0

(ii) 2x = −5y

2x + 5y + 0 = 0

Comparing this equation with ax + by + c = 0,

a = 2, b = 5, c = 0

(iii) 3x + 2 = 0

3x + 0.y + 2 = 0

Comparing this equation with ax + by + c = 0,

a = 3, b = 0, c = 2