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linear-combination MCQ Questions for Class 10

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6 questions tagged with linear-combination.

Question 1/6 Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि (5(2x-y)-3(x+y)=11) और (2(2x-y)+4(x+y)=50), तो (y) का मान क्या है?

If (5(2x-y)-3(x+y)=11) and (2(2x-y)+4(x+y)=50), what is the value of (y)?

Explanation opens after your attempt
Correct Answer

A. (3)

Step 1

Concept

Let (u=2x-y) and (v=x+y). Solving (5u-3v=11), (2u+4v=50) gives (u=7,v=9), hence \(y=\frac{11}{3}\).

Step 2

Why this answer is correct

The correct answer is A. (3). Let (u=2x-y) and (v=x+y). Solving (5u-3v=11), (2u+4v=50) gives (u=7,v=9), hence \(y=\frac{11}{3}\).

Step 3

Exam Tip

मान लें (u=2x-y) और (v=x+y)। (5u-3v=11), (2u+4v=50) से (u=7,v=9), इसलिए \(y=\frac{11}{3}\)।

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Question 2/6 Expert Mathematics Real Numbers Euclid’s Division Lemma Class 10 Level 3

यदि (a) को 23 से भाग देने पर शेषफल 14 है और (b) को 23 से भाग देने पर शेषफल 19 है, तो (6a+5b) को 23 से भाग देने पर शेषफल क्या होगा?

If (a) leaves remainder 14 when divided by 23 and (b) leaves remainder 19 when divided by 23, what is the remainder when (6a+5b) is divided by 23?

Explanation opens after your attempt
Correct Answer

C. 18

Step 1

Concept

In (6a+5b), the remainder part is \(6\times14+5\times19=179\).

Step 2

Why this answer is correct

\(179=23\times7+18\), so the remainder is 18.

Step 3

Exam Tip

In multi-term expressions, handle each term’s remainder separately. चरण 1: (6a+5b) में शेषफल \(6\times14+5\times19=179\) होगा। चरण 2: \(179=23\times7+18\), इसलिए शेषफल 18 है। चरण 3: कई पदों में हर पद के शेषफल को अलग संभालें।

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Question 3/6 Expert Mathematics Real Numbers Euclid’s Division Lemma Class 10 Level 2

यदि (a) को 19 से भाग देने पर शेषफल 11 है और (b) को 19 से भाग देने पर शेषफल 16 है, तो (5a+4b) को 19 से भाग देने पर शेषफल क्या होगा?

If (a) leaves remainder 11 when divided by 19 and (b) leaves remainder 16 when divided by 19, what is the remainder when (5a+4b) is divided by 19?

Explanation opens after your attempt
Correct Answer

B. 5

Step 1

Concept

In (5a+4b), the remainder part is \(5\times11+4\times16=119\).

Step 2

Why this answer is correct

\(119=19\times6+5\), so the remainder is 5.

Step 3

Exam Tip

In multi-term expressions, handle each term’s remainder separately. चरण 1: (5a+4b) में शेषफल \(5\times11+4\times16=119\) होगा। चरण 2: \(119=19\times6+5\), इसलिए शेषफल 5 है। चरण 3: कई पदों में हर पद के शेषफल को अलग संभालें।

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Question 4/6 Expert Mathematics Real Numbers Euclid’s Division Lemma Class 10 Level 1

यदि (a) को 17 से भाग देने पर शेषफल 9 है और (b) को 17 से भाग देने पर शेषफल 13 है, तो (4a+3b) को 17 से भाग देने पर शेषफल क्या होगा?

If (a) leaves remainder 9 when divided by 17 and (b) leaves remainder 13 when divided by 17, what is the remainder when (4a+3b) is divided by 17?

Explanation opens after your attempt
Correct Answer

C. 7

Step 1

Concept

In (4a+3b), the remainder part is \(4\times9+3\times13=75\).

Step 2

Why this answer is correct

\(75=17\times4+7\), so the remainder is 7.

Step 3

Exam Tip

In multi-term expressions, handle each term’s remainder separately. चरण 1: (4a+3b) में शेषफल \(4\times9+3\times13=75\) होगा। चरण 2: \(75=17\times4+7\), इसलिए शेषफल 7 है। चरण 3: कई पदों में हर पद के शेषफल को अलग संभालें।

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Question 5/6 Hard Mathematics Real Numbers Euclid’s Division Lemma Class 10 Level 3

यदि (a) को 11 से भाग देने पर शेषफल 6 है और (b) को 11 से भाग देने पर शेषफल 8 है, तो (3a+b) को 11 से भाग देने पर शेषफल क्या होगा?

If (a) leaves remainder 6 when divided by 11 and (b) leaves remainder 8 when divided by 11, what is the remainder when (3a+b) is divided by 11?

Explanation opens after your attempt
Correct Answer

A. 4

Step 1

Concept

In (3a+b), the remainder part is \(3\times6+8=26\).

Step 2

Why this answer is correct

\(26=11\times2+4\), so the remainder is 4.

Step 3

Exam Tip

In multi-term expressions, handle the remainder of each term separately. चरण 1: (3a+b) में शेषफल \(3\times6+8=26\) होगा। चरण 2: \(26=11\times2+4\), इसलिए शेषफल 4 है। चरण 3: कई पदों में हर पद के शेषफल को अलग संभालें।

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Question 6/6 Hard Mathematics Real Numbers Euclid’s Division Lemma Class 10 Level 2

यदि (a) को 9 से भाग देने पर शेषफल 4 है और (b) को 9 से भाग देने पर शेषफल 7 है, तो (2a+b) को 9 से भाग देने पर शेषफल क्या होगा?

If (a) leaves remainder 4 when divided by 9 and (b) leaves remainder 7 when divided by 9, what is the remainder when (2a+b) is divided by 9?

Explanation opens after your attempt
Correct Answer

B. 6

Step 1

Concept

In (2a+b), the remainder part is \(2\times4+7=15\).

Step 2

Why this answer is correct

(15=9+6), so the remainder is 6.

Step 3

Exam Tip

In such questions, handle the remainder of each term separately. चरण 1: (2a+b) में शेषफल \(2\times4+7=15\) होगा। चरण 2: (15=9+6), इसलिए शेषफल 6 है। चरण 3: ऐसे प्रश्नों में प्रत्येक पद का शेषफल अलग संभालें।

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