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कौन सा बहुपद मानक रूप में अवरोही घातों में लिखा गया है?

Which polynomial is written in standard form with descending powers?

Explanation opens after your attempt
Correct Answer

B. \(5x^3+2x-1\)

Step 1

Concept

In standard form, terms are written from highest power to lowest power. \(5x^3+2x-1\) follows this order.

Step 2

Why this answer is correct

The correct answer is B. \(5x^3+2x-1\). In standard form, terms are written from highest power to lowest power. \(5x^3+2x-1\) follows this order.

Step 3

Exam Tip

मानक रूप में बड़ी घात से छोटी घात की ओर लिखते हैं। \(5x^3+2x-1\) इसी क्रम में है।

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निम्न में से कौन सा बहुपद मानक रूप में व्यवस्थित है?

Which of the following polynomials is arranged in standard form?

Explanation opens after your attempt
Correct Answer

A. \(2x^3+x^2+5x+1\)

Step 1

Concept

In standard form, powers are written in descending order. \(2x^3+x^2+5x+1\) follows this order.

Step 2

Why this answer is correct

The correct answer is A. \(2x^3+x^2+5x+1\). In standard form, powers are written in descending order. \(2x^3+x^2+5x+1\) follows this order.

Step 3

Exam Tip

मानक रूप में घातें घटते क्रम में लिखी जाती हैं। \(2x^3+x^2+5x+1\) में यही क्रम है।

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यदि ((x-7)(x-15)=26), तो मानक द्विघात समीकरण क्या होगा?

If ((x-7)(x-15)=26), what is the standard quadratic equation?

Explanation opens after your attempt
Correct Answer

A. \(x^2-22x+79=0\)

Step 1

Concept

((x-7)(x-15)=x-2-22x+105), so \(x^2-22x+105=26\) gives \(x^2-22x+79=0\). In exams, bring all terms to one side after expansion.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-22x+79=0\). ((x-7)(x-15)=x-2-22x+105), so \(x^2-22x+105=26\) gives \(x^2-22x+79=0\). In exams, bring all terms to one side after expansion.

Step 3

Exam Tip

((x-7)(x-15)=x-2-22x+105), इसलिए \(x^2-22x+105=26\) से \(x^2-22x+79=0\) मिलता है। परीक्षा में विस्तार के बाद सभी पद एक तरफ लाएं।

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यदि ((x-6)(x-13)=22), तो मानक द्विघात समीकरण क्या होगा?

If ((x-6)(x-13)=22), what is the standard quadratic equation?

Explanation opens after your attempt
Correct Answer

A. \(x^2-19x+56=0\)

Step 1

Concept

((x-6)(x-13)=x-2-19x+78), so \(x^2-19x+78=22\) gives \(x^2-19x+56=0\). In exams, bring all terms to one side after expansion.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-19x+56=0\). ((x-6)(x-13)=x-2-19x+78), so \(x^2-19x+78=22\) gives \(x^2-19x+56=0\). In exams, bring all terms to one side after expansion.

Step 3

Exam Tip

((x-6)(x-13)=x-2-19x+78), इसलिए \(x^2-19x+78=22\) से \(x^2-19x+56=0\) मिलता है। परीक्षा में विस्तार के बाद सभी पद एक तरफ लाएं।

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यदि ((x-5)(x-11)=18), तो मानक द्विघात समीकरण क्या होगा?

If ((x-5)(x-11)=18), what is the standard quadratic equation?

Explanation opens after your attempt
Correct Answer

A. \(x^2-16x+37=0\)

Step 1

Concept

((x-5)(x-11)=x-2-16x+55), so \(x^2-16x+55=18\) gives \(x^2-16x+37=0\). In exams, bring all terms to one side after expansion.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-16x+37=0\). ((x-5)(x-11)=x-2-16x+55), so \(x^2-16x+55=18\) gives \(x^2-16x+37=0\). In exams, bring all terms to one side after expansion.

Step 3

Exam Tip

((x-5)(x-11)=x-2-16x+55), इसलिए \(x^2-16x+55=18\) से \(x^2-16x+37=0\) मिलता है। परीक्षा में विस्तार के बाद सभी पद एक तरफ लाएं।

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यदि ((x-4)(x-9)=14), तो मानक द्विघात समीकरण क्या होगा?

If ((x-4)(x-9)=14), what is the standard quadratic equation?

Explanation opens after your attempt
Correct Answer

A. \(x^2-13x+22=0\)

Step 1

Concept

((x-4)(x-9)=x-2-13x+36), so \(x^2-13x+36=14\) gives \(x^2-13x+22=0\). In exams, bring all terms to one side after expansion.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-13x+22=0\). ((x-4)(x-9)=x-2-13x+36), so \(x^2-13x+36=14\) gives \(x^2-13x+22=0\). In exams, bring all terms to one side after expansion.

Step 3

Exam Tip

((x-4)(x-9)=x-2-13x+36), इसलिए \(x^2-13x+36=14\) से \(x^2-13x+22=0\) मिलता है। परीक्षा में विस्तार के बाद सभी पद एक तरफ लाएं।

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यदि ((x-3)(x-7)=10), तो मानक द्विघात समीकरण क्या होगा?

If ((x-3)(x-7)=10), what is the standard quadratic equation?

Explanation opens after your attempt
Correct Answer

A. \(x^2-10x+11=0\)

Step 1

Concept

((x-3)(x-7)=x-2-10x+21), so \(x^2-10x+21=10\) gives \(x^2-10x+11=0\). In exams, bring all terms to one side after expansion.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-10x+11=0\). ((x-3)(x-7)=x-2-10x+21), so \(x^2-10x+21=10\) gives \(x^2-10x+11=0\). In exams, bring all terms to one side after expansion.

Step 3

Exam Tip

((x-3)(x-7)=x-2-10x+21), इसलिए \(x^2-10x+21=10\) से \(x^2-10x+11=0\) मिलता है। परीक्षा में विस्तार के बाद सभी पद एक तरफ लाएं।

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यदि ((x-2)(x-5)=6), तो मानक द्विघात समीकरण क्या होगा?

If ((x-2)(x-5)=6), what is the standard quadratic equation?

Explanation opens after your attempt
Correct Answer

A. \(x^2-7x+4=0\)

Step 1

Concept

((x-2)(x-5)=x-2-7x+10), so \(x^2-7x+10=6\) gives \(x^2-7x+4=0\). In exams, bring all terms to one side after expansion.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-7x+4=0\). ((x-2)(x-5)=x-2-7x+10), so \(x^2-7x+10=6\) gives \(x^2-7x+4=0\). In exams, bring all terms to one side after expansion.

Step 3

Exam Tip

((x-2)(x-5)=x-2-7x+10), इसलिए \(x^2-7x+10=6\) से \(x^2-7x+4=0\) मिलता है। परीक्षा में विस्तार के बाद सभी पद एक तरफ लाएं।

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\(3x^2+2=11x\) को मानक रूप में लिखने पर क्या मिलेगा?

What is obtained when \(3x^2+2=11x\) is written in standard form?

Explanation opens after your attempt
Correct Answer

A. \(3x^2-11x+2=0\)

Step 1

Concept

Bringing (11x) to the left gives \(3x^2-11x+2=0\). In exams, bring all terms to one side.

Step 2

Why this answer is correct

The correct answer is A. \(3x^2-11x+2=0\). Bringing (11x) to the left gives \(3x^2-11x+2=0\). In exams, bring all terms to one side.

Step 3

Exam Tip

(11x) को बाईं ओर लाने पर \(3x^2-11x+2=0\) बनता है। परीक्षा में सभी पदों को एक तरफ लाएं।

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यदि \(5x^2+9x=2\) है, तो मानक रूप में समीकरण क्या होगा?

If \(5x^2+9x=2\), what will be the equation in standard form?

Explanation opens after your attempt
Correct Answer

A. \(5x^2+9x-2=0\)

Step 1

Concept

Bringing (2) to the left gives \(5x^2+9x-2=0\). In exams, make standard form before solving.

Step 2

Why this answer is correct

The correct answer is A. \(5x^2+9x-2=0\). Bringing (2) to the left gives \(5x^2+9x-2=0\). In exams, make standard form before solving.

Step 3

Exam Tip

(2) को बाईं ओर लाने पर \(5x^2+9x-2=0\) मिलता है। परीक्षा में हल करने से पहले मानक रूप बनाएं।

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\(2x^2+1=7x\) को मानक रूप में लिखने पर क्या मिलेगा?

What is obtained when \(2x^2+1=7x\) is written in standard form?

Explanation opens after your attempt
Correct Answer

A. \(2x^2-7x+1=0\)

Step 1

Concept

Bringing (7x) to the left gives \(2x^2-7x+1=0\). In exams, bring all terms to one side.

Step 2

Why this answer is correct

The correct answer is A. \(2x^2-7x+1=0\). Bringing (7x) to the left gives \(2x^2-7x+1=0\). In exams, bring all terms to one side.

Step 3

Exam Tip

(7x) को बाईं ओर लाने पर \(2x^2-7x+1=0\) बनता है। परीक्षा में सभी पदों को एक तरफ लाएं।

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यदि \(3x^2+7x=6\) है, तो मानक रूप में समीकरण क्या होगा?

If \(3x^2+7x=6\), what will be the equation in standard form?

Explanation opens after your attempt
Correct Answer

A. \(3x^2+7x-6=0\)

Step 1

Concept

Bringing (6) to the left gives \(3x^2+7x-6=0\). In exams, make standard form before applying any method.

Step 2

Why this answer is correct

The correct answer is A. \(3x^2+7x-6=0\). Bringing (6) to the left gives \(3x^2+7x-6=0\). In exams, make standard form before applying any method.

Step 3

Exam Tip

(6) को बाईं ओर लाने पर \(3x^2+7x-6=0\) मिलता है। परीक्षा में सूत्र लगाने से पहले मानक रूप बनाएं।

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\(4x^2-1=8x\) को मानक रूप में लिखने पर क्या मिलेगा?

What is obtained when \(4x^2-1=8x\) is written in standard form?

Explanation opens after your attempt
Correct Answer

A. \(4x^2-8x-1=0\)

Step 1

Concept

Bringing (8x) to the left gives \(4x^2-8x-1=0\). In exams, do not miss any term while making standard form.

Step 2

Why this answer is correct

The correct answer is A. \(4x^2-8x-1=0\). Bringing (8x) to the left gives \(4x^2-8x-1=0\). In exams, do not miss any term while making standard form.

Step 3

Exam Tip

(8x) को बाईं तरफ लाने पर \(4x^2-8x-1=0\) बनता है। परीक्षा में मानक रूप बनाने से पहले कोई पद न छोड़ें।

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यदि \(2x^2+5x=3\) है, तो मानक रूप \(ax^2+bx+c=0\) में (a,b,c) क्या हैं?

If \(2x^2+5x=3\), what are (a,b,c) in standard form \(ax^2+bx+c=0\)?

Explanation opens after your attempt
Correct Answer

A. (a=2,b=5,c=-3)

Step 1

Concept

The standard form is \(2x^2+5x-3=0\), so (a=2,b=5,c=-3). In exams, bring all terms to one side first.

Step 2

Why this answer is correct

The correct answer is A. (a=2,b=5,c=-3). The standard form is \(2x^2+5x-3=0\), so (a=2,b=5,c=-3). In exams, bring all terms to one side first.

Step 3

Exam Tip

मानक रूप \(2x^2+5x-3=0\) है, इसलिए (a=2,b=5,c=-3) हैं। परीक्षा में सभी पदों को पहले एक तरफ लाएं।

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समीकरण \(\frac{x+3}{x-2}+\frac{x-2}{x+3}=\frac{13}{6}\) का मानक द्विघात रूप कौन-सा है?

What is the standard quadratic form of \(\frac{x+3}{x-2}+\frac{x-2}{x+3}=\frac{13}{6}\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2+x-156=0\)

Step 1

Concept

After clearing denominators, (6{(x+3)2+(x-2)2}=13(x+3)(x-2)). Simplifying gives the correct form \(x^2+x-156=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+x-156=0\). After clearing denominators, (6{(x+3)2+(x-2)2}=13(x+3)(x-2)). Simplifying gives the correct form \(x^2+x-156=0\).

Step 3

Exam Tip

हर हटाने पर (6{(x+3)2+(x-2)2}=13(x+3)(x-2)) मिलता है। सरल करने पर \(x^2+x-156=0\) सही रूप है।

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समीकरण ((x+6)2+(x-7)2=(x+3)2) का मानक रूप कौन-सा है?

What is the standard form of ((x+6)2+(x-7)2=(x+3)2)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-14x+76=0\)

Step 1

Concept

Expanding gives left side \(2x^2-2x+85\) and right side \(x^2+6x+9\). Subtracting gives \(x^2-8x+76=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-14x+76=0\). Expanding gives left side \(2x^2-2x+85\) and right side \(x^2+6x+9\). Subtracting gives \(x^2-8x+76=0\).

Step 3

Exam Tip

विस्तार करने पर बाईं ओर \(2x^2-2x+85\) और दाईं ओर \(x^2+6x+9\) है। घटाने पर \(x^2-8x+76=0\) नहीं बल्कि \(x^2-8x+76=0\) मिलता है।

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समीकरण ((x+5)(x+8)+(x-4)(x+7)=110) का मानक रूप कौन-सा है?

What is the standard form of ((x+5)(x+8)+(x-4)(x+7)=110)?

Explanation opens after your attempt
Correct Answer

A. \(2x^2+16x-98=0\)

Step 1

Concept

The left side is \(x^2+13x+40+x^2+3x-28=2x^2+16x+12\). Subtracting (110) gives \(2x^2+16x-98=0\).

Step 2

Why this answer is correct

The correct answer is A. \(2x^2+16x-98=0\). The left side is \(x^2+13x+40+x^2+3x-28=2x^2+16x+12\). Subtracting (110) gives \(2x^2+16x-98=0\).

Step 3

Exam Tip

बाईं ओर \(x^2+13x+40+x^2+3x-28=2x^2+16x+12\) है। (110) घटाने पर \(2x^2+16x-98=0\) मिलता है।

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समीकरण \(\frac{4x^2-3}{5}+\frac{x-2}{4}=3\) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?

What is the standard form with integer coefficients of \(\frac{4x^2-3}{5}+\frac{x-2}{4}=3\)?

Explanation opens after your attempt
Correct Answer

A. \(16x^2+5x-74=0\)

Step 1

Concept

Multiplying the whole equation by (20) gives \(16x^2-12+5x-10=60\). Therefore the standard form is \(16x^2+5x-82=0\).

Step 2

Why this answer is correct

The correct answer is A. \(16x^2+5x-74=0\). Multiplying the whole equation by (20) gives \(16x^2-12+5x-10=60\). Therefore the standard form is \(16x^2+5x-82=0\).

Step 3

Exam Tip

पूरे समीकरण को (20) से गुणा करने पर \(16x^2-12+5x-10=60\) मिलता है। इसलिए \(16x^2+5x-82=0\) नहीं बल्कि \(16x^2+5x-82=0\) मिलेगा।

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समीकरण ((4x-3)(x+5)=2(3x-1)) का मानक द्विघात रूप कौन-सा है?

What is the standard quadratic form of ((4x-3)(x+5)=2(3x-1))?

Explanation opens after your attempt
Correct Answer

A. \(4x^2+11x-13=0\)

Step 1

Concept

Here ((4x-3)(x+5)=4x-2+17x-15) and (2(3x-1)=6x-2). Bringing all terms to one side gives \(4x^2+11x-13=0\).

Step 2

Why this answer is correct

The correct answer is A. \(4x^2+11x-13=0\). Here ((4x-3)(x+5)=4x-2+17x-15) and (2(3x-1)=6x-2). Bringing all terms to one side gives \(4x^2+11x-13=0\).

Step 3

Exam Tip

((4x-3)(x+5)=4x-2+17x-15) और (2(3x-1)=6x-2) है। सभी पद एक ओर लाने पर \(4x^2+11x-13=0\) मिलता है।

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समीकरण \(\frac{x+2}{x-1}+\frac{x-1}{x+2}=\frac{5}{2}\) का मानक द्विघात रूप कौन-सा है?

What is the standard quadratic form of \(\frac{x+2}{x-1}+\frac{x-1}{x+2}=\frac{5}{2}\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2+x-20=0\)

Step 1

Concept

After clearing denominators, (2(x+2)2+2(x-1)2=5(x-1)(x+2)). Simplifying gives the correct form \(x^2+x-20=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+x-20=0\). After clearing denominators, (2(x+2)2+2(x-1)2=5(x-1)(x+2)). Simplifying gives the correct form \(x^2+x-20=0\).

Step 3

Exam Tip

हर हटाने पर (2(x+2)2+2(x-1)2=5(x-1)(x+2)) मिलता है। सरल करने पर \(x^2+x-20=0\) सही रूप है।

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समीकरण ((x+5)2+(x-6)2=(x+2)2) का मानक रूप कौन-सा है?

What is the standard form of ((x+5)2+(x-6)2=(x+2)2)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-10x+57=0\)

Step 1

Concept

Expanding gives left side \(2x^2-2x+61\) and right side \(x^2+4x+4\). Subtracting gives \(x^2-6x+57=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-10x+57=0\). Expanding gives left side \(2x^2-2x+61\) and right side \(x^2+4x+4\). Subtracting gives \(x^2-6x+57=0\).

Step 3

Exam Tip

विस्तार करने पर बाईं ओर \(2x^2-2x+61\) और दाईं ओर \(x^2+4x+4\) है। घटाने पर \(x^2-6x+57=0\) नहीं बल्कि \(x^2-6x+57=0\) मिलता है।

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समीकरण ((x+4)(x+7)+(x-3)(x+6)=88) का मानक रूप कौन-सा है?

What is the standard form of ((x+4)(x+7)+(x-3)(x+6)=88)?

Explanation opens after your attempt
Correct Answer

A. \(2x^2+14x-78=0\)

Step 1

Concept

The left side is \(x^2+11x+28+x^2+3x-18=2x^2+14x+10\). Subtracting (88) gives \(2x^2+14x-78=0\).

Step 2

Why this answer is correct

The correct answer is A. \(2x^2+14x-78=0\). The left side is \(x^2+11x+28+x^2+3x-18=2x^2+14x+10\). Subtracting (88) gives \(2x^2+14x-78=0\).

Step 3

Exam Tip

बाईं ओर \(x^2+11x+28+x^2+3x-18=2x^2+14x+10\) है। (88) घटाने पर \(2x^2+14x-78=0\) मिलता है।

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समीकरण \(\frac{3x^2+2}{4}-\frac{x-5}{3}=6\) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?

What is the standard form with integer coefficients of \(\frac{3x^2+2}{4}-\frac{x-5}{3}=6\)?

Explanation opens after your attempt
Correct Answer

A. \(9x^2-4x-42=0\)

Step 1

Concept

Multiplying the whole equation by (12) gives \(9x^2+6-4x+20=72\). Therefore the standard form is \(9x^2-4x-46=0\).

Step 2

Why this answer is correct

The correct answer is A. \(9x^2-4x-42=0\). Multiplying the whole equation by (12) gives \(9x^2+6-4x+20=72\). Therefore the standard form is \(9x^2-4x-46=0\).

Step 3

Exam Tip

पूरे समीकरण को (12) से गुणा करने पर \(9x^2+6-4x+20=72\) मिलता है। इसलिए मानक रूप \(9x^2-4x-46=0\) नहीं बल्कि \(9x^2-4x-46=0\) होगा।

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समीकरण ((3x-2)(2x+5)=4(x+1)) का मानक द्विघात रूप कौन-सा है?

What is the standard quadratic form of ((3x-2)(2x+5)=4(x+1))?

Explanation opens after your attempt
Correct Answer

A. \(6x^2+7x-14=0\)

Step 1

Concept

Here ((3x-2)(2x+5)=6x-2+11x-10) and (4(x+1)=4x+4). Bringing all terms to one side gives \(6x^2+7x-14=0\).

Step 2

Why this answer is correct

The correct answer is A. \(6x^2+7x-14=0\). Here ((3x-2)(2x+5)=6x-2+11x-10) and (4(x+1)=4x+4). Bringing all terms to one side gives \(6x^2+7x-14=0\).

Step 3

Exam Tip

((3x-2)(2x+5)=6x-2+11x-10) और (4(x+1)=4x+4) है। सभी पद एक ओर लाने पर \(6x^2+7x-14=0\) मिलता है।

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समीकरण (\frac{(x+1)2}{2}+\frac{(x-3)2}{3}=10) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?

What is the standard form with integer coefficients of (\frac{(x+1)2}{2}+\frac{(x-3)2}{3}=10)?

Explanation opens after your attempt
Correct Answer

A. \(5x^2-6x-39=0\)

Step 1

Concept

Multiplying the whole equation by (6) gives (3(x+1)2+2(x-3)2=60). Simplifying gives the correct form \(5x^2-6x-39=0\).

Step 2

Why this answer is correct

The correct answer is A. \(5x^2-6x-39=0\). Multiplying the whole equation by (6) gives (3(x+1)2+2(x-3)2=60). Simplifying gives the correct form \(5x^2-6x-39=0\).

Step 3

Exam Tip

पूरे समीकरण को (6) से गुणा करने पर (3(x+1)2+2(x-3)2=60) मिलता है। सरल करने पर \(5x^2-6x-39=0\) सही रूप है।

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समीकरण ((x-3)2+(x+4)2=(x-1)2) का मानक रूप कौन-सा है?

What is the standard form of ((x-3)2+(x+4)2=(x-1)2)?

Explanation opens after your attempt
Correct Answer

A. \(x^2+4x+24=0\)

Step 1

Concept

Expanding gives left side \(2x^2+2x+25\) and right side \(x^2-2x+1\). Subtracting gives \(x^2+4x+24=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+4x+24=0\). Expanding gives left side \(2x^2+2x+25\) and right side \(x^2-2x+1\). Subtracting gives \(x^2+4x+24=0\).

Step 3

Exam Tip

विस्तार करने पर बाईं ओर \(2x^2+2x+25\) और दाईं ओर \(x^2-2x+1\) है। घटाने पर \(x^2+4x+24=0\) मिलता है।

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समीकरण ((x+3)(x+6)+(x-2)(x+5)=70) का मानक रूप कौन-सा है?

What is the standard form of ((x+3)(x+6)+(x-2)(x+5)=70)?

Explanation opens after your attempt
Correct Answer

A. \(2x^2+12x-62=0\)

Step 1

Concept

The left side is \(x^2+9x+18+x^2+3x-10=2x^2+12x+8\). Subtracting (70) gives \(2x^2+12x-62=0\).

Step 2

Why this answer is correct

The correct answer is A. \(2x^2+12x-62=0\). The left side is \(x^2+9x+18+x^2+3x-10=2x^2+12x+8\). Subtracting (70) gives \(2x^2+12x-62=0\).

Step 3

Exam Tip

बाईं ओर \(x^2+9x+18+x^2+3x-10=2x^2+12x+8\) है। (70) घटाने पर \(2x^2+12x-62=0\) मिलता है।

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समीकरण \(\frac{2x^2-1}{5}+\frac{x+3}{2}=7\) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?

What is the standard form with integer coefficients of \(\frac{2x^2-1}{5}+\frac{x+3}{2}=7\)?

Explanation opens after your attempt
Correct Answer

A. \(4x^2+5x-59=0\)

Step 1

Concept

Multiplying the whole equation by (10) gives \(4x^2-2+5x+15=70\). Therefore the standard form is \(4x^2+5x-57=0\).

Step 2

Why this answer is correct

The correct answer is A. \(4x^2+5x-59=0\). Multiplying the whole equation by (10) gives \(4x^2-2+5x+15=70\). Therefore the standard form is \(4x^2+5x-57=0\).

Step 3

Exam Tip

पूरे समीकरण को (10) से गुणा करने पर \(4x^2-2+5x+15=70\) मिलता है। इसलिए \(4x^2+5x-57=0\) नहीं बल्कि \(4x^2+5x-57=0\) मिलेगा।

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समीकरण ((2x+5)(3x-4)=4(x-1)) का मानक द्विघात रूप कौन-सा है?

What is the standard quadratic form of ((2x+5)(3x-4)=4(x-1))?

Explanation opens after your attempt
Correct Answer

A. \(6x^2+7x-16=0\)

Step 1

Concept

Here ((2x+5)(3x-4)=6x-2+7x-20) and (4(x-1)=4x-4). Bringing all terms to one side gives \(6x^2+3x-16=0\).

Step 2

Why this answer is correct

The correct answer is A. \(6x^2+7x-16=0\). Here ((2x+5)(3x-4)=6x-2+7x-20) and (4(x-1)=4x-4). Bringing all terms to one side gives \(6x^2+3x-16=0\).

Step 3

Exam Tip

((2x+5)(3x-4)=6x-2+7x-20) और (4(x-1)=4x-4) है। सभी पद एक ओर लाने पर \(6x^2+3x-16=0\) नहीं बल्कि सही रूप \(6x^2+3x-16=0\) मिलता है।

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समीकरण ((x-2)(x+3)+(2x-1)(x-4)=0) का मानक रूप कौन-सा है?

What is the standard form of ((x-2)(x+3)+(2x-1)(x-4)=0)?

Explanation opens after your attempt
Correct Answer

A. \(3x^2-8x-2=0\)

Step 1

Concept

Here ((x-2)(x+3)=x-2+x-6) and ((2x-1)(x-4)=2x-2-9x+4). Adding them gives \(3x^2-8x-2=0\).

Step 2

Why this answer is correct

The correct answer is A. \(3x^2-8x-2=0\). Here ((x-2)(x+3)=x-2+x-6) and ((2x-1)(x-4)=2x-2-9x+4). Adding them gives \(3x^2-8x-2=0\).

Step 3

Exam Tip

((x-2)(x+3)=x-2+x-6) और ((2x-1)(x-4)=2x-2-9x+4) है। जोड़ने पर \(3x^2-8x-2=0\) मिलता है।

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समीकरण ((x+2)2+(x-5)2=(x+1)2) का मानक रूप कौन-सा है?

What is the standard form of ((x+2)2+(x-5)2=(x+1)2)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-8x+28=0\)

Step 1

Concept

Expanding gives left side \(2x^2-6x+29\) and right side \(x^2+2x+1\). Subtracting gives \(x^2-8x+28=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-8x+28=0\). Expanding gives left side \(2x^2-6x+29\) and right side \(x^2+2x+1\). Subtracting gives \(x^2-8x+28=0\).

Step 3

Exam Tip

विस्तार करने पर बाईं ओर \(2x^2-6x+29\) और दाईं ओर \(x^2+2x+1\) है। घटाने पर \(x^2-8x+28=0\) मिलता है।

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समीकरण ((x+2)(x+5)+(x-1)(x+4)=60) का मानक रूप कौन-सा है?

What is the standard form of ((x+2)(x+5)+(x-1)(x+4)=60)?

Explanation opens after your attempt
Correct Answer

A. \(2x^2+10x-54=0\)

Step 1

Concept

The left side is \(x^2+7x+10+x^2+3x-4=2x^2+10x+6\). Subtracting (60) gives \(2x^2+10x-54=0\).

Step 2

Why this answer is correct

The correct answer is A. \(2x^2+10x-54=0\). The left side is \(x^2+7x+10+x^2+3x-4=2x^2+10x+6\). Subtracting (60) gives \(2x^2+10x-54=0\).

Step 3

Exam Tip

बाईं ओर \(x^2+7x+10+x^2+3x-4=2x^2+10x+6\) है। (60) घटाने पर \(2x^2+10x-54=0\) मिलता है।

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समीकरण \(\frac{x^2+1}{3}-\frac{x-2}{2}=5\) को पूर्णांक गुणांकों वाले मानक रूप में लिखिए।

Write \(\frac{x^2+1}{3}-\frac{x-2}{2}=5\) in standard form with integer coefficients.

Explanation opens after your attempt
Correct Answer

A. \(2x^2-3x-22=0\)

Step 1

Concept

Multiplying the whole equation by (6) gives \(2x^2+2-3x+6=30\). Therefore the standard form is \(2x^2-3x-22=0\).

Step 2

Why this answer is correct

The correct answer is A. \(2x^2-3x-22=0\). Multiplying the whole equation by (6) gives \(2x^2+2-3x+6=30\). Therefore the standard form is \(2x^2-3x-22=0\).

Step 3

Exam Tip

पूरे समीकरण को (6) से गुणा करने पर \(2x^2+2-3x+6=30\) मिलता है। इसलिए मानक रूप \(2x^2-3x-22=0\) है।

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समीकरण ((6x+1)(x-4)=5x) का मानक द्विघात रूप कौन-सा है?

What is the standard quadratic form of ((6x+1)(x-4)=5x)?

Explanation opens after your attempt
Correct Answer

A. \(6x^2-28x-4=0\)

Step 1

Concept

Here ((6x+1)(x-4)=6x-2-23x-4), and subtracting (5x) gives \(6x^2-28x-4=0\). First expand and then bring all terms to one side.

Step 2

Why this answer is correct

The correct answer is A. \(6x^2-28x-4=0\). Here ((6x+1)(x-4)=6x-2-23x-4), and subtracting (5x) gives \(6x^2-28x-4=0\). First expand and then bring all terms to one side.

Step 3

Exam Tip

((6x+1)(x-4)=6x-2-23x-4) है और (5x) घटाने पर \(6x^2-28x-4=0\) मिलता है। पहले विस्तार करें फिर सभी पद एक ओर लाएं।

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समीकरण ((x-1)2+(x-2)2=(x-3)2) का मानक रूप कौन-सा है?

What is the standard form of ((x-1)2+(x-2)2=(x-3)2)?

Explanation opens after your attempt
Correct Answer

B. \(x^2-2x-4=0\)

Step 1

Concept

Expanding gives left side \(2x^2-6x+5\) and right side \(x^2-6x+9\). Subtracting gives \(x^2-4=0\).

Step 2

Why this answer is correct

The correct answer is B. \(x^2-2x-4=0\). Expanding gives left side \(2x^2-6x+5\) and right side \(x^2-6x+9\). Subtracting gives \(x^2-4=0\).

Step 3

Exam Tip

विस्तार करने पर बाईं ओर \(2x^2-6x+5\) और दाईं ओर \(x^2-6x+9\) है। घटाने पर \(x^2-4=0\) नहीं बल्कि \(x^2-4=0\) मिलता है।

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समीकरण ((x+1)(x+2)+(x+3)(x+4)=50) का मानक रूप कौन-सा है?

What is the standard form of ((x+1)(x+2)+(x+3)(x+4)=50)?

Explanation opens after your attempt
Correct Answer

A. \(2x^2+10x-36=0\)

Step 1

Concept

The left side is \(x^2+3x+2+x^2+7x+12=2x^2+10x+14\). Subtracting (50) gives \(2x^2+10x-36=0\).

Step 2

Why this answer is correct

The correct answer is A. \(2x^2+10x-36=0\). The left side is \(x^2+3x+2+x^2+7x+12=2x^2+10x+14\). Subtracting (50) gives \(2x^2+10x-36=0\).

Step 3

Exam Tip

बाईं ओर \(x^2+3x+2+x^2+7x+12=2x^2+10x+14\) है। (50) घटाने पर \(2x^2+10x-36=0\) मिलता है।

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समीकरण \(\frac{x^2-3}{2}+\frac{x-1}{3}=4\) को पूर्णांक गुणांकों वाले मानक रूप में लिखिए।

Write \(\frac{x^2-3}{2}+\frac{x-1}{3}=4\) in standard form with integer coefficients.

Explanation opens after your attempt
Correct Answer

A. \(3x^2+2x-29=0\)

Step 1

Concept

Multiplying the whole equation by (6) gives \(3x^2-9+2x-2=24\). Thus the standard form is \(3x^2+2x-35=0\).

Step 2

Why this answer is correct

The correct answer is A. \(3x^2+2x-29=0\). Multiplying the whole equation by (6) gives \(3x^2-9+2x-2=24\). Thus the standard form is \(3x^2+2x-35=0\).

Step 3

Exam Tip

पूरे समीकरण को (6) से गुणा करने पर \(3x^2-9+2x-2=24\) मिलता है। इसलिए \(3x^2+2x-35=0\) नहीं बल्कि सही रूप \(3x^2+2x-35=0\) होगा।

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समीकरण ((5x-2)(2x+3)=7x) का मानक द्विघात रूप कौन-सा है?

What is the standard quadratic form of ((5x-2)(2x+3)=7x)?

Explanation opens after your attempt
Correct Answer

A. \(10x^2+4x-6=0\)

Step 1

Concept

Here ((5x-2)(2x+3)=10x-2+11x-6) and subtracting (7x) gives \(10x^2+4x-6=0\). First expand and then bring all terms to one side.

Step 2

Why this answer is correct

The correct answer is A. \(10x^2+4x-6=0\). Here ((5x-2)(2x+3)=10x-2+11x-6) and subtracting (7x) gives \(10x^2+4x-6=0\). First expand and then bring all terms to one side.

Step 3

Exam Tip

((5x-2)(2x+3)=10x-2+11x-6) है और (7x) घटाने पर \(10x^2+4x-6=0\) मिलता है। पहले विस्तार करें फिर सभी पद एक ओर लाएं।

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समीकरण ((3x+4)2=7x+16) का मानक रूप कौन-सा है?

What is the standard form of ((3x+4)2=7x+16)?

Explanation opens after your attempt
Correct Answer

A. \(9x^2+17x=0\)

Step 1

Concept

((3x+4)2=9x-2+24x+16). Subtracting (7x+16) gives \(9x^2+17x=0\).

Step 2

Why this answer is correct

The correct answer is A. \(9x^2+17x=0\). ((3x+4)2=9x-2+24x+16). Subtracting (7x+16) gives \(9x^2+17x=0\).

Step 3

Exam Tip

((3x+4)2=9x-2+24x+16) है। (7x+16) घटाने पर \(9x^2+17x=0\) मिलता है।

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समीकरण ((x-4)(x+9)=5x) का मानक रूप क्या है?

What is the standard form of ((x-4)(x+9)=5x)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-36=0\)

Step 1

Concept

The left side gives \(x^2+5x-36\). Subtracting (5x) gives \(x^2-36=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-36=0\). The left side gives \(x^2+5x-36\). Subtracting (5x) gives \(x^2-36=0\).

Step 3

Exam Tip

बाईं ओर \(x^2+5x-36\) मिलता है। (5x) घटाने पर \(x^2-36=0\) बनता है।

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समीकरण ((x-6)2=4x+5) का मानक रूप कौन-सा है?

What is the standard form of ((x-6)2=4x+5)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-16x+31=0\)

Step 1

Concept

((x-6)2=x-2-12x+36). Subtracting (4x+5) gives \(x^2-16x+31=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-16x+31=0\). ((x-6)2=x-2-12x+36). Subtracting (4x+5) gives \(x^2-16x+31=0\).

Step 3

Exam Tip

((x-6)2=x-2-12x+36) है। (4x+5) को घटाने पर \(x^2-16x+31=0\) मिलता है।

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समीकरण ((4x-1)(x+3)=0) का मानक द्विघात रूप कौन-सा है?

What is the standard quadratic form of ((4x-1)(x+3)=0)?

Explanation opens after your attempt
Correct Answer

A. \(4x^2+11x-3=0\)

Step 1

Concept

Expanding ((4x-1)(x+3)) gives \(4x^2+12x-x-3\). So the standard form is \(4x^2+11x-3=0\).

Step 2

Why this answer is correct

The correct answer is A. \(4x^2+11x-3=0\). Expanding ((4x-1)(x+3)) gives \(4x^2+12x-x-3\). So the standard form is \(4x^2+11x-3=0\).

Step 3

Exam Tip

((4x-1)(x+3)) को फैलाने पर \(4x^2+12x-x-3\) मिलता है। इसलिए मानक रूप \(4x^2+11x-3=0\) है।

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समीकरण ((2x-1)2=3x+5) का मानक रूप कौन-सा है?

What is the standard form of ((2x-1)2=3x+5)?

Explanation opens after your attempt
Correct Answer

A. \(4x^2-7x-4=0\)

Step 1

Concept

Here ((2x-1)2=4x-2-4x+1), and bringing all terms to one side gives \(4x^2-7x-4=0\). Apply the square identity and signs carefully.

Step 2

Why this answer is correct

The correct answer is A. \(4x^2-7x-4=0\). Here ((2x-1)2=4x-2-4x+1), and bringing all terms to one side gives \(4x^2-7x-4=0\). Apply the square identity and signs carefully.

Step 3

Exam Tip

((2x-1)2=4x-2-4x+1) है और सभी पद एक ओर लाने पर \(4x^2-7x-4=0\) मिलता है। वर्ग सूत्र और चिन्ह दोनों ध्यान से लगाएं।

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समीकरण ((x+2)(x-7)=3x) का मानक रूप क्या है?

What is the standard form of ((x+2)(x-7)=3x)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-8x-14=0\)

Step 1

Concept

The left side gives \(x^2-5x-14\). Subtracting (3x) gives \(x^2-8x-14=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-8x-14=0\). The left side gives \(x^2-5x-14\). Subtracting (3x) gives \(x^2-8x-14=0\).

Step 3

Exam Tip

बाईं ओर \(x^2-5x-14\) मिलता है। (3x) को घटाने पर \(x^2-8x-14=0\) बनता है।

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समीकरण ((x+4)2=5x+10) का मानक रूप कौन-सा है?

What is the standard form of ((x+4)2=5x+10)?

Explanation opens after your attempt
Correct Answer

A. \(x^2+3x+6=0\)

Step 1

Concept

((x+4)2=x-2+8x+16), and subtracting (5x+10) gives \(x^2+3x+6=0\). Keep the middle term correct in square identities.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+3x+6=0\). ((x+4)2=x-2+8x+16), and subtracting (5x+10) gives \(x^2+3x+6=0\). Keep the middle term correct in square identities.

Step 3

Exam Tip

((x+4)2=x-2+8x+16) है और (5x+10) हटाने पर \(x^2+3x+6=0\) मिलता है। वर्ग सूत्र में मध्य पद सही रखें।

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कौन-सा समीकरण द्विघात है लेकिन अभी मानक रूप में नहीं है?

Which equation is quadratic but not yet in standard form?

Explanation opens after your attempt
Correct Answer

B. \(4x^2+1=3x\)

Step 1

Concept

\(4x^2+1=3x\) can be written as \(4x^2-3x+1=0\). In standard form, all terms are on one side and (0) is on the other.

Step 2

Why this answer is correct

The correct answer is B. \(4x^2+1=3x\). \(4x^2+1=3x\) can be written as \(4x^2-3x+1=0\). In standard form, all terms are on one side and (0) is on the other.

Step 3

Exam Tip

\(4x^2+1=3x\) को \(4x^2-3x+1=0\) लिखा जा सकता है। मानक रूप में सभी पद एक ओर और दूसरी ओर (0) होता है।

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समीकरण \(8x-x^2=15\) का मानक रूप कौन-सा है जिसमें \(x^2\) का गुणांक धनात्मक हो?

What is the standard form of \(8x-x^2=15\) with positive coefficient of \(x^2\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-8x+15=0\)

Step 1

Concept

Bringing all terms to one side gives \(-x^2+8x-15=0\). Multiplying by (-1) gives \(x^2-8x+15=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-8x+15=0\). Bringing all terms to one side gives \(-x^2+8x-15=0\). Multiplying by (-1) gives \(x^2-8x+15=0\).

Step 3

Exam Tip

सभी पद एक ओर लाने पर \(-x^2+8x-15=0\) मिलता है। (-1) से गुणा करने पर \(x^2-8x+15=0\) मिलता है।

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समीकरण ((3x+2)(x-5)=0) का मानक द्विघात रूप कौन-सा है?

What is the standard quadratic form of ((3x+2)(x-5)=0)?

Explanation opens after your attempt
Correct Answer

A. \(3x^2-13x-10=0\)

Step 1

Concept

Expanding ((3x+2)(x-5)) gives \(3x^2-15x+2x-10\). So the standard form is \(3x^2-13x-10=0\).

Step 2

Why this answer is correct

The correct answer is A. \(3x^2-13x-10=0\). Expanding ((3x+2)(x-5)) gives \(3x^2-15x+2x-10\). So the standard form is \(3x^2-13x-10=0\).

Step 3

Exam Tip

((3x+2)(x-5)) को फैलाने पर \(3x^2-15x+2x-10\) मिलता है। इसलिए मानक रूप \(3x^2-13x-10=0\) है।

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समीकरण ((x+3)2=2x+15) का मानक रूप कौन-सा है?

What is the standard form of ((x+3)2=2x+15)?

Explanation opens after your attempt
Correct Answer

A. \(x^2+4x-6=0\)

Step 1

Concept

Here ((x+3)2=x-2+6x+9), and bringing all terms to one side gives \(x^2+4x-6=0\). Use the square identity and transposition carefully.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+4x-6=0\). Here ((x+3)2=x-2+6x+9), and bringing all terms to one side gives \(x^2+4x-6=0\). Use the square identity and transposition carefully.

Step 3

Exam Tip

((x+3)2=x-2+6x+9) है और सभी पद एक ओर लाने पर \(x^2+4x-6=0\) मिलता है। वर्ग सूत्र और स्थानांतरण दोनों सावधानी से करें।

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समीकरण ((x-1)(x+6)=2x) का मानक रूप क्या है?

What is the standard form of ((x-1)(x+6)=2x)?

Explanation opens after your attempt
Correct Answer

A. \(x^2+3x-6=0\)

Step 1

Concept

The left side gives \(x^2+5x-6\), and subtracting (2x) gives \(x^2+3x-6=0\). First expand and then bring all terms to one side.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+3x-6=0\). The left side gives \(x^2+5x-6\), and subtracting (2x) gives \(x^2+3x-6=0\). First expand and then bring all terms to one side.

Step 3

Exam Tip

बाईं ओर \(x^2+5x-6\) मिलता है, फिर (2x) घटाने पर \(x^2+3x-6=0\) बनता है। पहले फैलाएं फिर सभी पद एक ओर लाएं।

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समीकरण \(\frac{x^2}{2}+3x-5=0\) को बिना भिन्न के मानक रूप में कौन-सा लिखा जाएगा?

How will \(\frac{x^2}{2}+3x-5=0\) be written in standard form without fractions?

Explanation opens after your attempt
Correct Answer

A. \(x^2+6x-10=0\)

Step 1

Concept

Multiplying the whole equation by (2) gives \(x^2+6x-10=0\). To remove fractions, multiply by the denominator.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+6x-10=0\). Multiplying the whole equation by (2) gives \(x^2+6x-10=0\). To remove fractions, multiply by the denominator.

Step 3

Exam Tip

पूरे समीकरण को (2) से गुणा करने पर \(x^2+6x-10=0\) मिलता है। भिन्न हटाने के लिए हर से गुणा करें।

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समीकरण ((x-5)2=16) का मानक रूप कौन-सा है?

What is the standard form of ((x-5)2=16)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-10x+9=0\)

Step 1

Concept

((x-5)2=x-2-10x+25), so \(x^2-10x+25-16=0\). Do not forget the middle term while using square identities.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-10x+9=0\). ((x-5)2=x-2-10x+25), so \(x^2-10x+25-16=0\). Do not forget the middle term while using square identities.

Step 3

Exam Tip

((x-5)2=x-2-10x+25), इसलिए \(x^2-10x+25-16=0\) मिलता है। वर्ग सूत्र लगाते समय मध्य पद न भूलें।

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कौन-सा समीकरण द्विघात है लेकिन मानक रूप में नहीं लिखा गया है?

Which equation is quadratic but not written in standard form?

Explanation opens after your attempt
Correct Answer

B. \(x^2=5x-4\)

Step 1

Concept

\(x^2=5x-4\) can be written as \(x^2-5x+4=0\), so it is quadratic. In standard form, the right side must be (0).

Step 2

Why this answer is correct

The correct answer is B. \(x^2=5x-4\). \(x^2=5x-4\) can be written as \(x^2-5x+4=0\), so it is quadratic. In standard form, the right side must be (0).

Step 3

Exam Tip

\(x^2=5x-4\) को \(x^2-5x+4=0\) बनाया जा सकता है, इसलिए यह द्विघात है। मानक रूप में दायां पक्ष (0) होना चाहिए।

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समीकरण \(5x-2x^2=9\) का मानक रूप कौन-सा है जिसमें \(x^2\) का गुणांक धनात्मक हो?

What is the standard form of \(5x-2x^2=9\) with positive coefficient of \(x^2\)?

Explanation opens after your attempt
Correct Answer

A. \(2x^2-5x+9=0\)

Step 1

Concept

Bringing all terms to one side gives \(-2x^2+5x-9=0\), and multiplying by (-1) gives \(2x^2-5x+9=0\). Change signs carefully in standard form.

Step 2

Why this answer is correct

The correct answer is A. \(2x^2-5x+9=0\). Bringing all terms to one side gives \(-2x^2+5x-9=0\), and multiplying by (-1) gives \(2x^2-5x+9=0\). Change signs carefully in standard form.

Step 3

Exam Tip

सभी पद एक ओर लाकर \(-2x^2+5x-9=0\) मिलता है और (-1) से गुणा करने पर \(2x^2-5x+9=0\) मिलता है। मानक रूप में चिन्ह सावधानी से बदलें।

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समीकरण ((2x-3)(x+4)=0) का मानक द्विघात रूप कौन-सा है?

What is the standard quadratic form of ((2x-3)(x+4)=0)?

Explanation opens after your attempt
Correct Answer

A. \(2x^2+5x-12=0\)

Step 1

Concept

Multiplying gives \(2x^2+8x-3x-12=0\), so \(2x^2+5x-12=0\). Adding middle terms correctly is important in exams.

Step 2

Why this answer is correct

The correct answer is A. \(2x^2+5x-12=0\). Multiplying gives \(2x^2+8x-3x-12=0\), so \(2x^2+5x-12=0\). Adding middle terms correctly is important in exams.

Step 3

Exam Tip

गुणा करने पर \(2x^2+8x-3x-12=0\), इसलिए \(2x^2+5x-12=0\) मिलता है। मध्य पदों को सही जोड़ना परीक्षा में जरूरी है।

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मानक द्विघात समीकरण \(ax^2+bx+c=0\) में अधिकतम कितने अलग-अलग पद हो सकते हैं?

In the standard quadratic equation \(ax^2+bx+c=0\), what is the maximum number of different terms?

Explanation opens after your attempt
Correct Answer

C. (3)

Step 1

Concept

The standard form may contain the \(x^2\) term, the (x) term, and the constant term. So the maximum number of terms is (3).

Step 2

Why this answer is correct

The correct answer is C. (3). The standard form may contain the \(x^2\) term, the (x) term, and the constant term. So the maximum number of terms is (3).

Step 3

Exam Tip

मानक रूप में \(x^2\) पद, (x) पद और स्थिर पद हो सकते हैं। इसलिए अधिकतम (3) पद होते हैं।

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मानक रूप \(ax^2+bx+c=0\) में \(x^2\) का गुणांक किससे दर्शाया जाता है?

In the standard form \(ax^2+bx+c=0\), which symbol denotes the coefficient of \(x^2\)?

Explanation opens after your attempt
Correct Answer

B. (a)

Step 1

Concept

In standard form, the coefficient of \(x^2\) is (a). This coefficient must not be (0).

Step 2

Why this answer is correct

The correct answer is B. (a). In standard form, the coefficient of \(x^2\) is (a). This coefficient must not be (0).

Step 3

Exam Tip

मानक रूप में \(x^2\) का गुणांक (a) होता है। यही गुणांक (0) नहीं होना चाहिए।

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((x+1)2=0) का मानक रूप क्या है?

What is the standard form of ((x+1)2=0)?

Explanation opens after your attempt
Correct Answer

C. \(x^2+2x+1=0\)

Step 1

Concept

((x+1)2=x-2+2x+1). Remember the formula ((a+b)2=a-2+2ab+b-2).

Step 2

Why this answer is correct

The correct answer is C. \(x^2+2x+1=0\). ((x+1)2=x-2+2x+1). Remember the formula ((a+b)2=a-2+2ab+b-2).

Step 3

Exam Tip

((x+1)2=x-2+2x+1) होता है। सूत्र ((a+b)2=a-2+2ab+b-2) याद रखें।

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समीकरण \(x^2=6x\) का मानक रूप कौन-सा है?

What is the standard form of \(x^2=6x\)?

Explanation opens after your attempt
Correct Answer

B. \(x^2-6x=0\)

Step 1

Concept

Bringing (6x) to the left gives \(x^2-6x=0\). The sign changes during transposition.

Step 2

Why this answer is correct

The correct answer is B. \(x^2-6x=0\). Bringing (6x) to the left gives \(x^2-6x=0\). The sign changes during transposition.

Step 3

Exam Tip

(6x) को बाईं ओर लाने पर \(x^2-6x=0\) मिलता है। स्थानांतरण करते समय चिन्ह बदलता है।

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समीकरण (x(x-5)=0) का मानक रूप कौन-सा है?

What is the standard form of (x(x-5)=0)?

Explanation opens after your attempt
Correct Answer

B. \(x^2-5x=0\)

Step 1

Concept

Expanding (x(x-5)) gives \(x^2-5x\). Keep signs correct while removing brackets.

Step 2

Why this answer is correct

The correct answer is B. \(x^2-5x=0\). Expanding (x(x-5)) gives \(x^2-5x\). Keep signs correct while removing brackets.

Step 3

Exam Tip

(x(x-5)) को फैलाने पर \(x^2-5x\) मिलता है। कोष्ठक हटाते समय चिन्ह सही रखें।

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समीकरण \(x^2=7\) का मानक रूप कौन-सा है?

What is the standard form of \(x^2=7\)?

Explanation opens after your attempt
Correct Answer

D. \(x^2-7=0\)

Step 1

Concept

Bringing (7) to the left gives \(x^2-7=0\). In standard form, all terms are on one side.

Step 2

Why this answer is correct

The correct answer is D. \(x^2-7=0\). Bringing (7) to the left gives \(x^2-7=0\). In standard form, all terms are on one side.

Step 3

Exam Tip

(7) को बाईं ओर लाने पर \(x^2-7=0\) मिलता है। मानक रूप में सभी पद एक तरफ होते हैं।

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समीकरण \(4=3x-x^2\) का मानक रूप क्या है?

What is the standard form of \(4=3x-x^2\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-3x+4=0\)

Step 1

Concept

Bringing all terms to one side gives \(x^2-3x+4=0\). In standard form, keep the right side as (0).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-3x+4=0\). Bringing all terms to one side gives \(x^2-3x+4=0\). In standard form, keep the right side as (0).

Step 3

Exam Tip

सभी पद एक तरफ लाने पर \(x^2-3x+4=0\) मिलता है। मानक रूप में दायां पक्ष (0) रखें।

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((x+3)2=25) को मानक रूप में लिखने पर कौन सा समीकरण मिलेगा?

Which equation is obtained when ((x+3)2=25) is written in standard form?

Explanation opens after your attempt
Correct Answer

A. \(x^2+6x-16=0\)

Step 1

Concept

Here ((x+3)2=x-2+6x+9), and moving (25) left gives (-25). So \(x^2+6x-16=0\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+6x-16=0\). Here ((x+3)2=x-2+6x+9), and moving (25) left gives (-25). So \(x^2+6x-16=0\) is correct.

Step 3

Exam Tip

((x+3)2=x-2+6x+9) है और (25) को बाईं ओर लाने पर (-25) बनता है। इसलिए \(x^2+6x-16=0\) सही है।

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किस विकल्प में गलती है जब \(x^2=6x+7\) को मानक रूप में बदला जाता है?

Which option shows the mistake while converting \(x^2=6x+7\) to standard form?

Explanation opens after your attempt
Correct Answer

B. \(x^2+6x+7=0\)

Step 1

Concept

The correct standard form is \(x^2-6x-7=0\). In option (B), the signs of the right-side terms were not changed.

Step 2

Why this answer is correct

The correct answer is B. \(x^2+6x+7=0\). The correct standard form is \(x^2-6x-7=0\). In option (B), the signs of the right-side terms were not changed.

Step 3

Exam Tip

सही मानक रूप \(x^2-6x-7=0\) है। विकल्प (B) में दाईं ओर के पदों के चिन्ह नहीं बदले गए।

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कौन सा समीकरण मानक रूप में लाने पर \(x^2+2x-8=0\) बनता है?

Which equation becomes \(x^2+2x-8=0\) after writing in standard form?

Explanation opens after your attempt
Correct Answer

A. \(x^2+2x=8\)

Step 1

Concept

Moving (8) to the left makes it (-8). So we get \(x^2+2x-8=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+2x=8\). Moving (8) to the left makes it (-8). So we get \(x^2+2x-8=0\).

Step 3

Exam Tip

(8) को बाईं ओर लाने पर (-8) बनता है। इसलिए \(x^2+2x-8=0\) मिलता है।

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(4x(x-3)=0) का मानक रूप क्या है?

What is the standard form of (4x(x-3)=0)?

Explanation opens after your attempt
Correct Answer

A. \(4x^2-12x=0\)

Step 1

Concept

Multiplying (4x) by both terms gives \(4x^2-12x=0\). Pay attention to the negative sign.

Step 2

Why this answer is correct

The correct answer is A. \(4x^2-12x=0\). Multiplying (4x) by both terms gives \(4x^2-12x=0\). Pay attention to the negative sign.

Step 3

Exam Tip

(4x) को दोनों पदों से गुणा करने पर \(4x^2-12x=0\) मिलता है। ऋण चिन्ह पर ध्यान दें।

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((x-6)(x+2)=0) का मानक रूप कौन सा है?

Which is the standard form of ((x-6)(x+2)=0)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-4x-12=0\)

Step 1

Concept

Expansion gives \(x^2+2x-6x-12=0\). So \(x^2-4x-12=0\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-4x-12=0\). Expansion gives \(x^2+2x-6x-12=0\). So \(x^2-4x-12=0\) is correct.

Step 3

Exam Tip

विस्तार से \(x^2+2x-6x-12=0\) मिलता है। इसलिए \(x^2-4x-12=0\) सही है।

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(2x(x+7)=0) को मानक रूप में लिखिए।

Write (2x(x+7)=0) in standard form.

Explanation opens after your attempt
Correct Answer

A. \(2x^2+14x=0\)

Step 1

Concept

Multiply (2x) by both terms inside the bracket. This gives \(2x^2+14x=0\).

Step 2

Why this answer is correct

The correct answer is A. \(2x^2+14x=0\). Multiply (2x) by both terms inside the bracket. This gives \(2x^2+14x=0\).

Step 3

Exam Tip

(2x) को कोष्ठक के दोनों पदों से गुणा करें। इससे \(2x^2+14x=0\) मिलता है।

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समीकरण \(2x^2=5x+3\) का मानक रूप कौन सा है?

Which is the standard form of \(2x^2=5x+3\)?

Explanation opens after your attempt
Correct Answer

A. \(2x^2-5x-3=0\)

Step 1

Concept

Bringing all terms to one side gives \(2x^2-5x-3=0\). Changing signs is important.

Step 2

Why this answer is correct

The correct answer is A. \(2x^2-5x-3=0\). Bringing all terms to one side gives \(2x^2-5x-3=0\). Changing signs is important.

Step 3

Exam Tip

सभी पद एक तरफ लाने पर \(2x^2-5x-3=0\) मिलता है। चिन्ह बदलना जरूरी है।

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समीकरण \(4x^2+7x=9\) का मानक रूप क्या है?

What is the standard form of \(4x^2+7x=9\)?

Explanation opens after your attempt
Correct Answer

B. \(4x^2+7x-9=0\)

Step 1

Concept

Moving (9) to the left makes it (-9). So the standard form is \(4x^2+7x-9=0\).

Step 2

Why this answer is correct

The correct answer is B. \(4x^2+7x-9=0\). Moving (9) to the left makes it (-9). So the standard form is \(4x^2+7x-9=0\).

Step 3

Exam Tip

दाईं ओर के (9) को बाईं ओर लाने पर (-9) बनता है। इसलिए मानक रूप \(4x^2+7x-9=0\) है।

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किस विकल्प में सामान्य गलती है जब \(x^2=5x-6\) को मानक रूप में बदला जाता है?

Which option shows the common mistake while converting \(x^2=5x-6\) to standard form?

Explanation opens after your attempt
Correct Answer

B. \(x^2-5x-6=0\)

Step 1

Concept

The correct form is \(x^2-5x+6=0\). In option (B), the sign of (-6) was not changed.

Step 2

Why this answer is correct

The correct answer is B. \(x^2-5x-6=0\). The correct form is \(x^2-5x+6=0\). In option (B), the sign of (-6) was not changed.

Step 3

Exam Tip

सही रूप \(x^2-5x+6=0\) है। विकल्प (B) में (-6) का चिन्ह नहीं बदला गया।

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कौन सा समीकरण मानक रूप में लाने पर \(x^2-7x+10=0\) बनता है?

Which equation becomes \(x^2-7x+10=0\) after writing in standard form?

Explanation opens after your attempt
Correct Answer

A. \(x^2-7x=-10\)

Step 1

Concept

In \(x^2-7x=-10\), moving (-10) to the left gives (+10). So the standard form is \(x^2-7x+10=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-7x=-10\). In \(x^2-7x=-10\), moving (-10) to the left gives (+10). So the standard form is \(x^2-7x+10=0\).

Step 3

Exam Tip

\(x^2-7x=-10\) में (-10) को बाईं ओर लाने पर (+10) बनता है। इसलिए मानक रूप \(x^2-7x+10=0\) है।

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(3x(x-2)=0) का मानक रूप क्या है?

What is the standard form of (3x(x-2)=0)?

Explanation opens after your attempt
Correct Answer

A. \(3x^2-6x=0\)

Step 1

Concept

Multiplying (3x) by both terms gives \(3x^2-6x=0\). Watch the sign.

Step 2

Why this answer is correct

The correct answer is A. \(3x^2-6x=0\). Multiplying (3x) by both terms gives \(3x^2-6x=0\). Watch the sign.

Step 3

Exam Tip

(3x) को दोनों पदों से गुणा करने पर \(3x^2-6x=0\) मिलता है। चिन्ह पर ध्यान दें।

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((x-4)(x+1)=0) का मानक रूप कौन सा है?

Which is the standard form of ((x-4)(x+1)=0)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-3x-4=0\)

Step 1

Concept

Expanding gives \(x^2+x-4x-4=0\). So \(x^2-3x-4=0\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-3x-4=0\). Expanding gives \(x^2+x-4x-4=0\). So \(x^2-3x-4=0\) is correct.

Step 3

Exam Tip

विस्तार करने पर \(x^2+x-4x-4=0\) मिलता है। इसलिए \(x^2-3x-4=0\) सही है।

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(x(x+5)=0) को मानक रूप में लिखिए।

Write (x(x+5)=0) in standard form.

Explanation opens after your attempt
Correct Answer

A. \(x^2+5x=0\)

Step 1

Concept

Multiplying gives \(x^2+5x=0\). While opening brackets, multiply each term.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+5x=0\). Multiplying gives \(x^2+5x=0\). While opening brackets, multiply each term.

Step 3

Exam Tip

गुणा करने पर \(x^2+5x=0\) मिलता है। कोष्ठक खोलते समय हर पद से गुणा करें।

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कौन सा समीकरण \(ax^2+bx+c=0\) के मानक रूप में है?

Which equation is in the standard form \(ax^2+bx+c=0\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2+2x+1=0\)

Step 1

Concept

In standard form the right side is (0). Option (A) matches this form.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+2x+1=0\). In standard form the right side is (0). Option (A) matches this form.

Step 3

Exam Tip

मानक रूप में दाईं ओर (0) होता है। विकल्प (A) इसी रूप में है।

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समीकरण \(x^2=4x+12\) का मानक रूप कौन सा है?

Which is the standard form of \(x^2=4x+12\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-4x-12=0\)

Step 1

Concept

When terms from the right side move left, their signs change. Thus \(x^2-4x-12=0\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-4x-12=0\). When terms from the right side move left, their signs change. Thus \(x^2-4x-12=0\) is correct.

Step 3

Exam Tip

दाईं ओर के पदों को बाईं ओर लाने पर चिन्ह बदलते हैं। इसलिए \(x^2-4x-12=0\) सही है।

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समीकरण \(2x^2+5x=3\) का मानक रूप क्या है?

What is the standard form of \(2x^2+5x=3\)?

Explanation opens after your attempt
Correct Answer

B. \(2x^2+5x-3=0\)

Step 1

Concept

Bringing all terms to one side gives \(2x^2+5x-3=0\). Do not forget the sign change.

Step 2

Why this answer is correct

The correct answer is B. \(2x^2+5x-3=0\). Bringing all terms to one side gives \(2x^2+5x-3=0\). Do not forget the sign change.

Step 3

Exam Tip

सभी पद एक तरफ लाने पर \(2x^2+5x-3=0\) मिलता है। चिन्ह बदलना न भूलें।

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किसी धनात्मक पूर्णांक को (9) से भाग देने पर कौन-सा रूप मानक रूप नहीं है?

When a positive integer is divided by (9), which form is not a standard form?

Explanation opens after your attempt
Correct Answer

C. (9q+9)

Step 1

Concept

On division by (9), remainders can be from (0) to (8).

Step 2

Why this answer is correct

In (9q+9), the remainder is (9), which equals the divisor.

Step 3

Exam Tip

It should be written correctly as (9(q+1)). चरण 1: (9) से भाग देने पर शेषफल (0) से (8) तक हो सकते हैं। चरण 2: (9q+9) में शेषफल (9) है, जो भाजक के बराबर है। चरण 3: इसे सही रूप में (9(q+1)) लिखा जाना चाहिए।

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किसी धनात्मक पूर्णांक को (3) से भाग देने पर कौन-सा रूप मानक रूप नहीं है?

When a positive integer is divided by (3), which form is not a standard form?

Explanation opens after your attempt
Correct Answer

D. (3q+3)

Step 1

Concept

On division by (3), possible remainders are (0,1,2).

Step 2

Why this answer is correct

In (3q+3), the remainder is (3), which equals the divisor.

Step 3

Exam Tip

It should be written correctly as (3(q+1)). चरण 1: (3) से भाग देने पर शेषफल (0,1,2) हो सकते हैं। चरण 2: (3q+3) में शेषफल (3) है, जो भाजक के बराबर है। चरण 3: इसे सही रूप में (3(q+1)) लिखना चाहिए।

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यूक्लिड विभाजन प्रमेयिका का मानक रूप कौन सा है?

Which is the standard form of Euclid’s Division Lemma?

Explanation opens after your attempt
Correct Answer

A. \(a=bq+r,\ 0 \le r < b\)

Step 1

Concept

The lemma uses dividend (a), divisor (b), quotient (q), and remainder (r).

Step 2

Why this answer is correct

The correct relation is (a=bq+r).

Step 3

Exam Tip

Do not forget the condition \(0 \le r < b\). चरण 1: प्रमेयिका में भाज्य (a), भाजक (b), भागफल (q) और शेषफल (r) होते हैं। चरण 2: सही संबंध (a=bq+r) है। चरण 3: साथ में \(0 \le r < b\) लिखना न भूलें।

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संयुक्त राष्ट्र बजट में भुगतान क्षमता का सिद्धांत किस बात को न्यायसंगत बनाने की कोशिश करता है?

The capacity to pay principle in the UN budget tries to make what more equitable?

Explanation opens after your attempt
Correct Answer

A. सदस्य देशों का वित्तीय योगदानFinancial contribution of member states

Step 1

Concept

This principle tries to set contributions according to economic capacity. Exam tip: connect it with UN finance.

Step 2

Why this answer is correct

The correct answer is A. सदस्य देशों का वित्तीय योगदान / Financial contribution of member states. This principle tries to set contributions according to economic capacity. Exam tip: connect it with UN finance.

Step 3

Exam Tip

यह सिद्धांत आर्थिक क्षमता के अनुसार योगदान तय करने की कोशिश करता है। परीक्षा में इसे संयुक्त राष्ट्र वित्त व्यवस्था से जोड़ें।

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संयुक्त राष्ट्र बजट पर बहस संगठन की किस वास्तविकता को दिखाती है?

Debate over the UN budget shows which reality of the organization?

Explanation opens after your attempt
Correct Answer

A. कार्यक्रमों के लिए सदस्य देशों के योगदान और प्राथमिकताओं पर निर्भरताDependence on member contributions and priorities for programmes

Step 1

Concept

UN capacity is affected by resources and political will. For exams understand institutional limitations.

Step 2

Why this answer is correct

The correct answer is A. कार्यक्रमों के लिए सदस्य देशों के योगदान और प्राथमिकताओं पर निर्भरता / Dependence on member contributions and priorities for programmes. UN capacity is affected by resources and political will. For exams understand institutional limitations.

Step 3

Exam Tip

संयुक्त राष्ट्र की क्षमता संसाधनों और राजनीतिक इच्छा से प्रभावित होती है। परीक्षा में संस्था की सीमाएं समझें।

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संयुक्त राष्ट्र बजट में भुगतान क्षमता का सिद्धांत किस नैतिक तर्क से जुड़ा है?

The capacity to pay principle in the UN budget is linked with which ethical argument?

Explanation opens after your attempt
Correct Answer

A. आर्थिक क्षमता के अनुसार योगदान अधिक न्यायसंगत होता हैContribution according to economic capacity is more equitable

Step 1

Concept

Fixing contributions by capacity to pay is an attempt at financial fairness. Exam tip: connect it with UN finance.

Step 2

Why this answer is correct

The correct answer is A. आर्थिक क्षमता के अनुसार योगदान अधिक न्यायसंगत होता है / Contribution according to economic capacity is more equitable. Fixing contributions by capacity to pay is an attempt at financial fairness. Exam tip: connect it with UN finance.

Step 3

Exam Tip

भुगतान क्षमता से योगदान तय करना वित्तीय न्याय का प्रयास है। परीक्षा में इसे संयुक्त राष्ट्र वित्त व्यवस्था से जोड़ें।

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संयुक्त राष्ट्र बजट में भुगतान क्षमता का सिद्धांत किस समस्या को संबोधित करता है?

The principle of capacity to pay in the UN budget addresses which issue?

Explanation opens after your attempt
Correct Answer

A. देशों की आर्थिक क्षमता के अनुसार योगदान तय करनाFixing contributions according to countries' economic capacity

Step 1

Concept

Member contributions are linked with their capacity to pay. Exam tip: connect it with UN finance system.

Step 2

Why this answer is correct

The correct answer is A. देशों की आर्थिक क्षमता के अनुसार योगदान तय करना / Fixing contributions according to countries' economic capacity. Member contributions are linked with their capacity to pay. Exam tip: connect it with UN finance system.

Step 3

Exam Tip

सदस्य देशों का योगदान उनकी भुगतान क्षमता से जोड़ा जाता है। परीक्षा में इसे संयुक्त राष्ट्र वित्त व्यवस्था से जोड़ें।

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संयुक्त राष्ट्र बजट में सदस्य देशों के योगदान का आधार सामान्यतः किससे जुड़ता है?

The contribution of member states to the UN budget is generally linked with what?

Explanation opens after your attempt
Correct Answer

B. भुगतान क्षमताCapacity to pay

Step 1

Concept

Member contributions are generally linked with the principle of capacity to pay. Exam tip: connect it with UN finance.

Step 2

Why this answer is correct

The correct answer is B. भुगतान क्षमता / Capacity to pay. Member contributions are generally linked with the principle of capacity to pay. Exam tip: connect it with UN finance.

Step 3

Exam Tip

सदस्य देशों का योगदान सामान्यतः भुगतान क्षमता के सिद्धांत से जुड़ता है। परीक्षा में इसे संयुक्त राष्ट्र वित्त व्यवस्था से जोड़ें।

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संयुक्त राष्ट्र में बजट और प्रशासनिक प्रश्न सामान्यतः किस अंग में चर्चा किए जाते हैं?

Budget and administrative questions in the UN are generally discussed in which organ?

Explanation opens after your attempt
Correct Answer

A. महासभाGeneral Assembly

Step 1

Concept

The General Assembly plays an important role in budget and administrative matters. For exams understand it as a broad decision forum.

Step 2

Why this answer is correct

The correct answer is A. महासभा / General Assembly. The General Assembly plays an important role in budget and administrative matters. For exams understand it as a broad decision forum.

Step 3

Exam Tip

महासभा बजट और प्रशासनिक विषयों पर महत्वपूर्ण भूमिका निभाती है। परीक्षा में महासभा को व्यापक निर्णय मंच समझें।

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बेसनगर का गरुड़ ध्वज किस धर्म के प्रारंभिक विकास से जुड़ा है?

The Garuda standard at Besnagar is linked with the early development of which religion?

Explanation opens after your attempt
Correct Answer

A. वैष्णव धर्मVaishnavism

Step 1

Concept

The Garuda standard at Besnagar is evidence linked with Vasudeva Vishnu devotion. For exams, understand religious development through symbols.

Step 2

Why this answer is correct

The correct answer is A. वैष्णव धर्म / Vaishnavism. The Garuda standard at Besnagar is evidence linked with Vasudeva Vishnu devotion. For exams, understand religious development through symbols.

Step 3

Exam Tip

बेसनगर का गरुड़ ध्वज वासुदेव विष्णु भक्ति से जुड़ा प्रमाण है। परीक्षा में प्रतीकों से धर्म के विकास को समझें।

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हड़प्पाई ईंटों का मानक अनुपात सामान्यतः किस रूप में बताया जाता है?

The standard ratio of Harappan bricks is generally stated as what?

Explanation opens after your attempt
Correct Answer

B. 1:2:4

Step 1

Concept

Harappan bricks are famous for the 1:2:4 ratio. For exams, connect it with standardization and town planning.

Step 2

Why this answer is correct

The correct answer is B. 1:2:4. Harappan bricks are famous for the 1:2:4 ratio. For exams, connect it with standardization and town planning.

Step 3

Exam Tip

हड़प्पाई ईंटों में 1:2:4 का अनुपात प्रसिद्ध है। परीक्षा में इसे मानकीकरण और नगर योजना से जोड़ें।

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कौन-सा व्यंजक मानक बहुपद रूप में लिखा है?

Which expression is written in standard polynomial form?

Explanation opens after your attempt
Correct Answer

B. \(x^3+2x+5\)

Step 1

Concept

In standard form, terms are written from higher power to lower power. The expression \(x^3+2x+5\) follows this order.

Step 2

Why this answer is correct

The correct answer is B. \(x^3+2x+5\). In standard form, terms are written from higher power to lower power. The expression \(x^3+2x+5\) follows this order.

Step 3

Exam Tip

मानक रूप में पद बड़ी घात से छोटी घात की ओर लिखे जाते हैं। \(x^3+2x+5\) इसी क्रम में है।

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बहुपद \(4x^2+3x^4-x+2\) को मानक रूप में कैसे लिखा जाएगा?

How is \(4x^2+3x^4-x+2\) written in standard form?

Explanation opens after your attempt
Correct Answer

A. \(3x^4+4x^2-x+2\)

Step 1

Concept

In standard form, terms are written in decreasing powers. Therefore \(3x^4+4x^2-x+2\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(3x^4+4x^2-x+2\). In standard form, terms are written in decreasing powers. Therefore \(3x^4+4x^2-x+2\) is correct.

Step 3

Exam Tip

मानक रूप में पद घटती घातों में लिखे जाते हैं। इसलिए \(3x^4+4x^2-x+2\) सही है।

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समीकरण (3(x+1)2+2(x-4)2=74) का मानक रूप कौन-सा है?

What is the standard form of (3(x+1)2+2(x-4)2=74)?

Explanation opens after your attempt
Correct Answer

A. \(5x^2-10x-39=0\)

Step 1

Concept

Expanding gives \(3x^2+6x+3+2x^2-16x+32=74\). Simplifying gives \(5x^2-10x-39=0\).

Step 2

Why this answer is correct

The correct answer is A. \(5x^2-10x-39=0\). Expanding gives \(3x^2+6x+3+2x^2-16x+32=74\). Simplifying gives \(5x^2-10x-39=0\).

Step 3

Exam Tip

विस्तार करने पर \(3x^2+6x+3+2x^2-16x+32=74\) मिलता है। सरल करने पर \(5x^2-10x-39=0\) सही है।

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समीकरण (2(x-1)2+3(x+2)2=65) का मानक रूप कौन-सा है?

What is the standard form of (2(x-1)2+3(x+2)2=65)?

Explanation opens after your attempt
Correct Answer

A. \(5x^2+8x-51=0\)

Step 1

Concept

Expanding gives \(2x^2-4x+2+3x^2+12x+12=65\). Simplifying gives \(5x^2+8x-51=0\).

Step 2

Why this answer is correct

The correct answer is A. \(5x^2+8x-51=0\). Expanding gives \(2x^2-4x+2+3x^2+12x+12=65\). Simplifying gives \(5x^2+8x-51=0\).

Step 3

Exam Tip

विस्तार करने पर \(2x^2-4x+2+3x^2+12x+12=65\) मिलता है। सरल करने पर \(5x^2+8x-51=0\) सही है।

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समीकरण ((x+2)2+2(x-3)2=35) का मानक रूप कौन-सा है?

What is the standard form of ((x+2)2+2(x-3)2=35)?

Explanation opens after your attempt
Correct Answer

A. \(3x^2-8x-13=0\)

Step 1

Concept

Expanding gives \(x^2+4x+4+2x^2-12x+18=35\). Hence \(3x^2-8x-13=0\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(3x^2-8x-13=0\). Expanding gives \(x^2+4x+4+2x^2-12x+18=35\). Hence \(3x^2-8x-13=0\) is correct.

Step 3

Exam Tip

विस्तार करने पर \(x^2+4x+4+2x^2-12x+18=35\) मिलता है। इसलिए \(3x^2-8x-13=0\) सही है।

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समीकरण ((2x-3)2+(x+5)2=34) का मानक रूप कौन-सा है?

What is the standard form of ((2x-3)2+(x+5)2=34)?

Explanation opens after your attempt
Correct Answer

A. \(5x^2-2x=0\)

Step 1

Concept

Expanding gives \(4x^2-12x+9+x^2+10x+25=34\). Simplifying gives \(5x^2-2x=0\).

Step 2

Why this answer is correct

The correct answer is A. \(5x^2-2x=0\). Expanding gives \(4x^2-12x+9+x^2+10x+25=34\). Simplifying gives \(5x^2-2x=0\).

Step 3

Exam Tip

विस्तार करने पर \(4x^2-12x+9+x^2+10x+25=34\) मिलता है। सरल करने पर \(5x^2-2x=0\) बनता है।

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समीकरण ((x-2)2+(2x+1)2=25) का मानक रूप कौन-सा है?

What is the standard form of ((x-2)2+(2x+1)2=25)?

Explanation opens after your attempt
Correct Answer

D. \(5x^2-20=0\)

Step 1

Concept

Expanding gives \(x^2-4x+4+4x^2+4x+1=25\). This gives \(5x^2-20=0\).

Step 2

Why this answer is correct

The correct answer is D. \(5x^2-20=0\). Expanding gives \(x^2-4x+4+4x^2+4x+1=25\). This gives \(5x^2-20=0\).

Step 3

Exam Tip

विस्तार करने पर \(x^2-4x+4+4x^2+4x+1=25\) मिलता है। इससे \(5x^2-20=0\) बनता है।

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किसी धनात्मक पूर्णांक को (8) से भाग देने पर मानक सामान्य रूप कौन-सा हो सकता है?

What can be the standard general forms of a positive integer when divided by (8)?

Explanation opens after your attempt
Correct Answer

A. (8q,8q+1,8q+2,8q+3,8q+4,8q+5,8q+6,8q+7)

Step 1

Concept

On division by (8), remainders can be from (0) to (7).

Step 2

Why this answer is correct

So in (8q+r), (r=0,1,2,3,4,5,6,7).

Step 3

Exam Tip

Do not include (8q+8) while writing standard forms. चरण 1: (8) से भाग देने पर शेषफल (0) से (7) तक हो सकते हैं। चरण 2: इसलिए रूप (8q+r) में (r=0,1,2,3,4,5,6,7) होगा। चरण 3: सामान्य रूप लिखते समय (8q+8) शामिल न करें।

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किसी धनात्मक पूर्णांक को (3) से भाग देने पर कौन-सा रूप संभव नहीं है?

Which form is not possible as a standard form when a positive integer is divided by (3)?

Explanation opens after your attempt
Correct Answer

D. (3q+3)

Step 1

Concept

On division by (3), possible remainders are (0,1,2).

Step 2

Why this answer is correct

In (3q+3), the remainder is (3), which equals the divisor.

Step 3

Exam Tip

It should be written as (3(q+1)). चरण 1: (3) से भाग देने पर शेषफल (0,1,2) हो सकते हैं। चरण 2: (3q+3) में शेषफल (3) है, जो भाजक के बराबर है। चरण 3: इसे (3(q+1)) के रूप में लिखना चाहिए।

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किसी धनात्मक पूर्णांक को (4) से भाग देने पर वह किस रूप में नहीं लिखा जा सकता?

When a positive integer is divided by (4), which form cannot be a standard remainder form?

Explanation opens after your attempt
Correct Answer

D. (4q+4)

Step 1

Concept

On division by (4), possible remainders are (0,1,2,3).

Step 2

Why this answer is correct

In (4q+4), the remainder is (4), which equals the divisor.

Step 3

Exam Tip

Such a form should be written as (4(q+1)). चरण 1: (4) से भाग देने पर शेषफल (0,1,2,3) हो सकते हैं। चरण 2: (4q+4) में शेषफल (4) है, जो भाजक के बराबर है। चरण 3: ऐसे रूप को (4(q+1)) लिखना चाहिए।

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फ्रांसीसी क्रांति के बाद पुराने शाही ध्वज के स्थान पर कौन सा ध्वज अपनाया गया?

Which flag replaced the old royal standard after the French Revolution?

Explanation opens after your attempt
Correct Answer

C. त्रिवर्ण ध्वजTricolour flag

Step 1

Concept

The royal standard represented the old monarchy.

Step 2

Why this answer is correct

The tricolour became a symbol of new civic authority and national unity.

Step 3

Exam Tip

Link the change of flag with the change of power. चरण 1: शाही ध्वज पुराने राजतंत्र का प्रतीक था। चरण 2: त्रिवर्ण ध्वज नई नागरिक सत्ता और राष्ट्रीय एकता का प्रतीक बना। चरण 3: ध्वज परिवर्तन को सत्ता परिवर्तन से जोड़कर याद करें।

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