सरल करने के बाद (8(2x-1)-3(5x+4)) कौन सा रेखीय बहुपद बनेगा?
After simplifying (8(2x-1)-3(5x+4)), which linear polynomial is obtained?
#polynomial
#linear
#simplification
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A (x-20)
B (31x-20)
C (x+4)
D (16x-12)
Explanation opens after your attempt
Step 1
Concept
(16x-8-15x-12=x-20). After opening brackets, combine like terms.
Step 2
Why this answer is correct
The correct answer is A. (x-20). (16x-8-15x-12=x-20). After opening brackets, combine like terms.
Step 3
Exam Tip
(16x-8-15x-12=x-20) है। कोष्ठक खोलने के बाद समान पद मिलाएं।
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किस मान पर (\(v^2-36\)x-13) रेखीय बहुपद नहीं रहेगा?
For which value will (\(v^2-36\)x-13) not remain a linear polynomial?
#polynomial
#linear
#parameter_condition
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A (v=0)
B (v=6) या (v=-6) / (v=6) or (v=-6)
C (v=36)
D (v=3) या (v=-3) / (v=3) or (v=-3)
Explanation opens after your attempt
Correct Answer
B. (v=6) या (v=-6) / (v=6) or (v=-6)
Step 1
Concept
For it not to be linear, the coefficient of (x) must be (0). From \(v^2-36=0\), \(v=\pm6\).
Step 2
Why this answer is correct
The correct answer is B. (v=6) या (v=-6) / (v=6) or (v=-6). For it not to be linear, the coefficient of (x) must be (0). From \(v^2-36=0\), \(v=\pm6\).
Step 3
Exam Tip
रेखीय न रहने के लिए (x) का गुणांक (0) होना चाहिए। \(v^2-36=0\) से \(v=\pm6\) मिलता है।
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यदि (p(x)=(k-6)x+18) का शून्यक (-3) है, तो (k) क्या है?
If the zero of (p(x)=(k-6)x+18) is (-3), what is (k)?
#polynomial
#linear
#zero_parameter
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A (6)
B (9)
C (12)
D (18)
Explanation opens after your attempt
Step 1
Concept
From (-3(k-6)+18=0), we get (k=12). Substitute the zero into the polynomial to form the equation.
Step 2
Why this answer is correct
The correct answer is C. (12). From (-3(k-6)+18=0), we get (k=12). Substitute the zero into the polynomial to form the equation.
Step 3
Exam Tip
(-3(k-6)+18=0) से (k=12) मिलता है। शून्यक को बहुपद में रखकर समीकरण बनाएं।
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यदि (p(x)=8x-5) और (q(x)=3x+11), तो (2p(x)-5q(x)) क्या है?
If (p(x)=8x-5) and (q(x)=3x+11), what is (2p(x)-5q(x))?
#polynomial
#linear
#combination
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A (x-65)
B (31x+45)
C (x+45)
D (16x-55)
Explanation opens after your attempt
Step 1
Concept
(2(8x-5)-5(3x+11)=x-65). Multiply first and then combine like terms.
Step 2
Why this answer is correct
The correct answer is A. (x-65). (2(8x-5)-5(3x+11)=x-65). Multiply first and then combine like terms.
Step 3
Exam Tip
(2(8x-5)-5(3x+11)=x-65) है। पहले गुणा करें फिर समान पद मिलाएं।
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किस मान पर ((4a-5)x+30) का शून्यक (-2) होगा?
For which value will the zero of ((4a-5)x+30) be (-2)?
#polynomial
#linear
#parameter_zero
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A (a=5)
B (a=4)
C (a=0)
D \(a=\frac{5}{4}\)
Explanation opens after your attempt
Step 1
Concept
If the zero is (-2), then (-2(4a-5)+30=0). This gives (a=5).
Step 2
Why this answer is correct
The correct answer is A. (a=5). If the zero is (-2), then (-2(4a-5)+30=0). This gives (a=5).
Step 3
Exam Tip
शून्यक (-2) होने पर (-2(4a-5)+30=0) होगा। इससे (a=5) मिलता है।
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यदि (p(x)=ax+b) का शून्यक (7) है और (a=-4), तो (b) क्या है?
If the zero of (p(x)=ax+b) is (7) and (a=-4), what is (b)?
#polynomial
#linear
#general_form
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A (7)
B (-28)
C (28)
D (-7)
Explanation opens after your attempt
Step 1
Concept
From (p(7)=0), (7a+b=0). Substituting (a=-4) gives (b=28).
Step 2
Why this answer is correct
The correct answer is C. (28). From (p(7)=0), (7a+b=0). Substituting (a=-4) gives (b=28).
Step 3
Exam Tip
(p(7)=0) से (7a+b=0) होगा। (a=-4) रखने पर (b=28) मिलता है।
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यदि (p(x)=11x+c) और (p(4)=p(1)+33), तो (c) के बारे में क्या सही है?
If (p(x)=11x+c) and (p(4)=p(1)+33), 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=33) / Only (c=33)
Explanation opens after your attempt
Correct Answer
B. हर (c) सही है / Every (c) is valid
Step 1
Concept
(p(4)-p(1)=(44+c)-(11+c)=33). 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)=(44+c)-(11+c)=33). So the condition is true for every (c).
Step 3
Exam Tip
(p(4)-p(1)=(44+c)-(11+c)=33) है। इसलिए शर्त हर (c) के लिए सही है।
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किस विकल्प में रेखीय बहुपद का शून्यक \(-\frac{9}{13}\) है?
Which option has zero \(-\frac{9}{13}\) for a linear polynomial?
#polynomial
#linear
#fraction_zero
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A (13x-9)
B (9x+13)
C (13x+9)
D \(x+\frac{13}{9}\)
Explanation opens after your attempt
Correct Answer
C. (13x+9)
Step 1
Concept
From (13x+9=0), we get \(x=-\frac{9}{13}\). Pay attention to the sign and denominator in fractional zeros.
Step 2
Why this answer is correct
The correct answer is C. (13x+9). From (13x+9=0), we get \(x=-\frac{9}{13}\). Pay attention to the sign and denominator in fractional zeros.
Step 3
Exam Tip
(13x+9=0) से \(x=-\frac{9}{13}\) मिलता है। भिन्न शून्यक में चिन्ह और हर ध्यान रखें।
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यदि (p(x)=\frac{8}{15}x-16), तो किस मान पर (p(x)=0) होगा?
If (p(x)=\frac{8}{15}x-16), for which value will (p(x)=0)?
#polynomial
#linear
#fraction_equation
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A (x=15)
B (x=24)
C (x=30)
D (x=40)
Explanation opens after your attempt
Step 1
Concept
From \(\frac{8}{15}x-16=0\), \(\frac{8}{15}x=16\) and (x=30). With a fractional coefficient, multiply by the reciprocal.
Step 2
Why this answer is correct
The correct answer is C. (x=30). From \(\frac{8}{15}x-16=0\), \(\frac{8}{15}x=16\) and (x=30). With a fractional coefficient, multiply by the reciprocal.
Step 3
Exam Tip
\(\frac{8}{15}x-16=0\) से \(\frac{8}{15}x=16\) और (x=30) मिलता है। भिन्न गुणांक में उलटा गुणा करें।
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यदि (p(x)=x-10) और (q(x)=x+3), तो (p(x)q(x)) की डिग्री क्या है?
If (p(x)=x-10) and (q(x)=x+3), what is the degree of (p(x)q(x))?
#polynomial
#linear
#product_degree
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A (1)
B (2)
C (3)
D (10)
Explanation opens after your attempt
Step 1
Concept
In ((x-10)(x+3)), 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-10)(x+3)), the highest term is \(x^2\). Therefore the product has degree (2).
Step 3
Exam Tip
((x-10)(x+3)) में उच्चतम पद \(x^2\) है। इसलिए गुणनफल की डिग्री (2) है।
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यदि (p(x)=9x-17), तो (p(x+3)) क्या है?
If (p(x)=9x-17), what is (p(x+3))?
#polynomial
#linear
#composition
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A (9x+10)
B (9x-14)
C (9x+27)
D (x+10)
Explanation opens after your attempt
Correct Answer
A. (9x+10)
Step 1
Concept
(p(x+3)=9(x+3)-17=9x+10). Substitute the whole (x+3) in place of (x).
Step 2
Why this answer is correct
The correct answer is A. (9x+10). (p(x+3)=9(x+3)-17=9x+10). Substitute the whole (x+3) in place of (x).
Step 3
Exam Tip
(p(x+3)=9(x+3)-17=9x+10) है। (x) की जगह पूरा (x+3) रखें।
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यदि (p(x)=19-7x), तो (p(2x)) कौन सा है?
If (p(x)=19-7x), which is (p(2x))?
#polynomial
#linear
#substitution
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A (38-7x)
B (19-14x)
C (19-7x)
D (38-14x)
Explanation opens after your attempt
Correct Answer
B. (19-14x)
Step 1
Concept
(p(2x)=19-7(2x)=19-14x). While substituting, use the whole (2x).
Step 2
Why this answer is correct
The correct answer is B. (19-14x). (p(2x)=19-7(2x)=19-14x). While substituting, use the whole (2x).
Step 3
Exam Tip
(p(2x)=19-7(2x)=19-14x) है। प्रतिस्थापन करते समय पूरे (2x) को रखें।
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किस मान पर (\(t^2-8t+15\)x+(t-3)) रेखीय बहुपद नहीं रहेगा?
For which value will (\(t^2-8t+15\)x+(t-3)) not remain a linear polynomial?
#polynomial
#linear
#parameter_condition
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A (t=3) या (t=5) / (t=3) or (t=5)
B (t=0)
C (t=8)
D (t=-3)
Explanation opens after your attempt
Correct Answer
A. (t=3) या (t=5) / (t=3) or (t=5)
Step 1
Concept
For it to be linear, \(t^2-8t+15\neq0\) is needed. From \(t^2-8t+15=0\), (t=3) or (t=5).
Step 2
Why this answer is correct
The correct answer is A. (t=3) या (t=5) / (t=3) or (t=5). For it to be linear, \(t^2-8t+15\neq0\) is needed. From \(t^2-8t+15=0\), (t=3) or (t=5).
Step 3
Exam Tip
रेखीय होने के लिए \(t^2-8t+15\neq0\) चाहिए। \(t^2-8t+15=0\) से (t=3) या (t=5) मिलता है।
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यदि (p(x)=kx-14) और (p(7)=p(-1)), तो (p(x)) रेखीय कब रहेगा?
If (p(x)=kx-14) and (p(7)=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=14) / When (k=14)
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(7)=p(-1)), (7k-14=-k-14), 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(7)=p(-1)), (7k-14=-k-14), so (k=0). At (k=0), the polynomial is not linear.
Step 3
Exam Tip
(p(7)=p(-1)) से (7k-14=-k-14) और (k=0) मिलता है। (k=0) पर बहुपद रेखीय नहीं रहता।
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यदि (p(x)=7x+2) और (q(x)=15x-6), तो (q(x)-2p(x)) की डिग्री क्या है?
If (p(x)=7x+2) and (q(x)=15x-6), 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)=15x-6-2(7x+2)=x-10). Its degree is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). (q(x)-2p(x)=15x-6-2(7x+2)=x-10). Its degree is (1).
Step 3
Exam Tip
(q(x)-2p(x)=15x-6-2(7x+2)=x-10) है। इसकी डिग्री (1) है।
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किस विकल्प में रेखीय बहुपद का शून्यक \(\frac{29}{11}\) है?
Which option has zero \(\frac{29}{11}\) for a linear polynomial?
#polynomial
#linear
#fraction_zero
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A (11x-29)
B (29x-11)
C (11x+29)
D \(x-\frac{11}{29}\)
Explanation opens after your attempt
Correct Answer
A. (11x-29)
Step 1
Concept
From (11x-29=0), we get \(x=\frac{29}{11}\). Set the polynomial equal to (0) to find the zero.
Step 2
Why this answer is correct
The correct answer is A. (11x-29). From (11x-29=0), we get \(x=\frac{29}{11}\). Set the polynomial equal to (0) to find the zero.
Step 3
Exam Tip
(11x-29=0) से \(x=\frac{29}{11}\) मिलता है। शून्यक के लिए बहुपद को (0) के बराबर रखें।
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यदि (p(x)=12x-25), तो (p(x+1)-p(x)) क्या है?
If (p(x)=12x-25), what is (p(x+1)-p(x))?
#polynomial
#linear
#difference_value
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A (1)
B (12)
C (x+1)
D (12x)
Explanation opens after your attempt
Step 1
Concept
(p(x+1)=12x-13) and (p(x)=12x-25). The difference is (12).
Step 2
Why this answer is correct
The correct answer is B. (12). (p(x+1)=12x-13) and (p(x)=12x-25). The difference is (12).
Step 3
Exam Tip
(p(x+1)=12x-13) और (p(x)=12x-25) है। अंतर (12) मिलता है।
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यदि (p(x)=\lambda x+21) और इसका शून्यक (-7) से बड़ा है, तो \(\lambda>0\) होने पर कौन सी शर्त सही है?
If (p(x)=\lambda x+21) and its zero is greater than (-7), which condition is correct when \(\lambda>0\)?
#polynomial
#linear
#inequality
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A \(0<\lambda<3\)
B \(\lambda=3\)
C \(\lambda>3\)
D \(\lambda<0\)
Explanation opens after your attempt
Correct Answer
C. \(\lambda>3\)
Step 1
Concept
The zero is \(-\frac{21}{\lambda}\). From \(-\frac{21}{\lambda}>-7\) and \(\lambda>0\), we get \(\lambda>3\).
Step 2
Why this answer is correct
The correct answer is C. \(\lambda>3\). The zero is \(-\frac{21}{\lambda}\). From \(-\frac{21}{\lambda}>-7\) and \(\lambda>0\), we get \(\lambda>3\).
Step 3
Exam Tip
शून्यक \(-\frac{21}{\lambda}\) है। \(-\frac{21}{\lambda}>-7\) और \(\lambda>0\) से \(\lambda>3\) मिलता है।
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किस विकल्प में (p(x)=ax+b) का शून्यक (-11) होगा?
In which option will (p(x)=ax+b) have zero (-11)?
#polynomial
#linear
#general_condition
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A (b=11a) और \(a\neq0\) / (b=11a) and \(a\neq0\)
B (b=-11a) और \(a\neq0\) / (b=-11a) and \(a\neq0\)
C (a=0)
D (b=0)
Explanation opens after your attempt
Correct Answer
A. (b=11a) और \(a\neq0\) / (b=11a) and \(a\neq0\)
Step 1
Concept
If the zero is (-11), then (-11a+b=0). So (b=11a) and \(a\neq0\) are needed.
Step 2
Why this answer is correct
The correct answer is A. (b=11a) और \(a\neq0\) / (b=11a) and \(a\neq0\). If the zero is (-11), then (-11a+b=0). So (b=11a) and \(a\neq0\) are needed.
Step 3
Exam Tip
शून्यक (-11) होने पर (-11a+b=0) होगा। इसलिए (b=11a) और \(a\neq0\) चाहिए।
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यदि (p(x)=x+5r) और (q(x)=x-8r), तो (p(x)+q(x)) क्या है?
If (p(x)=x+5r) and (q(x)=x-8r), what is (p(x)+q(x))?
#polynomial
#linear
#parameter_sum
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A (2x-3r)
B (2x+13r)
C (x-3r)
D (13r)
Explanation opens after your attempt
Correct Answer
A. (2x-3r)
Step 1
Concept
On adding, (x+5r+x-8r=2x-3r). Combine the parameter terms too.
Step 2
Why this answer is correct
The correct answer is A. (2x-3r). On adding, (x+5r+x-8r=2x-3r). Combine the parameter terms too.
Step 3
Exam Tip
जोड़ने पर (x+5r+x-8r=2x-3r) मिलता है। पैरामीटर वाले पदों को भी मिलाएं।
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यदि (p(x)=x+5r) और (q(x)=x-8r), तो (p(x)-q(x)) किस प्रकार का बहुपद है?
If (p(x)=x+5r) and (q(x)=x-8r), 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)=13r). 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)=13r). With respect to (x), it is a constant polynomial.
Step 3
Exam Tip
(p(x)-q(x)=13r) है। (x) के संदर्भ में यह नियतांक बहुपद है।
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यदि (p(x)=10x-29), तो (p(p(3))) का सही मान क्या है?
If (p(x)=10x-29), what is the correct value of (p(p(3)))?
#polynomial
#linear
#composition_value
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A (1)
B (-19)
C (3)
D (10)
Explanation opens after your attempt
Step 1
Concept
(p(3)=1) and (p(1)=10-29=-19). Find the inner value first.
Step 2
Why this answer is correct
The correct answer is B. (-19). (p(3)=1) and (p(1)=10-29=-19). Find the inner value first.
Step 3
Exam Tip
(p(3)=1) और (p(1)=10-29=-19) है। अंदर वाले मान को पहले निकालें।
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यदि (p(x)=6x+5), तो (p(p(0))) का मान क्या है?
If (p(x)=6x+5), what is the value of (p(p(0)))?
#polynomial
#linear
#composition_value
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A (5)
B (30)
C (35)
D (36)
Explanation opens after your attempt
Step 1
Concept
(p(0)=5) and (p(5)=35). In composition, find the inner value first.
Step 2
Why this answer is correct
The correct answer is C. (35). (p(0)=5) and (p(5)=35). In composition, find the inner value first.
Step 3
Exam Tip
(p(0)=5) और (p(5)=35) है। रचना में अंदर वाला मान पहले निकालें।
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किस मान पर ((n+6)x+4n-3) का शून्यक (1) होगा?
For which value will the zero of ((n+6)x+4n-3) be (1)?
#polynomial
#linear
#parameter_zero
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A \(n=-\frac{3}{5}\)
B (n=1)
C (n=-1)
D (n=6)
Explanation opens after your attempt
Correct Answer
A. \(n=-\frac{3}{5}\)
Step 1
Concept
If the zero is (1), then (n+6+4n-3=0). Thus (5n+3=0) and \(n=-\frac{3}{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(n=-\frac{3}{5}\). If the zero is (1), then (n+6+4n-3=0). Thus (5n+3=0) and \(n=-\frac{3}{5}\).
Step 3
Exam Tip
शून्यक (1) होने पर (n+6+4n-3=0) होगा। इससे (5n+3=0) और \(n=-\frac{3}{5}\) मिलता है।
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यदि (p(x)=\frac{x}{8}+a) और (p(24)=17), तो (a) का मान क्या है?
If (p(x)=\frac{x}{8}+a) and (p(24)=17), what is the value of (a)?
#polynomial
#linear
#fraction_parameter
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A (12)
B (13)
C (14)
D (17)
Explanation opens after your attempt
Step 1
Concept
From (p(24)=3+a=17), we get (a=14). In fractional form, substitute the value of (x) first.
Step 2
Why this answer is correct
The correct answer is C. (14). From (p(24)=3+a=17), we get (a=14). In fractional form, substitute the value of (x) first.
Step 3
Exam Tip
(p(24)=3+a=17) से (a=14) मिलता है। भिन्न रूप में पहले (x) का मान रखें।
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यदि (p(x)=7x+a) और (q(x)=4x-12), तो (p(x)+q(x)) का शून्यक (2) होने पर (a) क्या है?
If (p(x)=7x+a) and (q(x)=4x-12), what is (a) if the zero of (p(x)+q(x)) is (2)?
#polynomial
#linear
#sum_zero_parameter
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A (-10)
B (0)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
(p(x)+q(x)=11x+a-12). Substituting (x=2) gives (22+a-12=0), so (a=-10).
Step 2
Why this answer is correct
The correct answer is A. (-10). (p(x)+q(x)=11x+a-12). Substituting (x=2) gives (22+a-12=0), so (a=-10).
Step 3
Exam Tip
(p(x)+q(x)=11x+a-12) है। (x=2) रखने पर (22+a-12=0) से (a=-10) मिलता है।
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किस मान पर (p(x)=(c-7)x+8c) का शून्यक (-4) होगा?
For which value will the zero of (p(x)=(c-7)x+8c) be (-4)?
#polynomial
#linear
#parameter_zero
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A (c=-7)
B (c=7)
C (c=1)
D कोई मान नहीं / No value
Explanation opens after your attempt
Step 1
Concept
From (-4(c-7)+8c=0), we get (4c+28=0). Therefore (c=-7).
Step 2
Why this answer is correct
The correct answer is A. (c=-7). From (-4(c-7)+8c=0), we get (4c+28=0). Therefore (c=-7).
Step 3
Exam Tip
(-4(c-7)+8c=0) से (4c+28=0) मिलता है। इसलिए (c=-7) है।
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यदि (p(x)=(c-3)x+6c) का शून्यक (-6) है, तो कौन सा निष्कर्ष सही है?
If the zero of (p(x)=(c-3)x+6c) is (-6), which conclusion is correct?
#polynomial
#linear
#no_solution
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A (c=3)
B (c=-3)
C कोई (c) नहीं / No (c)
D हर (c) / Every (c)
Explanation opens after your attempt
Correct Answer
C. कोई (c) नहीं / No (c)
Step 1
Concept
From (-6(c-3)+6c=0), we get the impossible result (18=0). Therefore no (c) exists.
Step 2
Why this answer is correct
The correct answer is C. कोई (c) नहीं / No (c). From (-6(c-3)+6c=0), we get the impossible result (18=0). Therefore no (c) exists.
Step 3
Exam Tip
(-6(c-3)+6c=0) से (18=0) जैसा असंभव परिणाम मिलता है। इसलिए कोई (c) नहीं है।
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यदि (p(x)=rx-12) और (p(6)=30), तो (p(-2)) का मान क्या है?
If (p(x)=rx-12) and (p(6)=30), what is the value of (p(-2))?
#polynomial
#linear
#two_step
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A (0)
B (-26)
C (-14)
D (14)
Explanation opens after your attempt
Step 1
Concept
From (6r-12=30), we get (r=7). Therefore (p(-2)=7(-2)-12=-26).
Step 2
Why this answer is correct
The correct answer is B. (-26). From (6r-12=30), we get (r=7). Therefore (p(-2)=7(-2)-12=-26).
Step 3
Exam Tip
(6r-12=30) से (r=7) मिलता है। इसलिए (p(-2)=7(-2)-12=-26) है।
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यदि (p(x)=ax+15) और (p(2)=p(8)-30), तो (a) क्या है?
If (p(x)=ax+15) and (p(2)=p(8)-30), what is (a)?
#polynomial
#linear
#parameter_equation
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A (3)
B (5)
C (6)
D (15)
Explanation opens after your attempt
Step 1
Concept
From (2a+15=(8a+15)-30), we get (2a=8a-30). Therefore (a=5).
Step 2
Why this answer is correct
The correct answer is B. (5). From (2a+15=(8a+15)-30), we get (2a=8a-30). Therefore (a=5).
Step 3
Exam Tip
(2a+15=(8a+15)-30) से (2a=8a-30) मिलता है। इसलिए (a=5) है।
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यदि (p(x)=7x-30), तो (p(a)=a) होने पर (a) क्या है?
If (p(x)=7x-30), what is (a) when (p(a)=a)?
#polynomial
#linear
#fixed_value
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A (4)
B (5)
C (6)
D (30)
Explanation opens after your attempt
Step 1
Concept
(p(a)=7a-30). From (7a-30=a), we get (a=5).
Step 2
Why this answer is correct
The correct answer is B. (5). (p(a)=7a-30). From (7a-30=a), we get (a=5).
Step 3
Exam Tip
(p(a)=7a-30) है। (7a-30=a) से (a=5) मिलता है।
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यदि (p(x)=mx+n), (p(0)=-8) और (p(5)=27), तो (m+n) क्या है?
If (p(x)=mx+n), (p(0)=-8) and (p(5)=27), what is (m+n)?
#polynomial
#linear
#coefficients
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A (-1)
B (7)
C (19)
D (27)
Explanation opens after your attempt
Step 1
Concept
(p(0)=n=-8) and (5m-8=27) gives (m=7). Therefore (m+n=-1).
Step 2
Why this answer is correct
The correct answer is A. (-1). (p(0)=n=-8) and (5m-8=27) gives (m=7). Therefore (m+n=-1).
Step 3
Exam Tip
(p(0)=n=-8) और (5m-8=27) से (m=7) मिलता है। इसलिए (m+n=-1) है।
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यदि (p(x)=mx+n), (p(-4)=3) और (p(2)=27), तो (m) क्या है?
If (p(x)=mx+n), (p(-4)=3) and (p(2)=27), what is (m)?
#polynomial
#linear
#slope_parameter
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A (2)
B (4)
C (6)
D (24)
Explanation opens after your attempt
Step 1
Concept
Subtracting the two values gives (p(2)-p(-4)=6m=24). Therefore (m=4).
Step 2
Why this answer is correct
The correct answer is B. (4). Subtracting the two values gives (p(2)-p(-4)=6m=24). Therefore (m=4).
Step 3
Exam Tip
दोनों मान घटाने पर (p(2)-p(-4)=6m=24) मिलता है। इसलिए (m=4) है।
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किस विकल्प में (p(9)=0) और (p(x)) रेखीय है?
Which option has (p(9)=0) and (p(x)) is linear?
#polynomial
#linear
#zero_identification
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A (p(x)=x+9)
B (p(x)=9x+9)
C (p(x)=x-2 -81)
D (p(x)=x-9)
Explanation opens after your attempt
Correct Answer
D. (p(x)=x-9)
Step 1
Concept
Substituting (x=9) in (x-9) gives (0). It is a linear polynomial of degree (1).
Step 2
Why this answer is correct
The correct answer is D. (p(x)=x-9). Substituting (x=9) in (x-9) gives (0). It is a linear polynomial of degree (1).
Step 3
Exam Tip
(x-9) में (x=9) रखने पर (0) मिलता है। यह डिग्री (1) वाला रेखीय बहुपद है।
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यदि (p(x)=8x-15), तो (p(x)+p(-x)) क्या है?
If (p(x)=8x-15), what is (p(x)+p(-x))?
#polynomial
#linear
#symmetry
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A (16x-30)
B (-30)
C (0)
D (8x-30)
Explanation opens after your attempt
Step 1
Concept
(p(-x)=-8x-15). Adding gives (8x-15-8x-15=-30).
Step 2
Why this answer is correct
The correct answer is B. (-30). (p(-x)=-8x-15). Adding gives (8x-15-8x-15=-30).
Step 3
Exam Tip
(p(-x)=-8x-15) है। जोड़ने पर (8x-15-8x-15=-30) मिलता है।
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यदि (p(x)=8x-15), तो (p(x)-p(-x)) क्या है?
If (p(x)=8x-15), what is (p(x)-p(-x))?
#polynomial
#linear
#symmetry
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A (16x)
B (0)
C (-30)
D (8x)
Explanation opens after your attempt
Step 1
Concept
(p(-x)=-8x-15). Subtracting gives (8x-15-(-8x-15)=16x).
Step 2
Why this answer is correct
The correct answer is A. (16x). (p(-x)=-8x-15). Subtracting gives (8x-15-(-8x-15)=16x).
Step 3
Exam Tip
(p(-x)=-8x-15) है। घटाने पर (8x-15-(-8x-15)=16x) मिलता है।
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किस मान पर ((s+9)x+6s) का शून्यक (0) होगा?
For which value will the zero of ((s+9)x+6s) be (0)?
#polynomial
#linear
#zero_at_origin
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A (s=0)
B (s=-9)
C (s=9)
D कोई मान नहीं / No value
Explanation opens after your attempt
Step 1
Concept
For the zero to be (0), the constant term (6s=0). At (s=0), the coefficient of (x) is (9), 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 (6s=0). At (s=0), the coefficient of (x) is (9), so the polynomial is linear.
Step 3
Exam Tip
शून्यक (0) होने के लिए नियतांक पद (6s=0) होना चाहिए। (s=0) पर (x) का गुणांक (9) है इसलिए बहुपद रेखीय है।
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यदि (p(x)=7x+a) और (q(x)=9x-a), तो (p(x)+q(x)) का शून्यक (2) होने पर (a) क्या है?
If (p(x)=7x+a) and (q(x)=9x-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 (2)
D (16)
Explanation opens after your attempt
Correct Answer
A. कोई मान नहीं / No value
Step 1
Concept
(p(x)+q(x)=16x), 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)=16x), whose zero is (0). Therefore the zero cannot be (2) for any (a).
Step 3
Exam Tip
(p(x)+q(x)=16x) है जिसका शून्यक (0) है। इसलिए शून्यक (2) किसी (a) पर नहीं हो सकता।
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यदि (p(x)=7x+a) और (q(x)=9x-a), तो (q(x)-p(x)) क्या है?
If (p(x)=7x+a) and (q(x)=9x-a), what is (q(x)-p(x))?
#polynomial
#linear
#parameter_difference
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A (16x)
B (2x-2a)
C (2x)
D (2a)
Explanation opens after your attempt
Correct Answer
B. (2x-2a)
Step 1
Concept
(9x-a-(7x+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). (9x-a-(7x+a)=2x-2a). Change the signs inside the bracket while subtracting.
Step 3
Exam Tip
(9x-a-(7x+a)=2x-2a) है। घटाते समय कोष्ठक के चिन्ह बदलें।
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किस विकल्प में ((6x-1)) और ((x+8)) का गुणनफल रेखीय नहीं है?
Which option correctly says that the product of ((6x-1)) and ((x+8)) is not linear?
#polynomial
#linear
#product_reason
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A क्योंकि डिग्री (1) है / Because degree is (1)
B क्योंकि यह नियतांक है / Because it is constant
C क्योंकि डिग्री (2) है / Because degree is (2)
D क्योंकि यह शून्य है / Because it is zero
Explanation opens after your attempt
Correct Answer
C. क्योंकि डिग्री (2) है / Because degree is (2)
Step 1
Concept
In ((6x-1)(x+8)), the highest term is \(6x^2\). So the product has degree (2) and is not linear.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि डिग्री (2) है / Because degree is (2). In ((6x-1)(x+8)), the highest term is \(6x^2\). So the product has degree (2) and is not linear.
Step 3
Exam Tip
((6x-1)(x+8)) में उच्चतम पद \(6x^2\) है। इसलिए गुणनफल की डिग्री (2) है और यह रेखीय नहीं है।
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यदि (p(x)=ax+7) और (p(p(0))=63), तो (a) क्या है?
If (p(x)=ax+7) and (p(p(0))=63), what is (a)?
#polynomial
#linear
#composition_parameter
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A (7)
B (8)
C (9)
D (63)
Explanation opens after your attempt
Step 1
Concept
(p(0)=7) and (p(7)=7a+7). From (7a+7=63), we get (a=8).
Step 2
Why this answer is correct
The correct answer is B. (8). (p(0)=7) and (p(7)=7a+7). From (7a+7=63), we get (a=8).
Step 3
Exam Tip
(p(0)=7) और (p(7)=7a+7) है। (7a+7=63) से (a=8) मिलता है।
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यदि (p(x)=x+a) और (p(p(5))=19), तो (a) का मान क्या है?
If (p(x)=x+a) and (p(p(5))=19), what is the value of (a)?
#polynomial
#linear
#composition_parameter
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A (5)
B (6)
C (7)
D (14)
Explanation opens after your attempt
Step 1
Concept
(p(5)=5+a) and (p(5+a)=5+2a). From (5+2a=19), we get (a=7).
Step 2
Why this answer is correct
The correct answer is C. (7). (p(5)=5+a) and (p(5+a)=5+2a). From (5+2a=19), we get (a=7).
Step 3
Exam Tip
(p(5)=5+a) और (p(5+a)=5+2a) है। (5+2a=19) से (a=7) मिलता है।
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यदि (p(x)=mx+n) और (p(-5)=p(3)), तो (p(x)) रेखीय कब हो सकता है?
If (p(x)=mx+n) and (p(-5)=p(3)), when can (p(x)) be linear?
#polynomial
#linear
#condition_check
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A जब (m=0) / When (m=0)
B जब (n=0) / When (n=0)
C कभी नहीं / Never
D हर (m) पर / For every (m)
Explanation opens after your attempt
Correct Answer
C. कभी नहीं / Never
Step 1
Concept
From (p(-5)=p(3)), (-5m+n=3m+n), so (m=0). At (m=0), the polynomial is not linear.
Step 2
Why this answer is correct
The correct answer is C. कभी नहीं / Never. From (p(-5)=p(3)), (-5m+n=3m+n), so (m=0). At (m=0), the polynomial is not linear.
Step 3
Exam Tip
(p(-5)=p(3)) से (-5m+n=3m+n) और (m=0) मिलता है। (m=0) पर बहुपद रेखीय नहीं रहता।
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किस विकल्प में (p(x)=ax+b) का शून्यक (12) होगा?
In which option will (p(x)=ax+b) have zero (12)?
#polynomial
#linear
#general_condition
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A (b=12a) और \(a\neq0\) / (b=12a) and \(a\neq0\)
B (b=-12a) और \(a\neq0\) / (b=-12a) and \(a\neq0\)
C (a=0)
D (b=0)
Explanation opens after your attempt
Correct Answer
B. (b=-12a) और \(a\neq0\) / (b=-12a) and \(a\neq0\)
Step 1
Concept
If the zero is (12), then (12a+b=0). So (b=-12a) and \(a\neq0\) are needed.
Step 2
Why this answer is correct
The correct answer is B. (b=-12a) और \(a\neq0\) / (b=-12a) and \(a\neq0\). If the zero is (12), then (12a+b=0). So (b=-12a) and \(a\neq0\) are needed.
Step 3
Exam Tip
शून्यक (12) होने पर (12a+b=0) होगा। इसलिए (b=-12a) और \(a\neq0\) चाहिए।
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यदि (p(x)=13x-7), तो (p(x+2)-p(x-1)) क्या है?
If (p(x)=13x-7), what is (p(x+2)-p(x-1))?
#polynomial
#linear
#shift_difference
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A (13)
B (26)
C (39)
D (52)
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Step 1
Concept
(p(x+2)=13x+19) and (p(x-1)=13x-20). The difference is (39).
Step 2
Why this answer is correct
The correct answer is C. (39). (p(x+2)=13x+19) and (p(x-1)=13x-20). The difference is (39).
Step 3
Exam Tip
(p(x+2)=13x+19) और (p(x-1)=13x-20) है। अंतर (39) है।
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यदि (p(x)=11x-32), तो (p(p(3))) का सही मान क्या है?
If (p(x)=11x-32), what is the correct value of (p(p(3)))?
#polynomial
#linear
#composition_value
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A (1)
B (-21)
C (3)
D (11)
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Step 1
Concept
(p(3)=1) and (p(1)=11-32=-21). Find the inner value first.
Step 2
Why this answer is correct
The correct answer is B. (-21). (p(3)=1) and (p(1)=11-32=-21). Find the inner value first.
Step 3
Exam Tip
(p(3)=1) और (p(1)=11-32=-21) है। अंदर वाले मान को पहले निकालें।
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यदि (p(x)=15x+a) और (p(p(0))=240), तो (a) का मान क्या है?
If (p(x)=15x+a) and (p(p(0))=240), what is the value of (a)?
#polynomial
#linear
#composition_parameter
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A (12)
B (15)
C (16)
D (240)
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Step 1
Concept
(p(0)=a) and (p(a)=15a+a=16a). From (16a=240), we get (a=15).
Step 2
Why this answer is correct
The correct answer is B. (15). (p(0)=a) and (p(a)=15a+a=16a). From (16a=240), we get (a=15).
Step 3
Exam Tip
(p(0)=a) और (p(a)=15a+a=16a) है। (16a=240) से (a=15) मिलता है।
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यदि (p(x)=mx+n), (p(-3)=4) और (p(2)=29), तो (m+n) क्या है?
If (p(x)=mx+n), (p(-3)=4) and (p(2)=29), what is (m+n)?
#polynomial
#linear
#coefficients
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A (20)
B (24)
C (25)
D (29)
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Step 1
Concept
Subtracting the two values gives (5m=25), so (m=5). Then (-3m+n=4) gives (n=19), so (m+n=24).
Step 2
Why this answer is correct
The correct answer is B. (24). Subtracting the two values gives (5m=25), so (m=5). Then (-3m+n=4) gives (n=19), so (m+n=24).
Step 3
Exam Tip
दोनों मान घटाने पर (5m=25) से (m=5) मिलता है। फिर (-3m+n=4) से (n=19), इसलिए (m+n=24) है।
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यदि (p(x)=16x-11), तो (p(x+2)+p(x-3)) क्या है?
If (p(x)=16x-11), what is (p(x+2)+p(x-3))?
#polynomial
#linear
#shift_sum
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A (32x-11)
B (32x+38)
C (16x-38)
D (32x-38)
Explanation opens after your attempt
Correct Answer
D. (32x-38)
Step 1
Concept
(p(x+2)=16x+21) and (p(x-3)=16x-59). Adding gives (32x-38).
Step 2
Why this answer is correct
The correct answer is D. (32x-38). (p(x+2)=16x+21) and (p(x-3)=16x-59). Adding gives (32x-38).
Step 3
Exam Tip
(p(x+2)=16x+21) और (p(x-3)=16x-59) है। जोड़ने पर (32x-38) मिलता है।
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किस मान पर (\(r^2-11r+30\)x+8) रेखीय बहुपद नहीं रहेगा?
For which value will (\(r^2-11r+30\)x+8) not remain a linear polynomial?
#polynomial
#linear
#parameter_condition
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A (r=5) या (r=6) / (r=5) or (r=6)
B (r=0) या (r=30) / (r=0) or (r=30)
C (r=11) ही / (r=11) only
D कोई मान नहीं / No value
Explanation opens after your attempt
Correct Answer
A. (r=5) या (r=6) / (r=5) or (r=6)
Step 1
Concept
For it not to be linear, the coefficient of (x) must be (0). From \(r^2-11r+30=0\), (r=5) or (r=6).
Step 2
Why this answer is correct
The correct answer is A. (r=5) या (r=6) / (r=5) or (r=6). For it not to be linear, the coefficient of (x) must be (0). From \(r^2-11r+30=0\), (r=5) or (r=6).
Step 3
Exam Tip
रेखीय न रहने के लिए (x) का गुणांक (0) होना चाहिए। \(r^2-11r+30=0\) से (r=5) या (r=6) मिलता है।
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