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?
#polynomial
#linear
#simplification
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A (2x-32)
B (34x-32)
C (2x+8)
D (18x-20)
Explanation opens after your attempt
Correct Answer
A. (2x-32)
Step 1
Concept
(18x-12-16x-20=2x-32). Open brackets and combine like terms.
Step 2
Why this answer is correct
The correct answer is A. (2x-32). (18x-12-16x-20=2x-32). Open brackets and combine like terms.
Step 3
Exam Tip
(18x-12-16x-20=2x-32) है। कोष्ठक खोलकर समान पद मिलाएं।
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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?
#polynomial
#linear
#parameter
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A (b=0)
B (b=5) या (b=-5) / (b=5) or (b=-5)
C (b=25)
D (b=1)
Explanation opens after your attempt
Correct Answer
B. (b=5) या (b=-5) / (b=5) or (b=-5)
Step 1
Concept
For it not to be linear, the coefficient of (x) must be (0). From \(b^2-25=0\), \(b=\pm5\).
Step 2
Why this answer is correct
The correct answer is B. (b=5) या (b=-5) / (b=5) or (b=-5). For it not to be linear, the coefficient of (x) must be (0). From \(b^2-25=0\), \(b=\pm5\).
Step 3
Exam Tip
रेखीय न रहने के लिए (x) का गुणांक (0) होना चाहिए। \(b^2-25=0\) से \(b=\pm5\) मिलता है।
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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)?
#polynomial
#linear
#zero_parameter
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A (0)
B (3)
C (6)
D (12)
Explanation opens after your attempt
Step 1
Concept
From (4(k+3)-12=0), we get (k=0). Substitute the zero into the polynomial and set it to (0).
Step 2
Why this answer is correct
The correct answer is A. (0). From (4(k+3)-12=0), we get (k=0). Substitute the zero into the polynomial and set it to (0).
Step 3
Exam Tip
(4(k+3)-12=0) से (k=0) मिलता है। शून्यक को बहुपद में रखकर (0) करें।
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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))?
#polynomial
#linear
#combination
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A (2x-36)
B (22x-36)
C (2x+6)
D (12x-15)
Explanation opens after your attempt
Correct Answer
A. (2x-36)
Step 1
Concept
(3(4x-7)-5(2x+3)=2x-36). Multiply and then combine like terms.
Step 2
Why this answer is correct
The correct answer is A. (2x-36). (3(4x-7)-5(2x+3)=2x-36). Multiply and then combine like terms.
Step 3
Exam Tip
(3(4x-7)-5(2x+3)=2x-36) है। गुणा करके समान पदों को मिलाएं।
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किस मान पर ((3m+1)x+8) का शून्यक (-2) होगा?
For which value will the zero of ((3m+1)x+8) be (-2)?
#polynomial
#linear
#parameter_zero
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A (m=1)
B \(m=\frac{1}{3}\)
C (m=-1)
D (m=2)
Explanation opens after your attempt
Step 1
Concept
If the zero is (-2), then (-2(3m+1)+8=0). This gives (m=1).
Step 2
Why this answer is correct
The correct answer is A. (m=1). If the zero is (-2), then (-2(3m+1)+8=0). This gives (m=1).
Step 3
Exam Tip
शून्यक (-2) होने पर (-2(3m+1)+8=0) होगा। इससे (m=1) मिलता है।
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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)?
#polynomial
#linear
#general_form
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A (6)
B (-6)
C (3)
D (-3)
Explanation opens after your attempt
Step 1
Concept
From (p(-3)=0), (-3a+b=0). Substituting (a=2) gives (b=6).
Step 2
Why this answer is correct
The correct answer is A. (6). From (p(-3)=0), (-3a+b=0). Substituting (a=2) gives (b=6).
Step 3
Exam Tip
(p(-3)=0) से (-3a+b=0) होगा। (a=2) रखने पर (b=6) मिलता है।
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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)?
#polynomial
#linear
#condition_check
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A केवल (c=0) / Only (c=0)
B हर (c) सही है / Every (c) is valid
C ऐसा कोई (c) नहीं / No such (c)
D केवल (c=15) / Only (c=15)
Explanation opens after your attempt
Correct Answer
B. हर (c) सही है / Every (c) is valid
Step 1
Concept
(p(4)-p(1)=(20+c)-(5+c)=15). So the condition is true for every (c).
Step 2
Why this answer is correct
The correct answer is B. हर (c) सही है / Every (c) is valid. (p(4)-p(1)=(20+c)-(5+c)=15). So the condition is true for every (c).
Step 3
Exam Tip
(p(4)-p(1)=(20+c)-(5+c)=15) है। इसलिए यह शर्त हर (c) के लिए सही है।
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किस विकल्प में रेखीय बहुपद का शून्यक \(-\frac{5}{8}\) है?
Which option has zero \(-\frac{5}{8}\) for a linear polynomial?
#polynomial
#linear
#fraction_zero
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A (8x-5)
B (5x+8)
C (8x+5)
D \(x+\frac{8}{5}\)
Explanation opens after your attempt
Step 1
Concept
From (8x+5=0), we get \(x=-\frac{5}{8}\). Pay attention to the sign and denominator in fractional zeros.
Step 2
Why this answer is correct
The correct answer is C. (8x+5). From (8x+5=0), we get \(x=-\frac{5}{8}\). Pay attention to the sign and denominator in fractional zeros.
Step 3
Exam Tip
(8x+5=0) से \(x=-\frac{5}{8}\) मिलता है। भिन्न शून्यक में चिन्ह और हर ध्यान रखें।
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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)?
#polynomial
#linear
#fraction_equation
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A (x=14)
B (x=21)
C (x=27)
D (x=63)
Explanation opens after your attempt
Step 1
Concept
From \(\frac{3}{7}x-9=0\), \(\frac{3}{7}x=9\) and (x=21). With a fractional coefficient, multiply by the reciprocal.
Step 2
Why this answer is correct
The correct answer is B. (x=21). From \(\frac{3}{7}x-9=0\), \(\frac{3}{7}x=9\) and (x=21). With a fractional coefficient, multiply by the reciprocal.
Step 3
Exam Tip
\(\frac{3}{7}x-9=0\) से \(\frac{3}{7}x=9\) और (x=21) मिलता है। भिन्न गुणांक में उलटा गुणा करें।
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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))?
#polynomial
#linear
#product_degree
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A (1)
B (2)
C (3)
D (0)
Explanation opens after your attempt
Step 1
Concept
In ((x-3)(x+8)), the highest term is \(x^2\). Therefore the product has degree (2).
Step 2
Why this answer is correct
The correct answer is B. (2). In ((x-3)(x+8)), the highest term is \(x^2\). Therefore the product has degree (2).
Step 3
Exam Tip
((x-3)(x+8)) में उच्चतम पद \(x^2\) है। इसलिए गुणनफल की डिग्री (2) है।
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यदि (p(x)=4x-9), तो (p(x+2)) क्या है?
If (p(x)=4x-9), what is (p(x+2))?
#polynomial
#linear
#composition
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A (4x-7)
B (4x-1)
C (4x+2)
D (x-7)
Explanation opens after your attempt
Step 1
Concept
(p(x+2)=4(x+2)-9=4x-1). Substitute the whole (x+2) in place of (x).
Step 2
Why this answer is correct
The correct answer is B. (4x-1). (p(x+2)=4(x+2)-9=4x-1). Substitute the whole (x+2) in place of (x).
Step 3
Exam Tip
(p(x+2)=4(x+2)-9=4x-1) है। (x) की जगह पूरा (x+2) रखें।
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यदि (p(x)=11-2x), तो (p(3x)) कौन सा है?
If (p(x)=11-2x), which is (p(3x))?
#polynomial
#linear
#substitution
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A (33-2x)
B (11-6x)
C (11-2x)
D (33-6x)
Explanation opens after your attempt
Correct Answer
B. (11-6x)
Step 1
Concept
(p(3x)=11-2(3x)=11-6x). While substituting, use the whole (3x).
Step 2
Why this answer is correct
The correct answer is B. (11-6x). (p(3x)=11-2(3x)=11-6x). While substituting, use the whole (3x).
Step 3
Exam Tip
(p(3x)=11-2(3x)=11-6x) है। प्रतिस्थापन करते समय पूरे (3x) को रखें।
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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?
#polynomial
#linear
#parameter_condition
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A (t=1) या (t=3) / (t=1) or (t=3)
B (t=0)
C (t=4)
D (t=-1)
Explanation opens after your attempt
Correct Answer
A. (t=1) या (t=3) / (t=1) or (t=3)
Step 1
Concept
For it to be linear, \(t^2-4t+3\neq0\) is needed. From \(t^2-4t+3=0\), (t=1) or (t=3).
Step 2
Why this answer is correct
The correct answer is A. (t=1) या (t=3) / (t=1) or (t=3). For it to be linear, \(t^2-4t+3\neq0\) is needed. From \(t^2-4t+3=0\), (t=1) or (t=3).
Step 3
Exam Tip
रेखीय होने के लिए \(t^2-4t+3\neq0\) चाहिए। \(t^2-4t+3=0\) से (t=1) या (t=3) मिलता है।
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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?
#polynomial
#linear
#condition_check
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A जब (k=0) / When (k=0)
B जब (k=5) / When (k=5)
C कभी नहीं / Never
D हर (k) पर / For every (k)
Explanation opens after your attempt
Correct Answer
C. कभी नहीं / Never
Step 1
Concept
From (p(3)=p(-1)), (3k-5=-k-5), so (k=0). At (k=0), the polynomial is not linear.
Step 2
Why this answer is correct
The correct answer is C. कभी नहीं / Never. From (p(3)=p(-1)), (3k-5=-k-5), so (k=0). At (k=0), the polynomial is not linear.
Step 3
Exam Tip
(p(3)=p(-1)) से (3k-5=-k-5) और (k=0) मिलता है। (k=0) पर बहुपद रेखीय नहीं रहता।
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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?
#polynomial
#linear
#general_condition
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A (a=0) और (b=0) / (a=0) and (b=0)
B (b=0) और \(a\neq0\) / (b=0) and \(a\neq0\)
C \(a=b\neq0\)
D (b=1)
Explanation opens after your attempt
Correct Answer
B. (b=0) और \(a\neq0\) / (b=0) and \(a\neq0\)
Step 1
Concept
If the zero is (0), then (p(0)=b=0). To remain linear, \(a\neq0\) is also necessary.
Step 2
Why this answer is correct
The correct answer is B. (b=0) और \(a\neq0\) / (b=0) and \(a\neq0\). If the zero is (0), then (p(0)=b=0). To remain linear, \(a\neq0\) is also necessary.
Step 3
Exam Tip
शून्यक (0) होने पर (p(0)=b=0) होना चाहिए। रेखीय रहने के लिए \(a\neq0\) भी जरूरी है।
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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))?
#polynomial
#linear
#degree_combination
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A (0)
B (1)
C (2)
D परिभाषित नहीं / Not defined
Explanation opens after your attempt
Step 1
Concept
(q(x)-2p(x)=7x-4-2(3x+2)=x-8). Its degree is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). (q(x)-2p(x)=7x-4-2(3x+2)=x-8). Its degree is (1).
Step 3
Exam Tip
(q(x)-2p(x)=7x-4-2(3x+2)=x-8) है। इसकी डिग्री (1) है।
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किस विकल्प में रेखीय बहुपद का शून्यक \(\frac{13}{6}\) है?
Which option has zero \(\frac{13}{6}\) for a linear polynomial?
#polynomial
#linear
#fraction_zero
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A (6x-13)
B (13x-6)
C (6x+13)
D \(x-\frac{6}{13}\)
Explanation opens after your attempt
Correct Answer
A. (6x-13)
Step 1
Concept
From (6x-13=0), we get \(x=\frac{13}{6}\). Set the polynomial equal to (0) to find the zero.
Step 2
Why this answer is correct
The correct answer is A. (6x-13). From (6x-13=0), we get \(x=\frac{13}{6}\). Set the polynomial equal to (0) to find the zero.
Step 3
Exam Tip
(6x-13=0) से \(x=\frac{13}{6}\) मिलता है। शून्यक के लिए बहुपद को (0) के बराबर रखें।
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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))?
#polynomial
#linear
#difference_value
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A (1)
B (5)
C (x+1)
D (5x)
Explanation opens after your attempt
Step 1
Concept
(p(x+1)=5x-1) and (p(x)=5x-6). The difference is (5).
Step 2
Why this answer is correct
The correct answer is B. (5). (p(x+1)=5x-1) and (p(x)=5x-6). The difference is (5).
Step 3
Exam Tip
(p(x+1)=5x-1) और (p(x)=5x-6) है। अंतर (5) मिलता है।
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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 \(\lambda>0\)?
#polynomial
#linear
#inequality
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A \(0<\lambda<5\)
B \(\lambda=5\)
C \(\lambda>5\)
D \(\lambda<0\)
Explanation opens after your attempt
Correct Answer
A. \(0<\lambda<5\)
Step 1
Concept
The zero is \(-\frac{10}{\lambda}\). From \(-\frac{10}{\lambda}<-2\) and \(\lambda>0\), we get \(0<\lambda<5\).
Step 2
Why this answer is correct
The correct answer is A. \(0<\lambda<5\). The zero is \(-\frac{10}{\lambda}\). From \(-\frac{10}{\lambda}<-2\) and \(\lambda>0\), we get \(0<\lambda<5\).
Step 3
Exam Tip
शून्यक \(-\frac{10}{\lambda}\) है। \(-\frac{10}{\lambda}<-2\) और \(\lambda>0\) से \(0<\lambda<5\) मिलता है।
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किस विकल्प में (p(x)=ax+b) का शून्यक (4) होगा?
In which option will (p(x)=ax+b) have zero (4)?
#polynomial
#linear
#general_condition
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A (b=4a) और \(a\neq0\) / (b=4a) and \(a\neq0\)
B (b=-4a) और \(a\neq0\) / (b=-4a) and \(a\neq0\)
C (a=0)
D (b=0)
Explanation opens after your attempt
Correct Answer
B. (b=-4a) और \(a\neq0\) / (b=-4a) and \(a\neq0\)
Step 1
Concept
If the zero is (4), then (4a+b=0). So (b=-4a) and \(a\neq0\) are needed.
Step 2
Why this answer is correct
The correct answer is B. (b=-4a) और \(a\neq0\) / (b=-4a) and \(a\neq0\). If the zero is (4), then (4a+b=0). So (b=-4a) and \(a\neq0\) are needed.
Step 3
Exam Tip
शून्यक (4) होने पर (4a+b=0) होगा। इसलिए (b=-4a) और \(a\neq0\) चाहिए।
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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))?
#polynomial
#linear
#parameter_sum
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A (2x-s)
B (2x+3s)
C (x-s)
D (2s)
Explanation opens after your attempt
Step 1
Concept
On adding, (x+s+x-2s=2x-s). Combine the (s)-terms like like terms.
Step 2
Why this answer is correct
The correct answer is A. (2x-s). On adding, (x+s+x-2s=2x-s). Combine the (s)-terms like like terms.
Step 3
Exam Tip
जोड़ने पर (x+s+x-2s=2x-s) मिलता है। (s) वाले पदों को भी समान पद की तरह मिलाएं।
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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))?
#polynomial
#linear
#constant_result
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A रेखीय बहुपद / Linear polynomial
B नियतांक बहुपद / Constant polynomial
C द्विघात बहुपद / Quadratic polynomial
D शून्य बहुपद / Zero polynomial
Explanation opens after your attempt
Correct Answer
B. नियतांक बहुपद / Constant polynomial
Step 1
Concept
(p(x)-q(x)=3s). With respect to (x), it is a constant polynomial.
Step 2
Why this answer is correct
The correct answer is B. नियतांक बहुपद / Constant polynomial. (p(x)-q(x)=3s). With respect to (x), it is a constant polynomial.
Step 3
Exam Tip
(p(x)-q(x)=3s) है। (x) के संदर्भ में यह नियतांक बहुपद है।
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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)))?
#polynomial
#linear
#composition_value
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A (2)
B (-1)
C (6)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(3)=2) and (p(2)=6-7=-1). Find the inner value first.
Step 2
Why this answer is correct
The correct answer is B. (-1). (p(3)=2) and (p(2)=6-7=-1). Find the inner value first.
Step 3
Exam Tip
(p(3)=2) और (p(2)=6-7=-1) है। अंदर वाले मान को पहले निकालें।
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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)))?
#polynomial
#linear
#composition_value
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A (5)
B (20)
C (21)
D (22)
Explanation opens after your attempt
Step 1
Concept
(p(1)=5) and (p(5)=21). In composition, find the inner value first.
Step 2
Why this answer is correct
The correct answer is C. (21). (p(1)=5) and (p(5)=21). In composition, find the inner value first.
Step 3
Exam Tip
(p(1)=5) और (p(5)=21) है। रचना में अंदर वाला मान पहले निकालें।
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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)?
#polynomial
#linear
#parameter_zero
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A \(n=-\frac{1}{4}\)
B (n=1)
C (n=-1)
D (n=2)
Explanation opens after your attempt
Correct Answer
A. \(n=-\frac{1}{4}\)
Step 1
Concept
If the zero is (1), then (n+2+3n-1=0). Thus (4n+1=0) and \(n=-\frac{1}{4}\).
Step 2
Why this answer is correct
The correct answer is A. \(n=-\frac{1}{4}\). If the zero is (1), then (n+2+3n-1=0). Thus (4n+1=0) and \(n=-\frac{1}{4}\).
Step 3
Exam Tip
शून्यक (1) होने पर (n+2+3n-1=0) होगा। इससे (4n+1=0) और \(n=-\frac{1}{4}\) मिलता है।
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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)?
#polynomial
#linear
#fraction_parameter
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A (3)
B (5)
C (7)
D (9)
Explanation opens after your attempt
Step 1
Concept
From (p(8)=2+a=7), we get (a=5). In fractional form, substitute the value of (x) first.
Step 2
Why this answer is correct
The correct answer is B. (5). From (p(8)=2+a=7), we get (a=5). In fractional form, substitute the value of (x) first.
Step 3
Exam Tip
(p(8)=2+a=7) से (a=5) मिलता है। भिन्न रूप में पहले (x) का मान रखें।
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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)?
#polynomial
#linear
#sum_zero_parameter
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A (0)
B (1)
C (-1)
D (5)
Explanation opens after your attempt
Step 1
Concept
(p(x)+q(x)=5x+a-5). Substituting (x=1) gives (a=0).
Step 2
Why this answer is correct
The correct answer is A. (0). (p(x)+q(x)=5x+a-5). Substituting (x=1) gives (a=0).
Step 3
Exam Tip
(p(x)+q(x)=5x+a-5) है। (x=1) रखने पर (a=0) मिलता है।
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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)?
#polynomial
#linear
#no_solution
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A (c=1)
B (c=-1)
C (c=3)
D (c=2)
Explanation opens after your attempt
Step 1
Concept
From (-3(c-2)+3c=0), we get (6=0), so there is no solution. Therefore none of the listed values should be correct.
Step 2
Why this answer is correct
The correct answer is B. (c=-1). From (-3(c-2)+3c=0), we get (6=0), so there is no solution. Therefore none of the listed values should be correct.
Step 3
Exam Tip
(-3(c-2)+3c=0) से (6=0) नहीं बल्कि कोई हल नहीं मिलता। इसलिए दिए गए विकल्पों में कोई सही नहीं होना चाहिए।
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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)?
#polynomial
#linear
#parameter_zero
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A (c=4)
B (c=-4)
C (c=1)
D (c=2)
Explanation opens after your attempt
Step 1
Concept
From (-2(c-2)+3c=0), we get (c+4=0). Hence (c=-4).
Step 2
Why this answer is correct
The correct answer is B. (c=-4). From (-2(c-2)+3c=0), we get (c+4=0). Hence (c=-4).
Step 3
Exam Tip
(-2(c-2)+3c=0) से (c+4=0) मिलता है। अतः (c=-4) है।
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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))?
#polynomial
#linear
#two_step
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A (0)
B (2)
C (-10)
D (10)
Explanation opens after your attempt
Step 1
Concept
From (3r-4=14), we get (r=6). Therefore (p(-1)=6(-1)-4=-10).
Step 2
Why this answer is correct
The correct answer is C. (-10). From (3r-4=14), we get (r=6). Therefore (p(-1)=6(-1)-4=-10).
Step 3
Exam Tip
(3r-4=14) से (r=6) मिलता है। इसलिए (p(-1)=6(-1)-4=-10) है।
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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)?
#polynomial
#linear
#parameter_equation
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A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
From (a+8=(4a+8)-12), we get (a=4a-12). Therefore (a=4).
Step 2
Why this answer is correct
The correct answer is C. (4). From (a+8=(4a+8)-12), we get (a=4a-12). Therefore (a=4).
Step 3
Exam Tip
(a+8=(4a+8)-12) से (a=4a-12) मिलता है। इसलिए (a=4) है।
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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)?
#polynomial
#linear
#fixed_value
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A (3)
B (5)
C (10)
D (15)
Explanation opens after your attempt
Step 1
Concept
(p(a)=3a-10). From (3a-10=a), we get (a=5).
Step 2
Why this answer is correct
The correct answer is B. (5). (p(a)=3a-10). From (3a-10=a), we get (a=5).
Step 3
Exam Tip
(p(a)=3a-10) है। (3a-10=a) से (a=5) मिलता है।
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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)?
#polynomial
#linear
#coefficients
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(0)=n=-2) and (4m-2=10) gives (m=3). Therefore (m+n=1).
Step 2
Why this answer is correct
The correct answer is A. (1). (p(0)=n=-2) and (4m-2=10) gives (m=3). Therefore (m+n=1).
Step 3
Exam Tip
(p(0)=n=-2) और (4m-2=10) से (m=3) मिलता है। इसलिए (m+n=1) है।
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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)?
#polynomial
#linear
#slope_parameter
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A (2)
B (4)
C (6)
D (12)
Explanation opens after your attempt
Step 1
Concept
Subtracting the two values gives (p(5)-p(2)=3m=12). Therefore (m=4).
Step 2
Why this answer is correct
The correct answer is B. (4). Subtracting the two values gives (p(5)-p(2)=3m=12). Therefore (m=4).
Step 3
Exam Tip
दोनों मान घटाने पर (p(5)-p(2)=3m=12) मिलता है। इसलिए (m=4) है।
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किस विकल्प में (p(-3)=0) और (p(x)) रेखीय है?
Which option has (p(-3)=0) and (p(x)) is linear?
#polynomial
#linear
#zero_identification
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A (p(x)=x-3)
B (p(x)=3x+3)
C (p(x)=x+3)
D (p(x)=x-2 -9)
Explanation opens after your attempt
Correct Answer
C. (p(x)=x+3)
Step 1
Concept
Substituting (x=-3) in (x+3) gives (0). It is a linear polynomial of degree (1).
Step 2
Why this answer is correct
The correct answer is C. (p(x)=x+3). Substituting (x=-3) in (x+3) gives (0). It is a linear polynomial of degree (1).
Step 3
Exam Tip
(x+3) में (x=-3) रखने पर (0) मिलता है। यह डिग्री (1) वाला रेखीय बहुपद है।
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यदि (p(x)=4x+9), तो (p(x)+p(-x)) क्या है?
If (p(x)=4x+9), what is (p(x)+p(-x))?
#polynomial
#linear
#symmetry
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A (8x+18)
B (18)
C (0)
D (4x+18)
Explanation opens after your attempt
Step 1
Concept
(p(-x)=-4x+9). Adding gives (4x+9-4x+9=18).
Step 2
Why this answer is correct
The correct answer is B. (18). (p(-x)=-4x+9). Adding gives (4x+9-4x+9=18).
Step 3
Exam Tip
(p(-x)=-4x+9) है। जोड़ने पर (4x+9-4x+9=18) मिलता है।
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यदि (p(x)=4x+9), तो (p(x)-p(-x)) क्या है?
If (p(x)=4x+9), what is (p(x)-p(-x))?
#polynomial
#linear
#symmetry
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A (8x)
B (0)
C (18)
D (4x)
Explanation opens after your attempt
Step 1
Concept
(p(-x)=-4x+9). Subtracting gives (4x+9-(-4x+9)=8x).
Step 2
Why this answer is correct
The correct answer is A. (8x). (p(-x)=-4x+9). Subtracting gives (4x+9-(-4x+9)=8x).
Step 3
Exam Tip
(p(-x)=-4x+9) है। घटाने पर (4x+9-(-4x+9)=8x) मिलता है।
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किस मान पर ((s+4)x+2s) का शून्यक (0) होगा?
For which value will the zero of ((s+4)x+2s) be (0)?
#polynomial
#linear
#zero_at_origin
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A (s=0)
B (s=-4)
C (s=4)
D कोई मान नहीं / No value
Explanation opens after your attempt
Step 1
Concept
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.
Step 2
Why this answer is correct
The correct answer is A. (s=0). 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.
Step 3
Exam Tip
शून्यक (0) होने के लिए नियतांक पद (2s=0) होना चाहिए। (s=0) पर (x) का गुणांक (4) है इसलिए बहुपद रेखीय है।
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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)?
#polynomial
#linear
#no_solution
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A कोई मान नहीं / No value
B (0)
C (1)
D (8)
Explanation opens after your attempt
Correct Answer
A. कोई मान नहीं / No value
Step 1
Concept
(p(x)+q(x)=8x), whose zero is (0). Therefore the zero cannot be (2) for any (a).
Step 2
Why this answer is correct
The correct answer is A. कोई मान नहीं / No value. (p(x)+q(x)=8x), whose zero is (0). Therefore the zero cannot be (2) for any (a).
Step 3
Exam Tip
(p(x)+q(x)=8x) है जिसका शून्यक (0) है। इसलिए शून्यक (2) किसी (a) पर नहीं हो सकता।
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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))?
#polynomial
#linear
#parameter_difference
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A (8x)
B (2x-2a)
C (2x)
D (2a)
Explanation opens after your attempt
Correct Answer
B. (2x-2a)
Step 1
Concept
(5x-a-(3x+a)=2x-2a). Change the signs inside the bracket while subtracting.
Step 2
Why this answer is correct
The correct answer is B. (2x-2a). (5x-a-(3x+a)=2x-2a). Change the signs inside the bracket while subtracting.
Step 3
Exam Tip
(5x-a-(3x+a)=2x-2a) है। घटाते समय कोष्ठक के चिन्ह बदलें।
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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?
#polynomial
#linear
#product_reason
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A क्योंकि डिग्री (1) है / Because degree is (1)
B क्योंकि डिग्री (2) है / Because degree is (2)
C क्योंकि यह नियतांक है / Because it is constant
D क्योंकि यह शून्य है / Because it is zero
Explanation opens after your attempt
Correct Answer
B. क्योंकि डिग्री (2) है / Because degree is (2)
Step 1
Concept
In ((2x+3)(x-4)), the highest term is \(2x^2\). So the product has degree (2) and is not linear.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि डिग्री (2) है / Because degree is (2). In ((2x+3)(x-4)), the highest term is \(2x^2\). So the product has degree (2) and is not linear.
Step 3
Exam Tip
((2x+3)(x-4)) में उच्चतम पद \(2x^2\) है। इसलिए गुणनफल की डिग्री (2) है और यह रेखीय नहीं है।
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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)?
#polynomial
#linear
#composition_parameter
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A (4)
B (-4)
C (6)
D (-6)
Explanation opens after your attempt
Step 1
Concept
(p(0)=-2) and (p(-2)=-2a-2). From (-2a-2=10), we get (a=-6).
Step 2
Why this answer is correct
The correct answer is D. (-6). (p(0)=-2) and (p(-2)=-2a-2). From (-2a-2=10), we get (a=-6).
Step 3
Exam Tip
(p(0)=-2) और (p(-2)=-2a-2) है। (-2a-2=10) से (a=-6) मिलता है।
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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)?
#polynomial
#linear
#composition_parameter
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A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1+a) and (p(1+a)=1+2a). From (1+2a=7), we get (a=3).
Step 2
Why this answer is correct
The correct answer is B. (3). (p(1)=1+a) and (p(1+a)=1+2a). From (1+2a=7), we get (a=3).
Step 3
Exam Tip
(p(1)=1+a) और (p(1+a)=1+2a) है। (1+2a=7) से (a=3) मिलता है।
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किस विकल्प में (p(x)=ax+b) का शून्यक (-5) होगा?
In which option will (p(x)=ax+b) have zero (-5)?
#polynomial
#linear
#general_condition
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A (b=5a) और \(a\neq0\) / (b=5a) and \(a\neq0\)
B (b=-5a) और \(a\neq0\) / (b=-5a) and \(a\neq0\)
C (a=0)
D (b=0)
Explanation opens after your attempt
Correct Answer
A. (b=5a) और \(a\neq0\) / (b=5a) and \(a\neq0\)
Step 1
Concept
If the zero is (-5), then (-5a+b=0). So (b=5a) and \(a\neq0\) are needed.
Step 2
Why this answer is correct
The correct answer is A. (b=5a) और \(a\neq0\) / (b=5a) and \(a\neq0\). If the zero is (-5), then (-5a+b=0). So (b=5a) and \(a\neq0\) are needed.
Step 3
Exam Tip
शून्यक (-5) होने पर (-5a+b=0) होगा। इसलिए (b=5a) और \(a\neq0\) चाहिए।
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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))?
#polynomial
#linear
#shift_difference
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A (12)
B (18)
C (30)
D (36)
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Step 1
Concept
(p(x+3)=6x+17) and (p(x-2)=6x-13). The difference is (30).
Step 2
Why this answer is correct
The correct answer is C. (30). (p(x+3)=6x+17) and (p(x-2)=6x-13). The difference is (30).
Step 3
Exam Tip
(p(x+3)=6x+17) और (p(x-2)=6x-13) है। अंतर (30) है।
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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)))?
#polynomial
#linear
#composition_value
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A (3)
B (9)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
(p(3)=3) and then (p(3)=3). Find the inner value first.
Step 2
Why this answer is correct
The correct answer is A. (3). (p(3)=3) and then (p(3)=3). Find the inner value first.
Step 3
Exam Tip
(p(3)=3) और (p(3)=3) ही है। अंदर वाले मान को पहले निकालें।
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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))?
#polynomial
#linear
#shift_sum
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A (10x+4)
B (10x)
C (5x+4)
D (10x+2)
Explanation opens after your attempt
Correct Answer
A. (10x+4)
Step 1
Concept
(p(x+1)=5x+7) and (p(x-1)=5x-3). Adding gives (10x+4).
Step 2
Why this answer is correct
The correct answer is A. (10x+4). (p(x+1)=5x+7) and (p(x-1)=5x-3). Adding gives (10x+4).
Step 3
Exam Tip
(p(x+1)=5x+7) और (p(x-1)=5x-3) है। जोड़ने पर (10x+4) मिलता है।
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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?
#polynomial
#linear
#parameter_condition
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A (r=0) या (r=2) / (r=0) or (r=2)
B (r=1) या (r=2) / (r=1) or (r=2)
C (r=2) ही / (r=2) only
D (r=-2) ही / (r=-2) only
Explanation opens after your attempt
Correct Answer
A. (r=0) या (r=2) / (r=0) or (r=2)
Step 1
Concept
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).
Step 2
Why this answer is correct
The correct answer is A. (r=0) या (r=2) / (r=0) or (r=2). 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).
Step 3
Exam Tip
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।
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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)?
#polynomial
#linear
#composition_parameter
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A (3)
B (5)
C (6)
D (15)
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Step 1
Concept
(p(0)=3) and (p(3)=3a+3). From (3a+3=18), we get (a=5).
Step 2
Why this answer is correct
The correct answer is B. (5). (p(0)=3) and (p(3)=3a+3). From (3a+3=18), we get (a=5).
Step 3
Exam Tip
(p(0)=3) और (p(3)=3a+3) है। (3a+3=18) से (a=5) मिलता है।
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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)?
#polynomial
#linear
#coefficients
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A (0)
B (1)
C (2)
D (3)
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Step 1
Concept
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.
Step 2
Why this answer is correct
The correct answer is C. (2). 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.
Step 3
Exam Tip
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।
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