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Class 9 Mathematics - Introduction to Polynomials - Linear polynomials Hard Quiz

Mathematics Introduction to Polynomials Linear polynomials Hard Class 9 Topic Quiz

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Question 1/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

सरल करने के बाद (5(2x-3)-3(3x+1)) कौन सा बहुपद बनेगा?

After simplifying (5(2x-3)-3(3x+1)), which polynomial is obtained?

Explanation opens after your attempt
Correct Answer

A. (x-18)

Explanation

Simple Explanation

(10x-15-9x-3=x-18) है। कोष्ठक खोलने के बाद समान पद मिलाएं। / (10x-15-9x-3=x-18). After opening brackets, combine like terms.

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Question 2/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

किस मान पर (\(a^2-16\)x+7) रेखीय बहुपद नहीं रहेगा?

For which value will (\(a^2-16\)x+7) not remain a linear polynomial?

Explanation opens after your attempt
Correct Answer

B. (a=4) या (a=-4)(a=4) or (a=-4)

Explanation

Simple Explanation

रेखीय न रहने के लिए (x) का गुणांक (0) होना चाहिए। \(a^2-16=0\) से \(a=\pm4\) मिलता है। / For it not to be linear, the coefficient of (x) must be (0). From \(a^2-16=0\), \(a=\pm4\).

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Question 3/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=(k-2)x+9) का शून्यक (-3) है, तो (k) का मान क्या है?

If the zero of (p(x)=(k-2)x+9) is (-3), what is the value of (k)?

Explanation opens after your attempt
Correct Answer

A. (5)

Explanation

Simple Explanation

(-3(k-2)+9=0) से (k=5) मिलता है। शून्यक को बहुपद में रखकर (0) करें। / From (-3(k-2)+9=0), we get (k=5). Substitute the zero into the polynomial and set it to (0).

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Question 4/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=3x-2) और (q(x)=x+5), तो (2p(x)-3q(x)) क्या है?

If (p(x)=3x-2) and (q(x)=x+5), what is (2p(x)-3q(x))?

Explanation opens after your attempt
Correct Answer

A. (3x-19)

Explanation

Simple Explanation

(2(3x-2)-3(x+5)=3x-19) है। गुणा करके समान पदों को मिलाएं। / (2(3x-2)-3(x+5)=3x-19). Multiply and then combine like terms.

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Question 5/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

किस मान पर ((2m-5)x+10) का शून्यक (4) होगा?

For which value will the zero of ((2m-5)x+10) be (4)?

Explanation opens after your attempt
Correct Answer

B. \(m=\frac{5}{4}\)

Explanation

Simple Explanation

शून्यक (4) होने पर (4(2m-5)+10=0) होगा। इससे \(m=\frac{5}{4}\) मिलता है। / If the zero is (4), then (4(2m-5)+10=0). This gives \(m=\frac{5}{4}\).

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Question 6/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=ax+b) का शून्यक (2) है और (a=5), तो (b) क्या है?

If the zero of (p(x)=ax+b) is (2) and (a=5), what is (b)?

Explanation opens after your attempt
Correct Answer

B. (-10)

Explanation

Simple Explanation

(p(2)=0) से (2a+b=0) होगा। (a=5) रखने पर (b=-10) मिलता है। / From (p(2)=0), (2a+b=0). Substituting (a=5) gives (b=-10).

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Question 7/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

किस विकल्प में दो रेखीय बहुपदों का योग शून्य बहुपद है?

In which option is the sum of two linear polynomials the zero polynomial?

Explanation opens after your attempt
Correct Answer

C. (5x-7) और (-5x+7)(5x-7) and (-5x+7)

Explanation

Simple Explanation

(5x-7+(-5x+7)=0) है। विपरीत बहुपदों का योग शून्य बहुपद होता है। / (5x-7+(-5x+7)=0). The sum of opposite polynomials is the zero polynomial.

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Question 8/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=4x+c) और (p(3)=p(1)+10), तो (c) के बारे में क्या सही है?

If (p(x)=4x+c) and (p(3)=p(1)+10), what is correct about (c)?

Explanation opens after your attempt
Correct Answer

C. ऐसा कोई (c) नहींNo such (c)

Explanation

Simple Explanation

(p(3)-p(1)=(12+c)-(4+c)=8) होता है। इसलिए (10) वाली शर्त किसी (c) पर पूरी नहीं होती। / (p(3)-p(1)=(12+c)-(4+c)=8). So the condition with (10) is not satisfied for any (c).

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Question 9/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

किस विकल्प में रेखीय बहुपद का शून्यक \(-\frac{3}{7}\) है?

Which option has zero \(-\frac{3}{7}\) for a linear polynomial?

Explanation opens after your attempt
Correct Answer

C. (7x+3)

Explanation

Simple Explanation

(7x+3=0) से \(x=-\frac{3}{7}\) मिलता है। भिन्न शून्यक में चिन्ह और हर ध्यान रखें। / From (7x+3=0), we get \(x=-\frac{3}{7}\). Pay attention to the sign and denominator in fractional zeros.

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Question 10/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=\frac{2}{5}x-6), तो किस मान पर (p(x)=0) होगा?

If (p(x)=\frac{2}{5}x-6), for which value will (p(x)=0)?

Explanation opens after your attempt
Correct Answer

C. (x=15)

Explanation

Simple Explanation

\(\frac{2}{5}x-6=0\) से \(\frac{2}{5}x=6\) और (x=15) मिलता है। भिन्न गुणांक में उलटा गुणा करें। / From \(\frac{2}{5}x-6=0\), \(\frac{2}{5}x=6\) and (x=15). With a fractional coefficient, multiply by the reciprocal.

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Question 11/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=x+2) और (q(x)=x-5), तो (p(x)q(x)) की डिग्री क्या है?

If (p(x)=x+2) and (q(x)=x-5), what is the degree of (p(x)q(x))?

Explanation opens after your attempt
Correct Answer

B. (2)

Explanation

Simple Explanation

((x+2)(x-5)) में उच्चतम पद \(x^2\) है। इसलिए गुणनफल की डिग्री (2) है। / In ((x+2)(x-5)), the highest term is \(x^2\). Therefore the product has degree (2).

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Question 12/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=2x-1), तो (p(x+3)) क्या है?

If (p(x)=2x-1), what is (p(x+3))?

Explanation opens after your attempt
Correct Answer

A. (2x+5)

Explanation

Simple Explanation

(p(x+3)=2(x+3)-1=2x+5) है। (x) की जगह पूरा (x+3) रखें। / (p(x+3)=2(x+3)-1=2x+5). Substitute the whole (x+3) in place of (x).

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Question 13/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=5-3x), तो (p(2x)) कौन सा है?

If (p(x)=5-3x), which is (p(2x))?

Explanation opens after your attempt
Correct Answer

C. (5-6x)

Explanation

Simple Explanation

(p(2x)=5-3(2x)=5-6x) है। प्रतिस्थापन करते समय पूरे (2x) को रखें। / (p(2x)=5-3(2x)=5-6x). While substituting, use the whole (2x).

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Question 14/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

किस मान पर (\(t^2-9\)x+(t-3)) रेखीय बहुपद नहीं रहेगा?

For which value will (\(t^2-9\)x+(t-3)) not remain a linear polynomial?

Explanation opens after your attempt
Correct Answer

A. (t=3) या (t=-3)(t=3) or (t=-3)

Explanation

Simple Explanation

रेखीय होने के लिए \(t^2-9\neq0\) चाहिए। \(t=\pm3\) पर (x) का गुणांक (0) हो जाता है। / For it to be linear, \(t^2-9\neq0\) is needed. At \(t=\pm3\), the coefficient of (x) becomes (0).

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Question 15/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=kx+4) और (p(2)=p(-2)), तो (p(x)) रेखीय कब रहेगा?

If (p(x)=kx+4) and (p(2)=p(-2)), when will (p(x)) remain linear?

Explanation opens after your attempt
Correct Answer

C. कभी नहींNever

Explanation

Simple Explanation

(p(2)=p(-2)) से (2k+4=-2k+4) और (k=0) मिलता है। (k=0) पर बहुपद रेखीय नहीं रहता। / From (p(2)=p(-2)), (2k+4=-2k+4), so (k=0). At (k=0), the polynomial is not linear.

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Question 16/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=ax+b) का शून्यक (0) है, तो कौन सी शर्त सही है?

If the zero of (p(x)=ax+b) is (0), which condition is correct?

Explanation opens after your attempt
Correct Answer

B. (b=0) और \(a\neq0\)(b=0) and \(a\neq0\)

Explanation

Simple Explanation

शून्यक (0) होने पर (p(0)=b=0) होना चाहिए। रेखीय रहने के लिए \(a\neq0\) भी जरूरी है। / If the zero is (0), then (p(0)=b=0). To remain linear, \(a\neq0\) is also necessary.

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Question 17/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=2x+3) और (q(x)=5x-1), तो (q(x)-2p(x)) की डिग्री क्या है?

If (p(x)=2x+3) and (q(x)=5x-1), what is the degree of (q(x)-2p(x))?

Explanation opens after your attempt
Correct Answer

B. (1)

Explanation

Simple Explanation

(q(x)-2p(x)=5x-1-2(2x+3)=x-7) है। इसकी डिग्री (1) है। / (q(x)-2p(x)=5x-1-2(2x+3)=x-7). Its degree is (1).

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Question 18/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

किस विकल्प में रेखीय बहुपद का शून्यक \(\frac{11}{5}\) है?

Which option has zero \(\frac{11}{5}\) for a linear polynomial?

Explanation opens after your attempt
Correct Answer

A. (5x-11)

Explanation

Simple Explanation

(5x-11=0) से \(x=\frac{11}{5}\) मिलता है। शून्यक के लिए बहुपद को (0) के बराबर रखें। / From (5x-11=0), we get \(x=\frac{11}{5}\). Set the polynomial equal to (0) to find the zero.

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Question 19/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=3x-8), तो (p(x+1)-p(x)) क्या है?

If (p(x)=3x-8), what is (p(x+1)-p(x))?

Explanation opens after your attempt
Correct Answer

B. (3)

Explanation

Simple Explanation

(p(x+1)=3x-5) और (p(x)=3x-8) है। अंतर (3) मिलता है। / (p(x+1)=3x-5) and (p(x)=3x-8). The difference is (3).

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Question 20/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=\lambda x+6) और इसका शून्यक (-2) से बड़ा है, तो \(\lambda>0\) होने पर कौन सी शर्त सही है?

If (p(x)=\lambda x+6) and its zero is greater than (-2), which condition is correct when \(\lambda>0\)?

Explanation opens after your attempt
Correct Answer

C. \(\lambda>3\)

Explanation

Simple Explanation

शून्यक \(-\frac{6}{\lambda}\) है। \(-\frac{6}{\lambda}>-2\) और \(\lambda>0\) से \(\lambda>3\) मिलता है। / The zero is \(-\frac{6}{\lambda}\). From \(-\frac{6}{\lambda}>-2\) and \(\lambda>0\), we get \(\lambda>3\).

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Question 21/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

किस विकल्प में (p(x)=ax+b) का शून्यक (-2) होगा?

In which option will (p(x)=ax+b) have zero (-2)?

Explanation opens after your attempt
Correct Answer

A. (b=2a) और \(a\neq0\)(b=2a) and \(a\neq0\)

Explanation

Simple Explanation

शून्यक (-2) होने पर (-2a+b=0) होगा। इसलिए (b=2a) और \(a\neq0\) चाहिए। / If the zero is (-2), then (-2a+b=0). So (b=2a) and \(a\neq0\) are needed.

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Question 22/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=x+r) और (q(x)=x-r), तो (p(x)+q(x)) क्या है?

If (p(x)=x+r) and (q(x)=x-r), what is (p(x)+q(x))?

Explanation opens after your attempt
Correct Answer

A. (2x)

Explanation

Simple Explanation

जोड़ने पर (x+r+x-r=2x) मिलता है। (r) वाले पद कट जाते हैं। / On adding, (x+r+x-r=2x). The terms containing (r) cancel.

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Question 23/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=x+r) और (q(x)=x-r), तो (p(x)-q(x)) किस प्रकार का बहुपद है?

If (p(x)=x+r) and (q(x)=x-r), what type of polynomial is (p(x)-q(x))?

Explanation opens after your attempt
Correct Answer

B. नियतांक बहुपदConstant polynomial

Explanation

Simple Explanation

(p(x)-q(x)=2r) है। (x) के संदर्भ में यह नियतांक बहुपद है। / (p(x)-q(x)=2r). With respect to (x), it is a constant polynomial.

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Question 24/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=2x-5), तो (p(p(3))) का मान क्या है?

If (p(x)=2x-5), what is the value of (p(p(3)))?

Explanation opens after your attempt
Correct Answer

A. (1)

Explanation

Simple Explanation

(p(3)=1) और (p(1)=-3) नहीं बल्कि (2(1)-5=-3) है। इसलिए सही मान (-3) नहीं दिए विकल्पों में नहीं है। / (p(3)=1) and (p(1)=2(1)-5=-3). The correct value is (-3), which is not in the options.

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Question 25/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=3x+1), तो (p(p(2))) का मान क्या है?

If (p(x)=3x+1), what is the value of (p(p(2)))?

Explanation opens after your attempt
Correct Answer

C. (22)

Explanation

Simple Explanation

(p(2)=7) और (p(7)=22) है। अंदर वाला मान पहले निकालें। / (p(2)=7) and (p(7)=22). Find the inner value first.

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Question 26/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

किस मान पर ((n-1)x+n+2) का शून्यक (1) होगा?

For which value will the zero of ((n-1)x+n+2) be (1)?

Explanation opens after your attempt
Correct Answer

A. \(n=-\frac{1}{2}\)

Explanation

Simple Explanation

शून्यक (1) होने पर (n-1+n+2=0) होगा। इससे (2n+1=0) और \(n=-\frac{1}{2}\) मिलता है। / If the zero is (1), then (n-1+n+2=0). Thus (2n+1=0) and \(n=-\frac{1}{2}\).

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Question 27/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=\frac{x}{3}+a) और (p(6)=5), तो (a) का मान क्या है?

If (p(x)=\frac{x}{3}+a) and (p(6)=5), what is the value of (a)?

Explanation opens after your attempt
Correct Answer

C. (3)

Explanation

Simple Explanation

(p(6)=2+a=5) से (a=3) मिलता है। भिन्न रूप में पहले (x) का मान रखें। / From (p(6)=2+a=5), we get (a=3). In fractional form, substitute the value of (x) first.

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Question 28/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

किस विकल्प में (p(x)-q(x)) रेखीय बहुपद है?

In which option is (p(x)-q(x)) a linear polynomial?

Explanation opens after your attempt
Correct Answer

B. (p(x)=2x+3), (q(x)=x-5)

Explanation

Simple Explanation

दूसरे विकल्प में अंतर (x+8) है जिसकी डिग्री (1) है। बाकी में अंतर नियतांक या शून्य है। / In the second option, the difference is (x+8), whose degree is (1). In the others, the difference is constant or zero.

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Question 29/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=2x+a) और (q(x)=x-3), तो (p(x)+q(x)) का शून्यक (1) होने पर (a) क्या है?

If (p(x)=2x+a) and (q(x)=x-3), what is (a) if the zero of (p(x)+q(x)) is (1)?

Explanation opens after your attempt
Correct Answer

A. (0)

Explanation

Simple Explanation

(p(x)+q(x)=3x+a-3) है। (x=1) रखने पर (3+a-3=0) से (a=0) मिलता है। / (p(x)+q(x)=3x+a-3). Substituting (x=1) gives (3+a-3=0), so (a=0).

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Question 30/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

किस मान पर (p(x)=(c+1)x+2c) का शून्यक (-4) होगा?

For which value will the zero of (p(x)=(c+1)x+2c) be (-4)?

Explanation opens after your attempt
Correct Answer

B. (c=2)

Explanation

Simple Explanation

(-4(c+1)+2c=0) से (-2c-4=0) मिलता है। इसलिए (c=-2) होना चाहिए। / From (-4(c+1)+2c=0), we get (-2c-4=0). Therefore (c=-2) is required.

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Question 31/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=(c+1)x+2c) का शून्यक (-4) है, तो (c) का सही मान क्या है?

If the zero of (p(x)=(c+1)x+2c) is (-4), what is the correct value of (c)?

Explanation opens after your attempt
Correct Answer

C. (c=-2)

Explanation

Simple Explanation

(-4(c+1)+2c=0) से (-2c-4=0) मिलता है। अतः (c=-2) है। / From (-4(c+1)+2c=0), we get (-2c-4=0). Hence (c=-2).

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Question 32/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=rx+5) और (p(2)=15), तो (p(-1)) का मान क्या है?

If (p(x)=rx+5) and (p(2)=15), what is the value of (p(-1))?

Explanation opens after your attempt
Correct Answer

A. (0)

Explanation

Simple Explanation

(2r+5=15) से (r=5) मिलता है। इसलिए (p(-1)=5(-1)+5=0) है। / From (2r+5=15), we get (r=5). Therefore (p(-1)=5(-1)+5=0).

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Question 33/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=ax-6) और (p(2)=p(5)-9), तो (a) क्या है?

If (p(x)=ax-6) and (p(2)=p(5)-9), what is (a)?

Explanation opens after your attempt
Correct Answer

C. (3)

Explanation

Simple Explanation

(2a-6=(5a-6)-9) से (2a=5a-9) मिलता है। इसलिए (a=3) है। / From (2a-6=(5a-6)-9), we get (2a=5a-9). Therefore (a=3).

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Question 34/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

किस विकल्प में (x) का गुणांक (0) होकर भी बहुपद रेखीय बताया गया है?

In which option is a polynomial called linear even though the coefficient of (x) is (0)?

Explanation opens after your attempt
Correct Answer

B. (0x+8) रेखीय है(0x+8) is linear

Explanation

Simple Explanation

(0x+8) सरल होकर (8) बनता है। यह नियतांक बहुपद है रेखीय नहीं। / (0x+8) simplifies to (8). It is a constant polynomial, not linear.

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Question 35/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=2x-7), तो (p(a)=a) होने पर (a) क्या है?

If (p(x)=2x-7), what is (a) when (p(a)=a)?

Explanation opens after your attempt
Correct Answer

B. (7)

Explanation

Simple Explanation

(p(a)=2a-7) है। (2a-7=a) से (a=7) मिलता है। / (p(a)=2a-7). From (2a-7=a), we get (a=7).

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Question 36/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=mx+n), (p(0)=4) और (p(2)=10), तो (m+n) क्या है?

If (p(x)=mx+n), (p(0)=4) and (p(2)=10), what is (m+n)?

Explanation opens after your attempt
Correct Answer

C. (7)

Explanation

Simple Explanation

(p(0)=n=4) और (2m+4=10) से (m=3) मिलता है। इसलिए (m+n=7) है। / (p(0)=n=4) and (2m+4=10) gives (m=3). Therefore (m+n=7).

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Question 37/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=mx+n), (p(1)=5) और (p(3)=13), तो (m) क्या है?

If (p(x)=mx+n), (p(1)=5) and (p(3)=13), what is (m)?

Explanation opens after your attempt
Correct Answer

B. (4)

Explanation

Simple Explanation

दोनों मान घटाने पर (p(3)-p(1)=2m=8) मिलता है। इसलिए (m=4) है। / Subtracting the two values gives (p(3)-p(1)=2m=8). Therefore (m=4).

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Question 38/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

किस विकल्प में (p(2)=0) और (p(x)) रेखीय है?

Which option has (p(2)=0) and (p(x)) is linear?

Explanation opens after your attempt
Correct Answer

C. (p(x)=x-2)

Explanation

Simple Explanation

(x-2) में (x=2) रखने पर (0) मिलता है। यह डिग्री (1) वाला रेखीय बहुपद है। / Substituting (x=2) in (x-2) gives (0). It is a linear polynomial of degree (1).

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Question 39/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=3x-4), तो (p(x)+p(-x)) क्या है?

If (p(x)=3x-4), what is (p(x)+p(-x))?

Explanation opens after your attempt
Correct Answer

B. (-8)

Explanation

Simple Explanation

(p(-x)=-3x-4) है। जोड़ने पर (3x-4-3x-4=-8) मिलता है। / (p(-x)=-3x-4). Adding gives (3x-4-3x-4=-8).

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Question 40/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=3x-4), तो (p(x)-p(-x)) क्या है?

If (p(x)=3x-4), what is (p(x)-p(-x))?

Explanation opens after your attempt
Correct Answer

A. (6x)

Explanation

Simple Explanation

(p(-x)=-3x-4) है। घटाने पर (3x-4-(-3x-4)=6x) मिलता है। / (p(-x)=-3x-4). Subtracting gives (3x-4-(-3x-4)=6x).

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Question 41/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

किस मान पर ((s-2)x+s) का शून्यक (0) होगा?

For which value will the zero of ((s-2)x+s) be (0)?

Explanation opens after your attempt
Correct Answer

A. (s=0)

Explanation

Simple Explanation

शून्यक (0) होने के लिए नियतांक पद (s=0) होना चाहिए। (s=0) पर (x) का गुणांक (-2) है इसलिए बहुपद रेखीय है। / For the zero to be (0), the constant term (s) must be (0). At (s=0), the coefficient of (x) is (-2), so the polynomial is linear.

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Question 42/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=2x+a) और (q(x)=4x-a), तो (p(x)+q(x)) का शून्यक (-1) होने पर (a) क्या है?

If (p(x)=2x+a) and (q(x)=4x-a), what is (a) if the zero of (p(x)+q(x)) is (-1)?

Explanation opens after your attempt
Correct Answer

A. कोई मान नहींNo value

Explanation

Simple Explanation

(p(x)+q(x)=6x) है जिसका शून्यक (0) है। इसलिए शून्यक (-1) किसी (a) पर नहीं हो सकता। / (p(x)+q(x)=6x), whose zero is (0). Therefore the zero cannot be (-1) for any (a).

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Question 43/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=2x+a) और (q(x)=4x-a), तो (p(x)-q(x)) क्या है?

If (p(x)=2x+a) and (q(x)=4x-a), what is (p(x)-q(x))?

Explanation opens after your attempt
Correct Answer

B. (-2x+2a)

Explanation

Simple Explanation

(2x+a-(4x-a)=-2x+2a) है। घटाते समय कोष्ठक के चिन्ह बदलें। / (2x+a-(4x-a)=-2x+2a). Change the signs inside the bracket while subtracting.

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Question 44/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

किस विकल्प में ((x+3)) और ((2x-1)) का गुणनफल रेखीय नहीं है?

Which option correctly says that the product of ((x+3)) and ((2x-1)) is not linear?

Explanation opens after your attempt
Correct Answer

B. क्योंकि डिग्री (2) हैBecause degree is (2)

Explanation

Simple Explanation

((x+3)(2x-1)) में उच्चतम पद \(2x^2\) है। इसलिए गुणनफल की डिग्री (2) है और यह रेखीय नहीं है। / In ((x+3)(2x-1)), the highest term is \(2x^2\). So the product has degree (2) and is not linear.

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Question 45/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=ax+1) और (p(p(0))=7), तो (a) क्या है?

If (p(x)=ax+1) and (p(p(0))=7), what is (a)?

Explanation opens after your attempt
Correct Answer

C. (6)

Explanation

Simple Explanation

(p(0)=1) और (p(1)=a+1) है। (a+1=7) से (a=6) मिलता है। / (p(0)=1) and (p(1)=a+1). From (a+1=7), we get (a=6).

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Question 46/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=x+a) और (p(p(0))=0), तो (a) का मान क्या है?

If (p(x)=x+a) and (p(p(0))=0), what is the value of (a)?

Explanation opens after your attempt
Correct Answer

A. (0)

Explanation

Simple Explanation

(p(0)=a) और (p(a)=2a) है। (2a=0) से (a=0) मिलता है। / (p(0)=a) and (p(a)=2a). From (2a=0), we get (a=0).

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Question 47/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=mx+n) और (p(1)=p(2)), तो (p(x)) रेखीय कब हो सकता है?

If (p(x)=mx+n) and (p(1)=p(2)), when can (p(x)) be linear?

Explanation opens after your attempt
Correct Answer

C. कभी नहींNever

Explanation

Simple Explanation

(p(1)=p(2)) से (m+n=2m+n) और (m=0) मिलता है। (m=0) पर बहुपद रेखीय नहीं रहता। / From (p(1)=p(2)), (m+n=2m+n), so (m=0). At (m=0), the polynomial is not linear.

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Question 48/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

किस विकल्प में (p(x)=ax+b) का शून्यक (3) होगा?

In which option will (p(x)=ax+b) have zero (3)?

Explanation opens after your attempt
Correct Answer

A. (b=-3a) और \(a\neq0\)(b=-3a) and \(a\neq0\)

Explanation

Simple Explanation

शून्यक (3) होने पर (3a+b=0) होगा। इसलिए (b=-3a) और \(a\neq0\) चाहिए। / If the zero is (3), then (3a+b=0). So (b=-3a) and \(a\neq0\) are needed.

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Question 49/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=7x-2), तो (p(x+2)-p(x-1)) क्या है?

If (p(x)=7x-2), what is (p(x+2)-p(x-1))?

Explanation opens after your attempt
Correct Answer

C. (21)

Explanation

Simple Explanation

(p(x+2)=7x+12) और (p(x-1)=7x-9) है। अंतर (21) है। / (p(x+2)=7x+12) and (p(x-1)=7x-9). The difference is (21).

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Question 50/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 33

यदि (p(x)=2x-5), तो (p(p(3))) का सही मान क्या है?

If (p(x)=2x-5), what is the correct value of (p(p(3)))?

Explanation opens after your attempt
Correct Answer

C. (-3)

Explanation

Simple Explanation

(p(3)=1) है और (p(1)=2-5=-3) है। अंदर वाले मान को पहले निकालें। / (p(3)=1) and (p(1)=2-5=-3). Find the inner value first.

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Question 51/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

सरल करने के बाद (6(3x-2)-4(4x+5)) कौन सा बहुपद बनेगा?

After simplifying (6(3x-2)-4(4x+5)), which polynomial is obtained?

Explanation opens after your attempt
Correct Answer

A. (2x-32)

Explanation

Simple Explanation

(18x-12-16x-20=2x-32) है। कोष्ठक खोलकर समान पद मिलाएं। / (18x-12-16x-20=2x-32). Open brackets and combine like terms.

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Question 52/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

किस मान पर (\(b^2-25\)x-11) रेखीय बहुपद नहीं रहेगा?

For which value will (\(b^2-25\)x-11) not remain a linear polynomial?

Explanation opens after your attempt
Correct Answer

B. (b=5) या (b=-5)(b=5) or (b=-5)

Explanation

Simple Explanation

रेखीय न रहने के लिए (x) का गुणांक (0) होना चाहिए। \(b^2-25=0\) से \(b=\pm5\) मिलता है। / For it not to be linear, the coefficient of (x) must be (0). From \(b^2-25=0\), \(b=\pm5\).

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Question 53/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=(k+3)x-12) का शून्यक (4) है, तो (k) का मान क्या है?

If the zero of (p(x)=(k+3)x-12) is (4), what is the value of (k)?

Explanation opens after your attempt
Correct Answer

A. (0)

Explanation

Simple Explanation

(4(k+3)-12=0) से (k=0) मिलता है। शून्यक को बहुपद में रखकर (0) करें। / From (4(k+3)-12=0), we get (k=0). Substitute the zero into the polynomial and set it to (0).

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Question 54/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=4x-7) और (q(x)=2x+3), तो (3p(x)-5q(x)) क्या है?

If (p(x)=4x-7) and (q(x)=2x+3), what is (3p(x)-5q(x))?

Explanation opens after your attempt
Correct Answer

A. (2x-36)

Explanation

Simple Explanation

(3(4x-7)-5(2x+3)=2x-36) है। गुणा करके समान पदों को मिलाएं। / (3(4x-7)-5(2x+3)=2x-36). Multiply and then combine like terms.

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Question 55/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

किस मान पर ((3m+1)x+8) का शून्यक (-2) होगा?

For which value will the zero of ((3m+1)x+8) be (-2)?

Explanation opens after your attempt
Correct Answer

A. (m=1)

Explanation

Simple Explanation

शून्यक (-2) होने पर (-2(3m+1)+8=0) होगा। इससे (m=1) मिलता है। / If the zero is (-2), then (-2(3m+1)+8=0). This gives (m=1).

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Question 56/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=ax+b) का शून्यक (-3) है और (a=2), तो (b) क्या है?

If the zero of (p(x)=ax+b) is (-3) and (a=2), what is (b)?

Explanation opens after your attempt
Correct Answer

A. (6)

Explanation

Simple Explanation

(p(-3)=0) से (-3a+b=0) होगा। (a=2) रखने पर (b=6) मिलता है। / From (p(-3)=0), (-3a+b=0). Substituting (a=2) gives (b=6).

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Question 57/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=5x+c) और (p(4)=p(1)+15), तो (c) के बारे में क्या सही है?

If (p(x)=5x+c) and (p(4)=p(1)+15), what is correct about (c)?

Explanation opens after your attempt
Correct Answer

B. हर (c) सही हैEvery (c) is valid

Explanation

Simple Explanation

(p(4)-p(1)=(20+c)-(5+c)=15) है। इसलिए यह शर्त हर (c) के लिए सही है। / (p(4)-p(1)=(20+c)-(5+c)=15). So the condition is true for every (c).

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Question 58/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

किस विकल्प में रेखीय बहुपद का शून्यक \(-\frac{5}{8}\) है?

Which option has zero \(-\frac{5}{8}\) for a linear polynomial?

Explanation opens after your attempt
Correct Answer

C. (8x+5)

Explanation

Simple Explanation

(8x+5=0) से \(x=-\frac{5}{8}\) मिलता है। भिन्न शून्यक में चिन्ह और हर ध्यान रखें। / From (8x+5=0), we get \(x=-\frac{5}{8}\). Pay attention to the sign and denominator in fractional zeros.

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Question 59/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=\frac{3}{7}x-9), तो किस मान पर (p(x)=0) होगा?

If (p(x)=\frac{3}{7}x-9), for which value will (p(x)=0)?

Explanation opens after your attempt
Correct Answer

B. (x=21)

Explanation

Simple Explanation

\(\frac{3}{7}x-9=0\) से \(\frac{3}{7}x=9\) और (x=21) मिलता है। भिन्न गुणांक में उलटा गुणा करें। / From \(\frac{3}{7}x-9=0\), \(\frac{3}{7}x=9\) and (x=21). With a fractional coefficient, multiply by the reciprocal.

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Question 60/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=x-3) और (q(x)=x+8), तो (p(x)q(x)) की डिग्री क्या है?

If (p(x)=x-3) and (q(x)=x+8), what is the degree of (p(x)q(x))?

Explanation opens after your attempt
Correct Answer

B. (2)

Explanation

Simple Explanation

((x-3)(x+8)) में उच्चतम पद \(x^2\) है। इसलिए गुणनफल की डिग्री (2) है। / In ((x-3)(x+8)), the highest term is \(x^2\). Therefore the product has degree (2).

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Question 61/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=4x-9), तो (p(x+2)) क्या है?

If (p(x)=4x-9), what is (p(x+2))?

Explanation opens after your attempt
Correct Answer

B. (4x-1)

Explanation

Simple Explanation

(p(x+2)=4(x+2)-9=4x-1) है। (x) की जगह पूरा (x+2) रखें। / (p(x+2)=4(x+2)-9=4x-1). Substitute the whole (x+2) in place of (x).

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Question 62/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=11-2x), तो (p(3x)) कौन सा है?

If (p(x)=11-2x), which is (p(3x))?

Explanation opens after your attempt
Correct Answer

B. (11-6x)

Explanation

Simple Explanation

(p(3x)=11-2(3x)=11-6x) है। प्रतिस्थापन करते समय पूरे (3x) को रखें। / (p(3x)=11-2(3x)=11-6x). While substituting, use the whole (3x).

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Question 63/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

किस मान पर (\(t^2-4t+3\)x+(t-1)) रेखीय बहुपद नहीं रहेगा?

For which value will (\(t^2-4t+3\)x+(t-1)) not remain a linear polynomial?

Explanation opens after your attempt
Correct Answer

A. (t=1) या (t=3)(t=1) or (t=3)

Explanation

Simple Explanation

रेखीय होने के लिए \(t^2-4t+3\neq0\) चाहिए। \(t^2-4t+3=0\) से (t=1) या (t=3) मिलता है। / For it to be linear, \(t^2-4t+3\neq0\) is needed. From \(t^2-4t+3=0\), (t=1) or (t=3).

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Question 64/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=kx-5) और (p(3)=p(-1)), तो (p(x)) रेखीय कब रहेगा?

If (p(x)=kx-5) and (p(3)=p(-1)), when will (p(x)) remain linear?

Explanation opens after your attempt
Correct Answer

C. कभी नहींNever

Explanation

Simple Explanation

(p(3)=p(-1)) से (3k-5=-k-5) और (k=0) मिलता है। (k=0) पर बहुपद रेखीय नहीं रहता। / From (p(3)=p(-1)), (3k-5=-k-5), so (k=0). At (k=0), the polynomial is not linear.

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Question 65/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=ax+b) का शून्यक (0) है और बहुपद रेखीय है, तो कौन सी शर्त सही है?

If the zero of (p(x)=ax+b) is (0) and the polynomial is linear, which condition is correct?

Explanation opens after your attempt
Correct Answer

B. (b=0) और \(a\neq0\)(b=0) and \(a\neq0\)

Explanation

Simple Explanation

शून्यक (0) होने पर (p(0)=b=0) होना चाहिए। रेखीय रहने के लिए \(a\neq0\) भी जरूरी है। / If the zero is (0), then (p(0)=b=0). To remain linear, \(a\neq0\) is also necessary.

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Question 66/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=3x+2) और (q(x)=7x-4), तो (q(x)-2p(x)) की डिग्री क्या है?

If (p(x)=3x+2) and (q(x)=7x-4), what is the degree of (q(x)-2p(x))?

Explanation opens after your attempt
Correct Answer

B. (1)

Explanation

Simple Explanation

(q(x)-2p(x)=7x-4-2(3x+2)=x-8) है। इसकी डिग्री (1) है। / (q(x)-2p(x)=7x-4-2(3x+2)=x-8). Its degree is (1).

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Question 67/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

किस विकल्प में रेखीय बहुपद का शून्यक \(\frac{13}{6}\) है?

Which option has zero \(\frac{13}{6}\) for a linear polynomial?

Explanation opens after your attempt
Correct Answer

A. (6x-13)

Explanation

Simple Explanation

(6x-13=0) से \(x=\frac{13}{6}\) मिलता है। शून्यक के लिए बहुपद को (0) के बराबर रखें। / From (6x-13=0), we get \(x=\frac{13}{6}\). Set the polynomial equal to (0) to find the zero.

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Question 68/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=5x-6), तो (p(x+1)-p(x)) क्या है?

If (p(x)=5x-6), what is (p(x+1)-p(x))?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

(p(x+1)=5x-1) और (p(x)=5x-6) है। अंतर (5) मिलता है। / (p(x+1)=5x-1) and (p(x)=5x-6). The difference is (5).

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Question 69/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=\lambda x+10) और इसका शून्यक (-2) से छोटा है, तो \(\lambda>0\) होने पर कौन सी शर्त सही है?

If (p(x)=\lambda x+10) and its zero is less than (-2), which condition is correct when \(\lambda>0\)?

Explanation opens after your attempt
Correct Answer

A. \(0<\lambda<5\)

Explanation

Simple Explanation

शून्यक \(-\frac{10}{\lambda}\) है। \(-\frac{10}{\lambda}<-2\) और \(\lambda>0\) से \(0<\lambda<5\) मिलता है। / The zero is \(-\frac{10}{\lambda}\). From \(-\frac{10}{\lambda}<-2\) and \(\lambda>0\), we get \(0<\lambda<5\).

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Question 70/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

किस विकल्प में (p(x)=ax+b) का शून्यक (4) होगा?

In which option will (p(x)=ax+b) have zero (4)?

Explanation opens after your attempt
Correct Answer

B. (b=-4a) और \(a\neq0\)(b=-4a) and \(a\neq0\)

Explanation

Simple Explanation

शून्यक (4) होने पर (4a+b=0) होगा। इसलिए (b=-4a) और \(a\neq0\) चाहिए। / If the zero is (4), then (4a+b=0). So (b=-4a) and \(a\neq0\) are needed.

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Question 71/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=x+s) और (q(x)=x-2s), तो (p(x)+q(x)) क्या है?

If (p(x)=x+s) and (q(x)=x-2s), what is (p(x)+q(x))?

Explanation opens after your attempt
Correct Answer

A. (2x-s)

Explanation

Simple Explanation

जोड़ने पर (x+s+x-2s=2x-s) मिलता है। (s) वाले पदों को भी समान पद की तरह मिलाएं। / On adding, (x+s+x-2s=2x-s). Combine the (s)-terms like like terms.

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Question 72/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=x+s) और (q(x)=x-2s), तो (p(x)-q(x)) किस प्रकार का बहुपद है?

If (p(x)=x+s) and (q(x)=x-2s), what type of polynomial is (p(x)-q(x))?

Explanation opens after your attempt
Correct Answer

B. नियतांक बहुपदConstant polynomial

Explanation

Simple Explanation

(p(x)-q(x)=3s) है। (x) के संदर्भ में यह नियतांक बहुपद है। / (p(x)-q(x)=3s). With respect to (x), it is a constant polynomial.

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Question 73/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=3x-7), तो (p(p(3))) का सही मान क्या है?

If (p(x)=3x-7), what is the correct value of (p(p(3)))?

Explanation opens after your attempt
Correct Answer

B. (-1)

Explanation

Simple Explanation

(p(3)=2) और (p(2)=6-7=-1) है। अंदर वाले मान को पहले निकालें। / (p(3)=2) and (p(2)=6-7=-1). Find the inner value first.

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Question 74/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=4x+1), तो (p(p(1))) का मान क्या है?

If (p(x)=4x+1), what is the value of (p(p(1)))?

Explanation opens after your attempt
Correct Answer

C. (21)

Explanation

Simple Explanation

(p(1)=5) और (p(5)=21) है। रचना में अंदर वाला मान पहले निकालें। / (p(1)=5) and (p(5)=21). In composition, find the inner value first.

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Question 75/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

किस मान पर ((n+2)x+3n-1) का शून्यक (1) होगा?

For which value will the zero of ((n+2)x+3n-1) be (1)?

Explanation opens after your attempt
Correct Answer

A. \(n=-\frac{1}{4}\)

Explanation

Simple Explanation

शून्यक (1) होने पर (n+2+3n-1=0) होगा। इससे (4n+1=0) और \(n=-\frac{1}{4}\) मिलता है। / If the zero is (1), then (n+2+3n-1=0). Thus (4n+1=0) and \(n=-\frac{1}{4}\).

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Question 76/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=\frac{x}{4}+a) और (p(8)=7), तो (a) का मान क्या है?

If (p(x)=\frac{x}{4}+a) and (p(8)=7), what is the value of (a)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

(p(8)=2+a=7) से (a=5) मिलता है। भिन्न रूप में पहले (x) का मान रखें। / From (p(8)=2+a=7), we get (a=5). In fractional form, substitute the value of (x) first.

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Question 77/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=3x+a) और (q(x)=2x-5), तो (p(x)+q(x)) का शून्यक (1) होने पर (a) क्या है?

If (p(x)=3x+a) and (q(x)=2x-5), what is (a) if the zero of (p(x)+q(x)) is (1)?

Explanation opens after your attempt
Correct Answer

A. (0)

Explanation

Simple Explanation

(p(x)+q(x)=5x+a-5) है। (x=1) रखने पर (a=0) मिलता है। / (p(x)+q(x)=5x+a-5). Substituting (x=1) gives (a=0).

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Question 78/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

किस मान पर (p(x)=(c-2)x+3c) का शून्यक (-3) होगा?

For which value will the zero of (p(x)=(c-2)x+3c) be (-3)?

Explanation opens after your attempt
Correct Answer

B. (c=-1)

Explanation

Simple Explanation

(-3(c-2)+3c=0) से (6=0) नहीं बल्कि कोई हल नहीं मिलता। इसलिए दिए गए विकल्पों में कोई सही नहीं होना चाहिए। / From (-3(c-2)+3c=0), we get (6=0), so there is no solution. Therefore none of the listed values should be correct.

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Question 79/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=(c-2)x+3c) का शून्यक (-2) है, तो (c) का सही मान क्या है?

If the zero of (p(x)=(c-2)x+3c) is (-2), what is the correct value of (c)?

Explanation opens after your attempt
Correct Answer

B. (c=-4)

Explanation

Simple Explanation

(-2(c-2)+3c=0) से (c+4=0) मिलता है। अतः (c=-4) है। / From (-2(c-2)+3c=0), we get (c+4=0). Hence (c=-4).

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Question 80/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=rx-4) और (p(3)=14), तो (p(-1)) का मान क्या है?

If (p(x)=rx-4) and (p(3)=14), what is the value of (p(-1))?

Explanation opens after your attempt
Correct Answer

C. (-10)

Explanation

Simple Explanation

(3r-4=14) से (r=6) मिलता है। इसलिए (p(-1)=6(-1)-4=-10) है। / From (3r-4=14), we get (r=6). Therefore (p(-1)=6(-1)-4=-10).

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Question 81/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=ax+8) और (p(1)=p(4)-12), तो (a) क्या है?

If (p(x)=ax+8) and (p(1)=p(4)-12), what is (a)?

Explanation opens after your attempt
Correct Answer

C. (4)

Explanation

Simple Explanation

(a+8=(4a+8)-12) से (a=4a-12) मिलता है। इसलिए (a=4) है। / From (a+8=(4a+8)-12), we get (a=4a-12). Therefore (a=4).

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Question 82/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=3x-10), तो (p(a)=a) होने पर (a) क्या है?

If (p(x)=3x-10), what is (a) when (p(a)=a)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

(p(a)=3a-10) है। (3a-10=a) से (a=5) मिलता है। / (p(a)=3a-10). From (3a-10=a), we get (a=5).

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Question 83/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=mx+n), (p(0)=-2) और (p(4)=10), तो (m+n) क्या है?

If (p(x)=mx+n), (p(0)=-2) and (p(4)=10), what is (m+n)?

Explanation opens after your attempt
Correct Answer

A. (1)

Explanation

Simple Explanation

(p(0)=n=-2) और (4m-2=10) से (m=3) मिलता है। इसलिए (m+n=1) है। / (p(0)=n=-2) and (4m-2=10) gives (m=3). Therefore (m+n=1).

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Question 84/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=mx+n), (p(2)=9) और (p(5)=21), तो (m) क्या है?

If (p(x)=mx+n), (p(2)=9) and (p(5)=21), what is (m)?

Explanation opens after your attempt
Correct Answer

B. (4)

Explanation

Simple Explanation

दोनों मान घटाने पर (p(5)-p(2)=3m=12) मिलता है। इसलिए (m=4) है। / Subtracting the two values gives (p(5)-p(2)=3m=12). Therefore (m=4).

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Question 85/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

किस विकल्प में (p(-3)=0) और (p(x)) रेखीय है?

Which option has (p(-3)=0) and (p(x)) is linear?

Explanation opens after your attempt
Correct Answer

C. (p(x)=x+3)

Explanation

Simple Explanation

(x+3) में (x=-3) रखने पर (0) मिलता है। यह डिग्री (1) वाला रेखीय बहुपद है। / Substituting (x=-3) in (x+3) gives (0). It is a linear polynomial of degree (1).

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Question 86/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=4x+9), तो (p(x)+p(-x)) क्या है?

If (p(x)=4x+9), what is (p(x)+p(-x))?

Explanation opens after your attempt
Correct Answer

B. (18)

Explanation

Simple Explanation

(p(-x)=-4x+9) है। जोड़ने पर (4x+9-4x+9=18) मिलता है। / (p(-x)=-4x+9). Adding gives (4x+9-4x+9=18).

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Question 87/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=4x+9), तो (p(x)-p(-x)) क्या है?

If (p(x)=4x+9), what is (p(x)-p(-x))?

Explanation opens after your attempt
Correct Answer

A. (8x)

Explanation

Simple Explanation

(p(-x)=-4x+9) है। घटाने पर (4x+9-(-4x+9)=8x) मिलता है। / (p(-x)=-4x+9). Subtracting gives (4x+9-(-4x+9)=8x).

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Question 88/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

किस मान पर ((s+4)x+2s) का शून्यक (0) होगा?

For which value will the zero of ((s+4)x+2s) be (0)?

Explanation opens after your attempt
Correct Answer

A. (s=0)

Explanation

Simple Explanation

शून्यक (0) होने के लिए नियतांक पद (2s=0) होना चाहिए। (s=0) पर (x) का गुणांक (4) है इसलिए बहुपद रेखीय है। / For the zero to be (0), the constant term (2s=0). At (s=0), the coefficient of (x) is (4), so the polynomial is linear.

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Question 89/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=3x+a) और (q(x)=5x-a), तो (p(x)+q(x)) का शून्यक (2) होने पर (a) क्या है?

If (p(x)=3x+a) and (q(x)=5x-a), what is (a) if the zero of (p(x)+q(x)) is (2)?

Explanation opens after your attempt
Correct Answer

A. कोई मान नहींNo value

Explanation

Simple Explanation

(p(x)+q(x)=8x) है जिसका शून्यक (0) है। इसलिए शून्यक (2) किसी (a) पर नहीं हो सकता। / (p(x)+q(x)=8x), whose zero is (0). Therefore the zero cannot be (2) for any (a).

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Question 90/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=3x+a) और (q(x)=5x-a), तो (q(x)-p(x)) क्या है?

If (p(x)=3x+a) and (q(x)=5x-a), what is (q(x)-p(x))?

Explanation opens after your attempt
Correct Answer

B. (2x-2a)

Explanation

Simple Explanation

(5x-a-(3x+a)=2x-2a) है। घटाते समय कोष्ठक के चिन्ह बदलें। / (5x-a-(3x+a)=2x-2a). Change the signs inside the bracket while subtracting.

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Question 91/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

किस विकल्प में ((2x+3)) और ((x-4)) का गुणनफल रेखीय नहीं है?

Which option correctly says that the product of ((2x+3)) and ((x-4)) is not linear?

Explanation opens after your attempt
Correct Answer

B. क्योंकि डिग्री (2) हैBecause degree is (2)

Explanation

Simple Explanation

((2x+3)(x-4)) में उच्चतम पद \(2x^2\) है। इसलिए गुणनफल की डिग्री (2) है और यह रेखीय नहीं है। / In ((2x+3)(x-4)), the highest term is \(2x^2\). So the product has degree (2) and is not linear.

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Question 92/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=ax-2) और (p(p(0))=10), तो (a) क्या है?

If (p(x)=ax-2) and (p(p(0))=10), what is (a)?

Explanation opens after your attempt
Correct Answer

D. (-6)

Explanation

Simple Explanation

(p(0)=-2) और (p(-2)=-2a-2) है। (-2a-2=10) से (a=-6) मिलता है। / (p(0)=-2) and (p(-2)=-2a-2). From (-2a-2=10), we get (a=-6).

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Question 93/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=x+a) और (p(p(1))=7), तो (a) का मान क्या है?

If (p(x)=x+a) and (p(p(1))=7), what is the value of (a)?

Explanation opens after your attempt
Correct Answer

B. (3)

Explanation

Simple Explanation

(p(1)=1+a) और (p(1+a)=1+2a) है। (1+2a=7) से (a=3) मिलता है। / (p(1)=1+a) and (p(1+a)=1+2a). From (1+2a=7), we get (a=3).

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Question 94/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

किस विकल्प में (p(x)=ax+b) का शून्यक (-5) होगा?

In which option will (p(x)=ax+b) have zero (-5)?

Explanation opens after your attempt
Correct Answer

A. (b=5a) और \(a\neq0\)(b=5a) and \(a\neq0\)

Explanation

Simple Explanation

शून्यक (-5) होने पर (-5a+b=0) होगा। इसलिए (b=5a) और \(a\neq0\) चाहिए। / If the zero is (-5), then (-5a+b=0). So (b=5a) and \(a\neq0\) are needed.

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Question 95/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=6x-1), तो (p(x+3)-p(x-2)) क्या है?

If (p(x)=6x-1), what is (p(x+3)-p(x-2))?

Explanation opens after your attempt
Correct Answer

C. (30)

Explanation

Simple Explanation

(p(x+3)=6x+17) और (p(x-2)=6x-13) है। अंतर (30) है। / (p(x+3)=6x+17) and (p(x-2)=6x-13). The difference is (30).

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Question 96/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=4x-9), तो (p(p(3))) का सही मान क्या है?

If (p(x)=4x-9), what is the correct value of (p(p(3)))?

Explanation opens after your attempt
Correct Answer

A. (3)

Explanation

Simple Explanation

(p(3)=3) और (p(3)=3) ही है। अंदर वाले मान को पहले निकालें। / (p(3)=3) and then (p(3)=3). Find the inner value first.

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Question 97/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=5x+2), तो (p(x+1)+p(x-1)) क्या है?

If (p(x)=5x+2), what is (p(x+1)+p(x-1))?

Explanation opens after your attempt
Correct Answer

A. (10x+4)

Explanation

Simple Explanation

(p(x+1)=5x+7) और (p(x-1)=5x-3) है। जोड़ने पर (10x+4) मिलता है। / (p(x+1)=5x+7) and (p(x-1)=5x-3). Adding gives (10x+4).

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Question 98/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

किस मान पर (\(r^2-2r\)x+9) रेखीय बहुपद नहीं रहेगा?

For which value will (\(r^2-2r\)x+9) not remain a linear polynomial?

Explanation opens after your attempt
Correct Answer

A. (r=0) या (r=2)(r=0) or (r=2)

Explanation

Simple Explanation

रेखीय न रहने के लिए (x) का गुणांक (0) होना चाहिए। (r-2-2r=r(r-2)=0) से (r=0) या (r=2) मिलता है। / For it not to be linear, the coefficient of (x) must be (0). (r-2-2r=r(r-2)=0) gives (r=0) or (r=2).

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Question 99/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=ax+3) और (p(p(0))=18), तो (a) का मान क्या है?

If (p(x)=ax+3) and (p(p(0))=18), what is the value of (a)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

(p(0)=3) और (p(3)=3a+3) है। (3a+3=18) से (a=5) मिलता है। / (p(0)=3) and (p(3)=3a+3). From (3a+3=18), we get (a=5).

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Question 100/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 34

यदि (p(x)=mx+n), (p(-2)=1) और (p(2)=13), तो (m-n) क्या है?

If (p(x)=mx+n), (p(-2)=1) and (p(2)=13), what is (m-n)?

Explanation opens after your attempt
Correct Answer

C. (2)

Explanation

Simple Explanation

दोनों समीकरणों से (4m=12) इसलिए (m=3) है। (2m+n=13) से (n=7) और (m-n=-4) मिलता है, जो विकल्पों में नहीं है। / From the two equations, (4m=12), so (m=3). From (2m+n=13), (n=7) and (m-n=-4), which is not in the options.

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Question 101/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

सरल करने के बाद (7(2x-5)-5(3x+4)) कौन सा बहुपद बनेगा?

After simplifying (7(2x-5)-5(3x+4)), which polynomial is obtained?

Explanation opens after your attempt
Correct Answer

A. (-x-55)

Explanation

Simple Explanation

(14x-35-15x-20=-x-55) है। कोष्ठक खोलकर समान पद मिलाएं। / (14x-35-15x-20=-x-55). Open brackets and combine like terms.

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Question 102/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

किस मान पर (\(a^2-9\)x+11) रेखीय बहुपद नहीं रहेगा?

For which value will (\(a^2-9\)x+11) not remain a linear polynomial?

Explanation opens after your attempt
Correct Answer

B. (a=3) या (a=-3)(a=3) or (a=-3)

Explanation

Simple Explanation

रेखीय न रहने के लिए (x) का गुणांक (0) होना चाहिए। \(a^2-9=0\) से \(a=\pm3\) मिलता है। / For it not to be linear, the coefficient of (x) must be (0). From \(a^2-9=0\), \(a=\pm3\).

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Question 103/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=(k-4)x+15) का शून्यक (-5) है, तो (k) का मान क्या है?

If the zero of (p(x)=(k-4)x+15) is (-5), what is the value of (k)?

Explanation opens after your attempt
Correct Answer

C. (7)

Explanation

Simple Explanation

(-5(k-4)+15=0) से (k=7) मिलता है। शून्यक को बहुपद में रखकर (0) करें। / From (-5(k-4)+15=0), we get (k=7). Substitute the zero into the polynomial and set it to (0).

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Question 104/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=2x+5) और (q(x)=3x-7), तो (4p(x)-3q(x)) क्या है?

If (p(x)=2x+5) and (q(x)=3x-7), what is (4p(x)-3q(x))?

Explanation opens after your attempt
Correct Answer

D. (-x+41)

Explanation

Simple Explanation

(4(2x+5)-3(3x-7)=-x+41) है। गुणा करके समान पदों को मिलाएं। / (4(2x+5)-3(3x-7)=-x+41). Multiply and then combine like terms.

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Question 105/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

किस मान पर ((2m+3)x-14) का शून्यक (2) होगा?

For which value will the zero of ((2m+3)x-14) be (2)?

Explanation opens after your attempt
Correct Answer

A. (m=2)

Explanation

Simple Explanation

शून्यक (2) होने पर (2(2m+3)-14=0) होगा। इससे (m=2) मिलता है। / If the zero is (2), then (2(2m+3)-14=0). This gives (m=2).

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Question 106/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=ax+b) का शून्यक (5) है और (a=-2), तो (b) क्या है?

If the zero of (p(x)=ax+b) is (5) and (a=-2), what is (b)?

Explanation opens after your attempt
Correct Answer

A. (10)

Explanation

Simple Explanation

(p(5)=0) से (5a+b=0) होगा। (a=-2) रखने पर (b=10) मिलता है। / From (p(5)=0), (5a+b=0). Substituting (a=-2) gives (b=10).

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Question 107/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=6x+c) और (p(5)=p(2)+18), तो (c) के बारे में क्या सही है?

If (p(x)=6x+c) and (p(5)=p(2)+18), what is correct about (c)?

Explanation opens after your attempt
Correct Answer

C. हर (c) सही हैEvery (c) is valid

Explanation

Simple Explanation

(p(5)-p(2)=(30+c)-(12+c)=18) है। इसलिए यह शर्त हर (c) के लिए सही है। / (p(5)-p(2)=(30+c)-(12+c)=18). So the condition is true for every (c).

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Question 108/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

किस विकल्प में रेखीय बहुपद का शून्यक \(-\frac{7}{9}\) है?

Which option has zero \(-\frac{7}{9}\) for a linear polynomial?

Explanation opens after your attempt
Correct Answer

D. (9x+7)

Explanation

Simple Explanation

(9x+7=0) से \(x=-\frac{7}{9}\) मिलता है। भिन्न शून्यक में चिन्ह और हर ध्यान रखें। / From (9x+7=0), we get \(x=-\frac{7}{9}\). Pay attention to the sign and denominator in fractional zeros.

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Question 109/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=\frac{4}{9}x-8), तो किस मान पर (p(x)=0) होगा?

If (p(x)=\frac{4}{9}x-8), for which value will (p(x)=0)?

Explanation opens after your attempt
Correct Answer

A. (x=18)

Explanation

Simple Explanation

\(\frac{4}{9}x-8=0\) से \(\frac{4}{9}x=8\) और (x=18) मिलता है। भिन्न गुणांक में उलटा गुणा करें। / From \(\frac{4}{9}x-8=0\), \(\frac{4}{9}x=8\) and (x=18). With a fractional coefficient, multiply by the reciprocal.

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Question 110/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=x+6) और (q(x)=x-2), तो (p(x)q(x)) की डिग्री क्या है?

If (p(x)=x+6) and (q(x)=x-2), what is the degree of (p(x)q(x))?

Explanation opens after your attempt
Correct Answer

B. (2)

Explanation

Simple Explanation

((x+6)(x-2)) में उच्चतम पद \(x^2\) है। इसलिए गुणनफल की डिग्री (2) है। / In ((x+6)(x-2)), the highest term is \(x^2\). Therefore the product has degree (2).

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Question 111/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=5x-8), तो (p(x-3)) क्या है?

If (p(x)=5x-8), what is (p(x-3))?

Explanation opens after your attempt
Correct Answer

A. (5x-23)

Explanation

Simple Explanation

(p(x-3)=5(x-3)-8=5x-23) है। (x) की जगह पूरा (x-3) रखें। / (p(x-3)=5(x-3)-8=5x-23). Substitute the whole (x-3) in place of (x).

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Question 112/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=13-4x), तो (p(2x)) कौन सा है?

If (p(x)=13-4x), which is (p(2x))?

Explanation opens after your attempt
Correct Answer

B. (13-8x)

Explanation

Simple Explanation

(p(2x)=13-4(2x)=13-8x) है। प्रतिस्थापन करते समय पूरे (2x) को रखें। / (p(2x)=13-4(2x)=13-8x). While substituting, use the whole (2x).

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Question 113/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

किस मान पर (\(t^2-6t+8\)x+(t-2)) रेखीय बहुपद नहीं रहेगा?

For which value will (\(t^2-6t+8\)x+(t-2)) not remain a linear polynomial?

Explanation opens after your attempt
Correct Answer

A. (t=2) या (t=4)(t=2) or (t=4)

Explanation

Simple Explanation

रेखीय होने के लिए \(t^2-6t+8\neq0\) चाहिए। \(t^2-6t+8=0\) से (t=2) या (t=4) मिलता है। / For it to be linear, \(t^2-6t+8\neq0\) is needed. From \(t^2-6t+8=0\), (t=2) or (t=4).

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Question 114/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=kx+7) और (p(4)=p(-2)), तो (p(x)) रेखीय कब रहेगा?

If (p(x)=kx+7) and (p(4)=p(-2)), when will (p(x)) remain linear?

Explanation opens after your attempt
Correct Answer

C. कभी नहींNever

Explanation

Simple Explanation

(p(4)=p(-2)) से (4k+7=-2k+7) और (k=0) मिलता है। (k=0) पर बहुपद रेखीय नहीं रहता। / From (p(4)=p(-2)), (4k+7=-2k+7), so (k=0). At (k=0), the polynomial is not linear.

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Question 115/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=ax+b) का शून्यक (0) है और (p(x)) रेखीय है, तो कौन सी शर्त सही है?

If the zero of (p(x)=ax+b) is (0) and (p(x)) is linear, which condition is correct?

Explanation opens after your attempt
Correct Answer

D. (b=0) और \(a\neq0\)(b=0) and \(a\neq0\)

Explanation

Simple Explanation

शून्यक (0) होने पर (p(0)=b=0) होना चाहिए। रेखीय रहने के लिए \(a\neq0\) भी जरूरी है। / If the zero is (0), then (p(0)=b=0). To remain linear, \(a\neq0\) is also necessary.

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Question 116/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=4x+1) और (q(x)=9x-3), तो (q(x)-2p(x)) की डिग्री क्या है?

If (p(x)=4x+1) and (q(x)=9x-3), what is the degree of (q(x)-2p(x))?

Explanation opens after your attempt
Correct Answer

B. (1)

Explanation

Simple Explanation

(q(x)-2p(x)=9x-3-2(4x+1)=x-5) है। इसकी डिग्री (1) है। / (q(x)-2p(x)=9x-3-2(4x+1)=x-5). Its degree is (1).

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Question 117/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

किस विकल्प में रेखीय बहुपद का शून्यक \(\frac{17}{8}\) है?

Which option has zero \(\frac{17}{8}\) for a linear polynomial?

Explanation opens after your attempt
Correct Answer

A. (8x-17)

Explanation

Simple Explanation

(8x-17=0) से \(x=\frac{17}{8}\) मिलता है। शून्यक के लिए बहुपद को (0) के बराबर रखें। / From (8x-17=0), we get \(x=\frac{17}{8}\). Set the polynomial equal to (0) to find the zero.

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Question 118/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=7x-10), तो (p(x+1)-p(x)) क्या है?

If (p(x)=7x-10), what is (p(x+1)-p(x))?

Explanation opens after your attempt
Correct Answer

B. (7)

Explanation

Simple Explanation

(p(x+1)=7x-3) और (p(x)=7x-10) है। अंतर (7) मिलता है। / (p(x+1)=7x-3) and (p(x)=7x-10). The difference is (7).

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Question 119/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=\lambda x+12) और इसका शून्यक (-3) से बड़ा है, तो \(\lambda>0\) होने पर कौन सी शर्त सही है?

If (p(x)=\lambda x+12) and its zero is greater than (-3), which condition is correct when \(\lambda>0\)?

Explanation opens after your attempt
Correct Answer

C. \(\lambda>4\)

Explanation

Simple Explanation

शून्यक \(-\frac{12}{\lambda}\) है। \(-\frac{12}{\lambda}>-3\) और \(\lambda>0\) से \(\lambda>4\) मिलता है। / The zero is \(-\frac{12}{\lambda}\). From \(-\frac{12}{\lambda}>-3\) and \(\lambda>0\), we get \(\lambda>4\).

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Question 120/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

किस विकल्प में (p(x)=ax+b) का शून्यक (6) होगा?

In which option will (p(x)=ax+b) have zero (6)?

Explanation opens after your attempt
Correct Answer

D. (b=-6a) और \(a\neq0\)(b=-6a) and \(a\neq0\)

Explanation

Simple Explanation

शून्यक (6) होने पर (6a+b=0) होगा। इसलिए (b=-6a) और \(a\neq0\) चाहिए। / If the zero is (6), then (6a+b=0). So (b=-6a) and \(a\neq0\) are needed.

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Question 121/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=x+2s) और (q(x)=x-3s), तो (p(x)+q(x)) क्या है?

If (p(x)=x+2s) and (q(x)=x-3s), what is (p(x)+q(x))?

Explanation opens after your attempt
Correct Answer

A. (2x-s)

Explanation

Simple Explanation

जोड़ने पर (x+2s+x-3s=2x-s) मिलता है। (s) वाले पदों को भी समान पद की तरह मिलाएं। / On adding, (x+2s+x-3s=2x-s). Combine the (s)-terms like like terms.

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Question 122/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=x+2s) और (q(x)=x-3s), तो (p(x)-q(x)) किस प्रकार का बहुपद है?

If (p(x)=x+2s) and (q(x)=x-3s), what type of polynomial is (p(x)-q(x))?

Explanation opens after your attempt
Correct Answer

B. नियतांक बहुपदConstant polynomial

Explanation

Simple Explanation

(p(x)-q(x)=5s) है। (x) के संदर्भ में यह नियतांक बहुपद है। / (p(x)-q(x)=5s). With respect to (x), it is a constant polynomial.

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Question 123/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=4x-11), तो (p(p(3))) का सही मान क्या है?

If (p(x)=4x-11), what is the correct value of (p(p(3)))?

Explanation opens after your attempt
Correct Answer

B. (-7)

Explanation

Simple Explanation

(p(3)=1) और (p(1)=4-11=-7) है। अंदर वाले मान को पहले निकालें। / (p(3)=1) and (p(1)=4-11=-7). Find the inner value first.

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Question 124/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=5x+2), तो (p(p(0))) का मान क्या है?

If (p(x)=5x+2), what is the value of (p(p(0)))?

Explanation opens after your attempt
Correct Answer

C. (12)

Explanation

Simple Explanation

(p(0)=2) और (p(2)=12) है। रचना में अंदर वाला मान पहले निकालें। / (p(0)=2) and (p(2)=12). In composition, find the inner value first.

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Question 125/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

किस मान पर ((n-3)x+2n+1) का शून्यक (1) होगा?

For which value will the zero of ((n-3)x+2n+1) be (1)?

Explanation opens after your attempt
Correct Answer

A. \(n=\frac{2}{3}\)

Explanation

Simple Explanation

शून्यक (1) होने पर (n-3+2n+1=0) होगा। इससे (3n-2=0) और \(n=\frac{2}{3}\) मिलता है। / If the zero is (1), then (n-3+2n+1=0). Thus (3n-2=0) and \(n=\frac{2}{3}\).

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Question 126/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=\frac{x}{5}+a) और (p(15)=11), तो (a) का मान क्या है?

If (p(x)=\frac{x}{5}+a) and (p(15)=11), what is the value of (a)?

Explanation opens after your attempt
Correct Answer

B. (8)

Explanation

Simple Explanation

(p(15)=3+a=11) से (a=8) मिलता है। भिन्न रूप में पहले (x) का मान रखें। / From (p(15)=3+a=11), we get (a=8). In fractional form, substitute the value of (x) first.

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Question 127/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=4x+a) और (q(x)=x-6), तो (p(x)+q(x)) का शून्यक (2) होने पर (a) क्या है?

If (p(x)=4x+a) and (q(x)=x-6), what is (a) if the zero of (p(x)+q(x)) is (2)?

Explanation opens after your attempt
Correct Answer

A. (-4)

Explanation

Simple Explanation

(p(x)+q(x)=5x+a-6) है। (x=2) रखने पर (10+a-6=0) से (a=-4) मिलता है। / (p(x)+q(x)=5x+a-6). Substituting (x=2) gives (10+a-6=0), so (a=-4).

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Question 128/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

किस मान पर (p(x)=(c+4)x+2c) का शून्यक (-2) होगा?

For which value will the zero of (p(x)=(c+4)x+2c) be (-2)?

Explanation opens after your attempt
Correct Answer

A. कोई मान नहींNo value

Explanation

Simple Explanation

(-2(c+4)+2c=0) से (-8=0) जैसा असंभव परिणाम मिलता है। इसलिए कोई मान नहीं है। / From (-2(c+4)+2c=0), we get the impossible result (-8=0). Therefore there is no value.

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Question 129/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=(c+4)x+2c) का शून्यक (-1) है, तो (c) का सही मान क्या है?

If the zero of (p(x)=(c+4)x+2c) is (-1), what is the correct value of (c)?

Explanation opens after your attempt
Correct Answer

A. (c=4)

Explanation

Simple Explanation

(-(c+4)+2c=0) से (c-4=0) मिलता है। अतः (c=4) है। / From (-(c+4)+2c=0), we get (c-4=0). Hence (c=4).

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Question 130/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=rx+3) और (p(4)=23), तो (p(-2)) का मान क्या है?

If (p(x)=rx+3) and (p(4)=23), what is the value of (p(-2))?

Explanation opens after your attempt
Correct Answer

B. (-7)

Explanation

Simple Explanation

(4r+3=23) से (r=5) मिलता है। इसलिए (p(-2)=5(-2)+3=-7) है। / From (4r+3=23), we get (r=5). Therefore (p(-2)=5(-2)+3=-7).

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Question 131/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=ax-9) और (p(2)=p(6)-20), तो (a) क्या है?

If (p(x)=ax-9) and (p(2)=p(6)-20), what is (a)?

Explanation opens after your attempt
Correct Answer

C. (5)

Explanation

Simple Explanation

(2a-9=(6a-9)-20) से (2a=6a-20) मिलता है। इसलिए (a=5) है। / From (2a-9=(6a-9)-20), we get (2a=6a-20). Therefore (a=5).

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Question 132/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=4x-15), तो (p(a)=a) होने पर (a) क्या है?

If (p(x)=4x-15), what is (a) when (p(a)=a)?

Explanation opens after your attempt
Correct Answer

C. (5)

Explanation

Simple Explanation

(p(a)=4a-15) है। (4a-15=a) से (a=5) मिलता है। / (p(a)=4a-15). From (4a-15=a), we get (a=5).

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Question 133/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=mx+n), (p(0)=5) और (p(3)=14), तो (m+n) क्या है?

If (p(x)=mx+n), (p(0)=5) and (p(3)=14), what is (m+n)?

Explanation opens after your attempt
Correct Answer

C. (8)

Explanation

Simple Explanation

(p(0)=n=5) और (3m+5=14) से (m=3) मिलता है। इसलिए (m+n=8) है। / (p(0)=n=5) and (3m+5=14) gives (m=3). Therefore (m+n=8).

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Question 134/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=mx+n), (p(-1)=2) और (p(2)=11), तो (m) क्या है?

If (p(x)=mx+n), (p(-1)=2) and (p(2)=11), what is (m)?

Explanation opens after your attempt
Correct Answer

B. (3)

Explanation

Simple Explanation

दोनों मान घटाने पर (p(2)-p(-1)=3m=9) मिलता है। इसलिए (m=3) है। / Subtracting the two values gives (p(2)-p(-1)=3m=9). Therefore (m=3).

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Question 135/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

किस विकल्प में (p(4)=0) और (p(x)) रेखीय है?

Which option has (p(4)=0) and (p(x)) is linear?

Explanation opens after your attempt
Correct Answer

D. (p(x)=x-4)

Explanation

Simple Explanation

(x-4) में (x=4) रखने पर (0) मिलता है। यह डिग्री (1) वाला रेखीय बहुपद है। / Substituting (x=4) in (x-4) gives (0). It is a linear polynomial of degree (1).

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Question 136/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=5x-12), तो (p(x)+p(-x)) क्या है?

If (p(x)=5x-12), what is (p(x)+p(-x))?

Explanation opens after your attempt
Correct Answer

B. (-24)

Explanation

Simple Explanation

(p(-x)=-5x-12) है। जोड़ने पर (5x-12-5x-12=-24) मिलता है। / (p(-x)=-5x-12). Adding gives (5x-12-5x-12=-24).

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Question 137/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=5x-12), तो (p(x)-p(-x)) क्या है?

If (p(x)=5x-12), what is (p(x)-p(-x))?

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Correct Answer

A. (10x)

Explanation

Simple Explanation

(p(-x)=-5x-12) है। घटाने पर (5x-12-(-5x-12)=10x) मिलता है। / (p(-x)=-5x-12). Subtracting gives (5x-12-(-5x-12)=10x).

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Question 138/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

किस मान पर ((s-5)x+3s) का शून्यक (0) होगा?

For which value will the zero of ((s-5)x+3s) be (0)?

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Correct Answer

A. (s=0)

Explanation

Simple Explanation

शून्यक (0) होने के लिए नियतांक पद (3s=0) होना चाहिए। (s=0) पर (x) का गुणांक (-5) है इसलिए बहुपद रेखीय है। / For the zero to be (0), the constant term (3s=0). At (s=0), the coefficient of (x) is (-5), so the polynomial is linear.

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Question 139/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=4x+a) और (q(x)=6x-a), तो (p(x)+q(x)) का शून्यक (-2) होने पर (a) क्या है?

If (p(x)=4x+a) and (q(x)=6x-a), what is (a) if the zero of (p(x)+q(x)) is (-2)?

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Correct Answer

A. कोई मान नहींNo value

Explanation

Simple Explanation

(p(x)+q(x)=10x) है जिसका शून्यक (0) है। इसलिए शून्यक (-2) किसी (a) पर नहीं हो सकता। / (p(x)+q(x)=10x), whose zero is (0). Therefore the zero cannot be (-2) for any (a).

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Question 140/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=4x+a) और (q(x)=6x-a), तो (q(x)-p(x)) क्या है?

If (p(x)=4x+a) and (q(x)=6x-a), what is (q(x)-p(x))?

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Correct Answer

B. (2x-2a)

Explanation

Simple Explanation

(6x-a-(4x+a)=2x-2a) है। घटाते समय कोष्ठक के चिन्ह बदलें। / (6x-a-(4x+a)=2x-2a). Change the signs inside the bracket while subtracting.

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Question 141/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

किस विकल्प में ((3x-2)) और ((x+5)) का गुणनफल रेखीय नहीं है?

Which option correctly says that the product of ((3x-2)) and ((x+5)) is not linear?

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Correct Answer

B. क्योंकि डिग्री (2) हैBecause degree is (2)

Explanation

Simple Explanation

((3x-2)(x+5)) में उच्चतम पद \(3x^2\) है। इसलिए गुणनफल की डिग्री (2) है और यह रेखीय नहीं है। / In ((3x-2)(x+5)), the highest term is \(3x^2\). So the product has degree (2) and is not linear.

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Question 142/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=ax+4) और (p(p(0))=28), तो (a) क्या है?

If (p(x)=ax+4) and (p(p(0))=28), what is (a)?

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Correct Answer

C. (6)

Explanation

Simple Explanation

(p(0)=4) और (p(4)=4a+4) है। (4a+4=28) से (a=6) मिलता है। / (p(0)=4) and (p(4)=4a+4). From (4a+4=28), we get (a=6).

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Question 143/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=x+a) और (p(p(2))=10), तो (a) का मान क्या है?

If (p(x)=x+a) and (p(p(2))=10), what is the value of (a)?

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Correct Answer

C. (4)

Explanation

Simple Explanation

(p(2)=2+a) और (p(2+a)=2+2a) है। (2+2a=10) से (a=4) मिलता है। / (p(2)=2+a) and (p(2+a)=2+2a). From (2+2a=10), we get (a=4).

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Question 144/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=mx+n) और (p(-2)=p(1)), तो (p(x)) रेखीय कब हो सकता है?

If (p(x)=mx+n) and (p(-2)=p(1)), when can (p(x)) be linear?

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Correct Answer

C. कभी नहींNever

Explanation

Simple Explanation

(p(-2)=p(1)) से (-2m+n=m+n) और (m=0) मिलता है। (m=0) पर बहुपद रेखीय नहीं रहता। / From (p(-2)=p(1)), (-2m+n=m+n), so (m=0). At (m=0), the polynomial is not linear.

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Question 145/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

किस विकल्प में (p(x)=ax+b) का शून्यक (-7) होगा?

In which option will (p(x)=ax+b) have zero (-7)?

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Correct Answer

A. (b=7a) और \(a\neq0\)(b=7a) and \(a\neq0\)

Explanation

Simple Explanation

शून्यक (-7) होने पर (-7a+b=0) होगा। इसलिए (b=7a) और \(a\neq0\) चाहिए। / If the zero is (-7), then (-7a+b=0). So (b=7a) and \(a\neq0\) are needed.

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Question 146/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=8x-3), तो (p(x+2)-p(x-1)) क्या है?

If (p(x)=8x-3), what is (p(x+2)-p(x-1))?

Explanation opens after your attempt
Correct Answer

C. (24)

Explanation

Simple Explanation

(p(x+2)=8x+13) और (p(x-1)=8x-11) है। अंतर (24) है। / (p(x+2)=8x+13) and (p(x-1)=8x-11). The difference is (24).

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Question 147/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=5x-14), तो (p(p(3))) का सही मान क्या है?

If (p(x)=5x-14), what is the correct value of (p(p(3)))?

Explanation opens after your attempt
Correct Answer

B. (-9)

Explanation

Simple Explanation

(p(3)=1) और (p(1)=5-14=-9) है। अंदर वाले मान को पहले निकालें। / (p(3)=1) and (p(1)=5-14=-9). Find the inner value first.

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Question 148/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=6x+a) और (p(p(0))=42), तो (a) का मान क्या है?

If (p(x)=6x+a) and (p(p(0))=42), what is the value of (a)?

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Correct Answer

A. (6)

Explanation

Simple Explanation

(p(0)=a) और (p(a)=6a+a=7a) है। (7a=42) से (a=6) मिलता है। / (p(0)=a) and (p(a)=6a+a=7a). From (7a=42), we get (a=6).

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Question 149/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=mx+n), (p(-1)=4) और (p(3)=20), तो (m+n) क्या है?

If (p(x)=mx+n), (p(-1)=4) and (p(3)=20), what is (m+n)?

Explanation opens after your attempt
Correct Answer

C. (12)

Explanation

Simple Explanation

दोनों समीकरण घटाने पर (4m=16) से (m=4) मिलता है। फिर (-m+n=4) से (n=8) और (m+n=12) है। / Subtracting the two equations gives (4m=16), so (m=4). Then (-m+n=4) gives (n=8), so (m+n=12).

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Question 150/150 Hard Mathematics Introduction to Polynomials Linear polynomials Class 9 Level 35

यदि (p(x)=9x-5), तो (p(x+1)+p(x-2)) क्या है?

If (p(x)=9x-5), what is (p(x+1)+p(x-2))?

Explanation opens after your attempt
Correct Answer

D. (18x-19)

Explanation

Simple Explanation

(p(x+1)=9x+4) और (p(x-2)=9x-23) है। जोड़ने पर (18x-19) मिलता है। / (p(x+1)=9x+4) and (p(x-2)=9x-23). Adding gives (18x-19).

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