Concept-wise Practice

symbolic MCQ Questions for Class 10

symbolic se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

Practice Questions

22 questions tagged with symbolic.

यदि किसी समान्तर श्रेणी का (m)वां पद (2m+3) और (d=2) है तो ((m+5))वां पद क्या होगा?

If the (m)th term of an AP is (2m+3) and (d=2), what is the ((m+5))th term?

Explanation opens after your attempt
Correct Answer

D. (2m+13)

Step 1

Concept

The ((m+5))th term is (5d) ahead of the (m)th term, so (2m+3+10=2m+13). In symbolic terms, look at the position gap.

Step 2

Why this answer is correct

The correct answer is D. (2m+13). The ((m+5))th term is (5d) ahead of the (m)th term, so (2m+3+10=2m+13). In symbolic terms, look at the position gap.

Step 3

Exam Tip

((m+5))वां पद (m)वें पद से (5d) आगे है इसलिए (2m+3+10=2m+13)। प्रतीकात्मक पदों में भी स्थान अंतर देखें।

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यदि किसी AP का (p)वां पद (q) और (q)वां पद (p) है, तो उसका ((p+q))वां पद क्या होगा?

If the (p)th term of an AP is (q) and the (q)th term is (p), what is its ((p+q))th term?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

Subtracting the relations gives (d=-1), and substitution gives \(a_{p+q}=0\). Even in symbolic APs, use (a_n=a+(n-1)d).

Step 2

Why this answer is correct

The correct answer is A. (0). Subtracting the relations gives (d=-1), and substitution gives \(a_{p+q}=0\). Even in symbolic APs, use (a_n=a+(n-1)d).

Step 3

Exam Tip

संबंधों को घटाने पर (d=-1) और आगे रखने पर \(a_{p+q}=0\) मिलता है। प्रतीकात्मक AP में भी (a_n=a+(n-1)d) ही लगाएं।

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(49x-2-49(r+s)x+49rs=0) को सरल करने के बाद मूल क्या होंगे?

After simplifying (49x-2-49(r+s)x+49rs=0), what will be the roots?

Explanation opens after your attempt
Correct Answer

A. (x=r,s)

Step 1

Concept

Dividing the whole equation by (49) gives (x-2-(r+s)x+rs=0). In exams, removing the common factor first shortens the solution.

Step 2

Why this answer is correct

The correct answer is A. (x=r,s). Dividing the whole equation by (49) gives (x-2-(r+s)x+rs=0). In exams, removing the common factor first shortens the solution.

Step 3

Exam Tip

पूरे समीकरण को (49) से भाग देने पर (x-2-(r+s)x+rs=0) मिलता है। परीक्षा में पहले सामान्य गुणक हटाना हल को छोटा करता है।

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यदि \(x^2-2ux+u^2-v^2=0\), तो इसके मूल कौनसे हैं?

If \(x^2-2ux+u^2-v^2=0\), what are its roots?

Explanation opens after your attempt
Correct Answer

A. (x=u+v,u-v)

Step 1

Concept

It is ((x-u)2-v-2=0), so \(x-u=\pm v\) and \(x=u\pm v\). In exams, quickly recognize the difference of squares.

Step 2

Why this answer is correct

The correct answer is A. (x=u+v,u-v). It is ((x-u)2-v-2=0), so \(x-u=\pm v\) and \(x=u\pm v\). In exams, quickly recognize the difference of squares.

Step 3

Exam Tip

यह ((x-u)2-v-2=0) है, इसलिए \(x-u=\pm v\) और \(x=u\pm v\) हैं। परीक्षा में वर्गों के अंतर को जल्दी पहचानें।

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(x-2-(p+q)x+pq=0) के मूल कौनसे हैं?

What are the roots of (x-2-(p+q)x+pq=0)?

Explanation opens after your attempt
Correct Answer

A. (x=p,q)

Step 1

Concept

The equation is equivalent to ((x-p)(x-q)=0), so the roots are (p) and (q). In exams, apply zero product rule to symbolic factors too.

Step 2

Why this answer is correct

The correct answer is A. (x=p,q). The equation is equivalent to ((x-p)(x-q)=0), so the roots are (p) and (q). In exams, apply zero product rule to symbolic factors too.

Step 3

Exam Tip

यह समीकरण ((x-p)(x-q)=0) के बराबर है, इसलिए मूल (p) और (q) हैं। परीक्षा में प्रतीकात्मक गुणनखंडों पर भी शून्य गुणनफल नियम लगाएं।

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(36x-2-36(m+n)x+36mn=0) को सरल करने के बाद मूल क्या होंगे?

After simplifying (36x-2-36(m+n)x+36mn=0), what will be the roots?

Explanation opens after your attempt
Correct Answer

A. (x=m,n)

Step 1

Concept

Dividing the whole equation by (36) gives (x-2-(m+n)x+mn=0). In exams, removing the common factor first shortens the solution.

Step 2

Why this answer is correct

The correct answer is A. (x=m,n). Dividing the whole equation by (36) gives (x-2-(m+n)x+mn=0). In exams, removing the common factor first shortens the solution.

Step 3

Exam Tip

पूरे समीकरण को (36) से भाग देने पर (x-2-(m+n)x+mn=0) मिलता है। परीक्षा में पहले सामान्य गुणक हटाना हल को छोटा करता है।

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यदि \(x^2-2rx+r^2-s^2=0\), तो इसके मूल कौनसे हैं?

If \(x^2-2rx+r^2-s^2=0\), what are its roots?

Explanation opens after your attempt
Correct Answer

A. (x=r+s,r-s)

Step 1

Concept

It is ((x-r)2-s-2=0), so \(x-r=\pm s\) and \(x=r\pm s\). In exams, quickly recognize the difference of squares.

Step 2

Why this answer is correct

The correct answer is A. (x=r+s,r-s). It is ((x-r)2-s-2=0), so \(x-r=\pm s\) and \(x=r\pm s\). In exams, quickly recognize the difference of squares.

Step 3

Exam Tip

यह ((x-r)2-s-2=0) है, इसलिए \(x-r=\pm s\) और \(x=r\pm s\) हैं। परीक्षा में वर्गों के अंतर को जल्दी पहचानें।

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(x-2-(s+t)x+st=0) के मूल कौनसे हैं?

What are the roots of (x-2-(s+t)x+st=0)?

Explanation opens after your attempt
Correct Answer

A. (x=s,t)

Step 1

Concept

The equation is equivalent to ((x-s)(x-t)=0), so the roots are (s) and (t). In exams, apply zero product rule to symbolic factors too.

Step 2

Why this answer is correct

The correct answer is A. (x=s,t). The equation is equivalent to ((x-s)(x-t)=0), so the roots are (s) and (t). In exams, apply zero product rule to symbolic factors too.

Step 3

Exam Tip

यह समीकरण ((x-s)(x-t)=0) के बराबर है, इसलिए मूल (s) और (t) हैं। परीक्षा में प्रतीकात्मक गुणनखंडों पर भी शून्य गुणनफल नियम लगाएं।

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(25x-2-25(a+b)x+25ab=0) को सरल करने के बाद मूल क्या होंगे?

After simplifying (25x-2-25(a+b)x+25ab=0), what will be the roots?

Explanation opens after your attempt
Correct Answer

A. (x=a,b)

Step 1

Concept

Dividing the whole equation by (25) gives (x-2-(a+b)x+ab=0). In exams, removing the common factor first shortens the solution.

Step 2

Why this answer is correct

The correct answer is A. (x=a,b). Dividing the whole equation by (25) gives (x-2-(a+b)x+ab=0). In exams, removing the common factor first shortens the solution.

Step 3

Exam Tip

पूरे समीकरण को (25) से भाग देने पर (x-2-(a+b)x+ab=0) मिलता है। परीक्षा में पहले सामान्य गुणक हटाना हल को छोटा करता है।

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यदि \(x^2-2cx+c^2-d^2=0\), तो इसके मूल कौनसे हैं?

If \(x^2-2cx+c^2-d^2=0\), what are its roots?

Explanation opens after your attempt
Correct Answer

A. (x=c+d,c-d)

Step 1

Concept

It is ((x-c)2-d-2=0), so \(x-c=\pm d\) and \(x=c\pm d\). In exams, quickly recognize the difference of squares.

Step 2

Why this answer is correct

The correct answer is A. (x=c+d,c-d). It is ((x-c)2-d-2=0), so \(x-c=\pm d\) and \(x=c\pm d\). In exams, quickly recognize the difference of squares.

Step 3

Exam Tip

यह ((x-c)2-d-2=0) है, इसलिए \(x-c=\pm d\) और \(x=c\pm d\) हैं। परीक्षा में वर्गों के अंतर को जल्दी पहचानें।

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(x-2-(r+t)x+rt=0) के मूल कौनसे हैं?

What are the roots of (x-2-(r+t)x+rt=0)?

Explanation opens after your attempt
Correct Answer

A. (x=r,t)

Step 1

Concept

The equation is equivalent to ((x-r)(x-t)=0), so the roots are (r) and (t). In exams, apply zero product rule to symbolic factors too.

Step 2

Why this answer is correct

The correct answer is A. (x=r,t). The equation is equivalent to ((x-r)(x-t)=0), so the roots are (r) and (t). In exams, apply zero product rule to symbolic factors too.

Step 3

Exam Tip

यह समीकरण ((x-r)(x-t)=0) के बराबर है, इसलिए मूल (r) और (t) हैं। परीक्षा में प्रतीकात्मक गुणनखंडों पर भी शून्य गुणनफल नियम लगाएं।

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(16x-2-16(a+b)x+16ab=0) को सरल करने के बाद मूल क्या होंगे?

After simplifying (16x-2-16(a+b)x+16ab=0), what will be the roots?

Explanation opens after your attempt
Correct Answer

A. (x=a,b)

Step 1

Concept

Dividing the whole equation by (16) gives (x-2-(a+b)x+ab=0). In exams, removing the common factor first makes solving easier.

Step 2

Why this answer is correct

The correct answer is A. (x=a,b). Dividing the whole equation by (16) gives (x-2-(a+b)x+ab=0). In exams, removing the common factor first makes solving easier.

Step 3

Exam Tip

पूरे समीकरण को (16) से भाग देने पर (x-2-(a+b)x+ab=0) मिलता है। परीक्षा में पहले सामान्य गुणक हटाना हल को आसान करता है।

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यदि \(x^2-2mx+m^2-n^2=0\), तो इसके मूल कौनसे हैं?

If \(x^2-2mx+m^2-n^2=0\), what are its roots?

Explanation opens after your attempt
Correct Answer

A. (x=m+n,m-n)

Step 1

Concept

It is ((x-m)2-n-2=0), so \(x-m=\pm n\) and \(x=m\pm n\). In exams, recognize the difference of squares.

Step 2

Why this answer is correct

The correct answer is A. (x=m+n,m-n). It is ((x-m)2-n-2=0), so \(x-m=\pm n\) and \(x=m\pm n\). In exams, recognize the difference of squares.

Step 3

Exam Tip

यह ((x-m)2-n-2=0) है, इसलिए \(x-m=\pm n\) और \(x=m\pm n\) हैं। परीक्षा में वर्गों के अंतर को पहचानें।

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(x-2-(u+v)x+uv=0) के मूल कौनसे हैं?

What are the roots of (x-2-(u+v)x+uv=0)?

Explanation opens after your attempt
Correct Answer

A. (x=u,v)

Step 1

Concept

The equation is equivalent to ((x-u)(x-v)=0), so the roots are (u) and (v). In exams, apply the same rule to symbolic factors.

Step 2

Why this answer is correct

The correct answer is A. (x=u,v). The equation is equivalent to ((x-u)(x-v)=0), so the roots are (u) and (v). In exams, apply the same rule to symbolic factors.

Step 3

Exam Tip

यह समीकरण ((x-u)(x-v)=0) के बराबर है, इसलिए मूल (u) और (v) हैं। परीक्षा में प्रतीकात्मक गुणनखंडों पर भी वही नियम लागू करें।

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(9x-2-9(r+s)x+9rs=0) को सरल करने के बाद मूल क्या होंगे?

After simplifying (9x-2-9(r+s)x+9rs=0), what will be the roots?

Explanation opens after your attempt
Correct Answer

A. (x=r,s)

Step 1

Concept

Dividing the whole equation by (9) gives (x-2-(r+s)x+rs=0). In exams, removing the common factor first makes solving easier.

Step 2

Why this answer is correct

The correct answer is A. (x=r,s). Dividing the whole equation by (9) gives (x-2-(r+s)x+rs=0). In exams, removing the common factor first makes solving easier.

Step 3

Exam Tip

पूरे समीकरण को (9) से भाग देने पर (x-2-(r+s)x+rs=0) मिलता है। परीक्षा में पहले सामान्य गुणक हटाने से हल आसान होता है।

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यदि \(x^2-2px+p^2-q^2=0\), तो इसके मूल कौनसे हैं?

If \(x^2-2px+p^2-q^2=0\), what are its roots?

Explanation opens after your attempt
Correct Answer

A. (x=p+q,p-q)

Step 1

Concept

It is ((x-p)2-q-2=0), so \(x-p=\pm q\) and \(x=p\pm q\). In exams, recognize the difference of squares.

Step 2

Why this answer is correct

The correct answer is A. (x=p+q,p-q). It is ((x-p)2-q-2=0), so \(x-p=\pm q\) and \(x=p\pm q\). In exams, recognize the difference of squares.

Step 3

Exam Tip

यह ((x-p)2-q-2=0) है, इसलिए \(x-p=\pm q\) और \(x=p\pm q\) हैं। परीक्षा में वर्गों के अंतर को पहचानें।

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(x-2-(m+n)x+mn=0) के मूल कौनसे हैं?

What are the roots of (x-2-(m+n)x+mn=0)?

Explanation opens after your attempt
Correct Answer

A. (x=m,n)

Step 1

Concept

The equation is equivalent to ((x-m)(x-n)=0), so the roots are (m) and (n). In exams, the same rule applies to symbolic factors.

Step 2

Why this answer is correct

The correct answer is A. (x=m,n). The equation is equivalent to ((x-m)(x-n)=0), so the roots are (m) and (n). In exams, the same rule applies to symbolic factors.

Step 3

Exam Tip

यह समीकरण ((x-m)(x-n)=0) के बराबर है, इसलिए मूल (m) और (n) हैं। परीक्षा में प्रतीकात्मक गुणनखंडों पर भी वही नियम लागू होता है।

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(4x-2-4(a+b)x+4ab=0) को सरल करने के बाद मूल क्या होंगे?

After simplifying (4x-2-4(a+b)x+4ab=0), what will be the roots?

Explanation opens after your attempt
Correct Answer

A. (x=a,b)

Step 1

Concept

Dividing the whole equation by (4) gives (x-2-(a+b)x+ab=0). In exams, removing the common factor first is easier.

Step 2

Why this answer is correct

The correct answer is A. (x=a,b). Dividing the whole equation by (4) gives (x-2-(a+b)x+ab=0). In exams, removing the common factor first is easier.

Step 3

Exam Tip

पूरे समीकरण को (4) से भाग देने पर (x-2-(a+b)x+ab=0) मिलता है। परीक्षा में पहले सामान्य गुणक हटाना आसान रहता है।

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यदि \(x^2-2ax+a^2-b^2=0\), तो इसके मूल कौनसे हैं?

If \(x^2-2ax+a^2-b^2=0\), what are its roots?

Explanation opens after your attempt
Correct Answer

A. (x=a+b,a-b)

Step 1

Concept

It is ((x-a)2-b-2=0), so \(x-a=\pm b\) and \(x=a\pm b\). In exams, use the difference of squares.

Step 2

Why this answer is correct

The correct answer is A. (x=a+b,a-b). It is ((x-a)2-b-2=0), so \(x-a=\pm b\) and \(x=a\pm b\). In exams, use the difference of squares.

Step 3

Exam Tip

यह ((x-a)2-b-2=0) है, इसलिए \(x-a=\pm b\) और \(x=a\pm b\) हैं। परीक्षा में वर्गों के अंतर का प्रयोग करें।

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यदि किसी द्विघात का ग्राफ (x)-अक्ष को ((m,0)) और ((n,0)) पर काटता है तो कौन सा बहुपद उन्हीं शून्यकों वाला हो सकता है?

If a quadratic graph cuts the (x)-axis at ((m,0)) and ((n,0)), which polynomial can have the same zeroes?

Explanation opens after your attempt
Correct Answer

A. (k(x-m)(x-n)), जहाँ \(k\neq0\)(k(x-m)(x-n)), where \(k\neq0\)

Step 1

Concept

For zeroes (m) and (n), the factors are ((x-m)) and ((x-n)). A non-zero multiplier does not change zeroes.

Step 2

Why this answer is correct

The correct answer is A. (k(x-m)(x-n)), जहाँ \(k\neq0\) / (k(x-m)(x-n)), where \(k\neq0\). For zeroes (m) and (n), the factors are ((x-m)) and ((x-n)). A non-zero multiplier does not change zeroes.

Step 3

Exam Tip

शून्यक (m) और (n) के लिए गुणनखंड ((x-m)) और ((x-n)) होते हैं। गैर शून्य गुणक शून्यक नहीं बदलता।

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किसी बहुपद का ग्राफ (x)-अक्ष को ((r,0)) पर मिलता है। कौन सा कथन हमेशा सत्य है?

A polynomial graph meets the (x)-axis at ((r,0)). Which statement is always true?

Explanation opens after your attempt
Correct Answer

A. (p(r)=0)

Step 1

Concept

((r,0)) means (y=0) when (x=r). This is the definition of a zero.

Step 2

Why this answer is correct

The correct answer is A. (p(r)=0). ((r,0)) means (y=0) when (x=r). This is the definition of a zero.

Step 3

Exam Tip

((r,0)) का अर्थ (x=r) पर (y=0) है। यही शून्यक की परिभाषा है।

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यदि किसी बहुपद के ग्राफ का (x)-अक्ष कटान ((0,0)) और ((a,0)) है, जहाँ \(a\neq0\), तो शून्यकों का गुणनफल क्या होगा?

If a polynomial graph has (x)-axis intersections ((0,0)) and ((a,0)), where \(a\neq0\), what will be the product of the zeroes?

Explanation opens after your attempt
Correct Answer

B. (0)

Step 1

Concept

The zeroes are (0) and (a), so the product is (0). Tip: if (0) is included, the product is (0).

Step 2

Why this answer is correct

The correct answer is B. (0). The zeroes are (0) and (a), so the product is (0). Tip: if (0) is included, the product is (0).

Step 3

Exam Tip

शून्यक (0) और (a) हैं, इसलिए गुणनफल (0) है। टिप: (0) शामिल हो तो गुणनफल (0) होगा।

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