सरल करने के बाद (4(3x-2)-5(2x+7)) कौन सा रेखीय बहुपद बनेगा?
After simplifying (4(3x-2)-5(2x+7)), which linear polynomial is obtained?
#polynomial
#linear
#simplification
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A (2x+43)
B (2x-43)
C (22x-43)
D (2x-27)
Explanation opens after your attempt
Correct Answer
B. (2x-43)
Step 1
Concept
(12x-8-10x-35=2x-43). Multiply every term while opening brackets.
Step 2
Why this answer is correct
The correct answer is B. (2x-43). (12x-8-10x-35=2x-43). Multiply every term while opening brackets.
Step 3
Exam Tip
(12x-8-10x-35=2x-43) है। कोष्ठक खोलते समय सभी पदों पर गुणा करें।
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किस मान पर (\(u^2-16\)x+5) रेखीय बहुपद नहीं रहेगा?
For which value will (\(u^2-16\)x+5) not remain a linear polynomial?
#polynomial
#linear
#parameter_condition
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A (u=4) या (u=-4) / (u=4) or (u=-4)
B (u=0)
C (u=16)
D (u=2) या (u=-2) / (u=2) or (u=-2)
Explanation opens after your attempt
Correct Answer
A. (u=4) या (u=-4) / (u=4) or (u=-4)
Step 1
Concept
For it not to be linear, the coefficient of (x) must be (0). From \(u^2-16=0\), \(u=\pm4\).
Step 2
Why this answer is correct
The correct answer is A. (u=4) या (u=-4) / (u=4) or (u=-4). For it not to be linear, the coefficient of (x) must be (0). From \(u^2-16=0\), \(u=\pm4\).
Step 3
Exam Tip
रेखीय न रहने के लिए (x) का गुणांक (0) होना चाहिए। \(u^2-16=0\) से \(u=\pm4\) मिलता है।
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यदि (p(x)=(k+2)x-20) का शून्यक (4) है, तो (k) क्या है?
If the zero of (p(x)=(k+2)x-20) is (4), what is (k)?
#polynomial
#linear
#zero_parameter
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A (1)
B (2)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (4(k+2)-20=0), we get (k=3). Substitute the zero into the polynomial and set it to (0).
Step 2
Why this answer is correct
The correct answer is C. (3). From (4(k+2)-20=0), we get (k=3). Substitute the zero into the polynomial and set it to (0).
Step 3
Exam Tip
(4(k+2)-20=0) से (k=3) मिलता है। शून्यक को बहुपद में रखकर (0) करें।
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यदि (p(x)=7x-3) और (q(x)=4x+5), तो (2p(x)-3q(x)) क्या है?
If (p(x)=7x-3) and (q(x)=4x+5), what is (2p(x)-3q(x))?
#polynomial
#linear
#combination
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A (2x-21)
B (26x+9)
C (2x+21)
D (14x-15)
Explanation opens after your attempt
Correct Answer
A. (2x-21)
Step 1
Concept
(2(7x-3)-3(4x+5)=2x-21). Multiply first and then combine like terms.
Step 2
Why this answer is correct
The correct answer is A. (2x-21). (2(7x-3)-3(4x+5)=2x-21). Multiply first and then combine like terms.
Step 3
Exam Tip
(2(7x-3)-3(4x+5)=2x-21) है। गुणा करने के बाद समान पद मिलाएं।
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किस मान पर ((3a-4)x+16) का शून्यक (-2) होगा?
For which value will the zero of ((3a-4)x+16) be (-2)?
#polynomial
#linear
#parameter_zero
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A (a=4)
B (a=-4)
C (a=2)
D (a=0)
Explanation opens after your attempt
Step 1
Concept
If the zero is (-2), then (-2(3a-4)+16=0). This gives (a=4).
Step 2
Why this answer is correct
The correct answer is A. (a=4). If the zero is (-2), then (-2(3a-4)+16=0). This gives (a=4).
Step 3
Exam Tip
शून्यक (-2) होने पर (-2(3a-4)+16=0) होगा। इससे (a=4) मिलता है।
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यदि (p(x)=ax+b) का शून्यक (6) है और (a=-3), तो (b) क्या है?
If the zero of (p(x)=ax+b) is (6) and (a=-3), what is (b)?
#polynomial
#linear
#general_form
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A (3)
B (6)
C (-18)
D (18)
Explanation opens after your attempt
Step 1
Concept
From (p(6)=0), (6a+b=0). Substituting (a=-3) gives (b=18).
Step 2
Why this answer is correct
The correct answer is D. (18). From (p(6)=0), (6a+b=0). Substituting (a=-3) gives (b=18).
Step 3
Exam Tip
(p(6)=0) से (6a+b=0) होगा। (a=-3) रखने पर (b=18) मिलता है।
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यदि (p(x)=9x+c) और (p(5)=p(1)+36), तो (c) के बारे में क्या सही है?
If (p(x)=9x+c) and (p(5)=p(1)+36), what is correct about (c)?
#polynomial
#linear
#condition_check
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A केवल (c=0) / Only (c=0)
B ऐसा कोई (c) नहीं / No such (c)
C हर (c) सही है / Every (c) is valid
D केवल (c=36) / Only (c=36)
Explanation opens after your attempt
Correct Answer
C. हर (c) सही है / Every (c) is valid
Step 1
Concept
(p(5)-p(1)=(45+c)-(9+c)=36). So the condition is true for every (c).
Step 2
Why this answer is correct
The correct answer is C. हर (c) सही है / Every (c) is valid. (p(5)-p(1)=(45+c)-(9+c)=36). So the condition is true for every (c).
Step 3
Exam Tip
(p(5)-p(1)=(45+c)-(9+c)=36) है। इसलिए शर्त हर (c) के लिए सही है।
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किस विकल्प में रेखीय बहुपद का शून्यक \(-\frac{8}{11}\) है?
Which option has zero \(-\frac{8}{11}\) for a linear polynomial?
#polynomial
#linear
#fraction_zero
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A (11x-8)
B (8x+11)
C \(x+\frac{11}{8}\)
D (11x+8)
Explanation opens after your attempt
Correct Answer
D. (11x+8)
Step 1
Concept
From (11x+8=0), we get \(x=-\frac{8}{11}\). Pay attention to the sign and denominator in fractional zeros.
Step 2
Why this answer is correct
The correct answer is D. (11x+8). From (11x+8=0), we get \(x=-\frac{8}{11}\). Pay attention to the sign and denominator in fractional zeros.
Step 3
Exam Tip
(11x+8=0) से \(x=-\frac{8}{11}\) मिलता है। भिन्न शून्यक में चिन्ह और हर ध्यान रखें।
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यदि (p(x)=\frac{7}{10}x-14), तो किस मान पर (p(x)=0) होगा?
If (p(x)=\frac{7}{10}x-14), for which value will (p(x)=0)?
#polynomial
#linear
#fraction_equation
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A (x=10)
B (x=14)
C (x=20)
D (x=28)
Explanation opens after your attempt
Step 1
Concept
From \(\frac{7}{10}x-14=0\), \(\frac{7}{10}x=14\) and (x=20). With a fractional coefficient, multiply by the reciprocal.
Step 2
Why this answer is correct
The correct answer is C. (x=20). From \(\frac{7}{10}x-14=0\), \(\frac{7}{10}x=14\) and (x=20). With a fractional coefficient, multiply by the reciprocal.
Step 3
Exam Tip
\(\frac{7}{10}x-14=0\) से \(\frac{7}{10}x=14\) और (x=20) मिलता है। भिन्न गुणांक में उलटा गुणा करें।
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यदि (p(x)=x+9) और (q(x)=x-5), तो (p(x)q(x)) की डिग्री क्या है?
If (p(x)=x+9) and (q(x)=x-5), what is the degree of (p(x)q(x))?
#polynomial
#linear
#product_degree
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A (1)
B (2)
C (5)
D (9)
Explanation opens after your attempt
Step 1
Concept
In ((x+9)(x-5)), 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+9)(x-5)), the highest term is \(x^2\). Therefore the product has degree (2).
Step 3
Exam Tip
((x+9)(x-5)) में उच्चतम पद \(x^2\) है। इसलिए गुणनफल की डिग्री (2) है।
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यदि (p(x)=8x-15), तो (p(x-2)) क्या है?
If (p(x)=8x-15), what is (p(x-2))?
#polynomial
#linear
#composition
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A (8x-17)
B (8x-31)
C (8x+1)
D (x-31)
Explanation opens after your attempt
Correct Answer
B. (8x-31)
Step 1
Concept
(p(x-2)=8(x-2)-15=8x-31). Substitute the whole (x-2) in place of (x).
Step 2
Why this answer is correct
The correct answer is B. (8x-31). (p(x-2)=8(x-2)-15=8x-31). Substitute the whole (x-2) in place of (x).
Step 3
Exam Tip
(p(x-2)=8(x-2)-15=8x-31) है। (x) की जगह पूरा (x-2) रखें।
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यदि (p(x)=17-6x), तो (p(3x)) कौन सा है?
If (p(x)=17-6x), which is (p(3x))?
#polynomial
#linear
#substitution
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A (17-18x)
B (51-6x)
C (17-6x)
D (51-18x)
Explanation opens after your attempt
Correct Answer
A. (17-18x)
Step 1
Concept
(p(3x)=17-6(3x)=17-18x). While substituting, use the whole (3x).
Step 2
Why this answer is correct
The correct answer is A. (17-18x). (p(3x)=17-6(3x)=17-18x). While substituting, use the whole (3x).
Step 3
Exam Tip
(p(3x)=17-6(3x)=17-18x) है। प्रतिस्थापन करते समय पूरे (3x) को रखें।
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किस मान पर (\(t^2-7t+12\)x+(t-4)) रेखीय बहुपद नहीं रहेगा?
For which value will (\(t^2-7t+12\)x+(t-4)) not remain a linear polynomial?
#polynomial
#linear
#parameter_condition
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A (t=3) या (t=4) / (t=3) or (t=4)
B (t=0)
C (t=7)
D (t=-3)
Explanation opens after your attempt
Correct Answer
A. (t=3) या (t=4) / (t=3) or (t=4)
Step 1
Concept
For it to be linear, \(t^2-7t+12\neq0\) is needed. From \(t^2-7t+12=0\), (t=3) or (t=4).
Step 2
Why this answer is correct
The correct answer is A. (t=3) या (t=4) / (t=3) or (t=4). For it to be linear, \(t^2-7t+12\neq0\) is needed. From \(t^2-7t+12=0\), (t=3) or (t=4).
Step 3
Exam Tip
रेखीय होने के लिए \(t^2-7t+12\neq0\) चाहिए। \(t^2-7t+12=0\) से (t=3) या (t=4) मिलता है।
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यदि (p(x)=kx+11) और (p(6)=p(-2)), तो (p(x)) रेखीय कब रहेगा?
If (p(x)=kx+11) and (p(6)=p(-2)), when will (p(x)) remain linear?
#polynomial
#linear
#condition_check
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A जब (k=0) / When (k=0)
B जब (k=11) / When (k=11)
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(6)=p(-2)), (6k+11=-2k+11), 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(6)=p(-2)), (6k+11=-2k+11), so (k=0). At (k=0), the polynomial is not linear.
Step 3
Exam Tip
(p(6)=p(-2)) से (6k+11=-2k+11) और (k=0) मिलता है। (k=0) पर बहुपद रेखीय नहीं रहता।
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यदि (p(x)=6x+4) और (q(x)=13x-1), तो (q(x)-2p(x)) की डिग्री क्या है?
If (p(x)=6x+4) and (q(x)=13x-1), 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)=13x-1-2(6x+4)=x-9). Its degree is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). (q(x)-2p(x)=13x-1-2(6x+4)=x-9). Its degree is (1).
Step 3
Exam Tip
(q(x)-2p(x)=13x-1-2(6x+4)=x-9) है। इसकी डिग्री (1) है।
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किस विकल्प में रेखीय बहुपद का शून्यक \(\frac{23}{9}\) है?
Which option has zero \(\frac{23}{9}\) for a linear polynomial?
#polynomial
#linear
#fraction_zero
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A (23x-9)
B (9x-23)
C (9x+23)
D \(x-\frac{9}{23}\)
Explanation opens after your attempt
Correct Answer
B. (9x-23)
Step 1
Concept
From (9x-23=0), we get \(x=\frac{23}{9}\). Set the polynomial equal to (0) to find the zero.
Step 2
Why this answer is correct
The correct answer is B. (9x-23). From (9x-23=0), we get \(x=\frac{23}{9}\). Set the polynomial equal to (0) to find the zero.
Step 3
Exam Tip
(9x-23=0) से \(x=\frac{23}{9}\) मिलता है। शून्यक के लिए बहुपद को (0) के बराबर रखें।
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यदि (p(x)=10x-21), तो (p(x+1)-p(x)) क्या है?
If (p(x)=10x-21), what is (p(x+1)-p(x))?
#polynomial
#linear
#difference_value
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A (1)
B (10)
C (x+1)
D (10x)
Explanation opens after your attempt
Step 1
Concept
(p(x+1)=10x-11) and (p(x)=10x-21). The difference is (10).
Step 2
Why this answer is correct
The correct answer is B. (10). (p(x+1)=10x-11) and (p(x)=10x-21). The difference is (10).
Step 3
Exam Tip
(p(x+1)=10x-11) और (p(x)=10x-21) है। अंतर (10) मिलता है।
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यदि (p(x)=\lambda x+18) और इसका शून्यक (-6) से बड़ा है, तो \(\lambda>0\) होने पर कौन सी शर्त सही है?
If (p(x)=\lambda x+18) and its zero is greater than (-6), 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 \(-\frac{18}{\lambda}\). From \(-\frac{18}{\lambda}>-6\) and \(\lambda>0\), we get \(\lambda>3\).
Step 2
Why this answer is correct
The correct answer is C. \(\lambda>3\). The zero is \(-\frac{18}{\lambda}\). From \(-\frac{18}{\lambda}>-6\) and \(\lambda>0\), we get \(\lambda>3\).
Step 3
Exam Tip
शून्यक \(-\frac{18}{\lambda}\) है। \(-\frac{18}{\lambda}>-6\) और \(\lambda>0\) से \(\lambda>3\) मिलता है।
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किस विकल्प में (p(x)=ax+b) का शून्यक (-9) होगा?
In which option will (p(x)=ax+b) have zero (-9)?
#polynomial
#linear
#general_condition
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A (b=9a) और \(a\neq0\) / (b=9a) and \(a\neq0\)
B (b=-9a) और \(a\neq0\) / (b=-9a) and \(a\neq0\)
C (a=0)
D (b=0)
Explanation opens after your attempt
Correct Answer
A. (b=9a) और \(a\neq0\) / (b=9a) and \(a\neq0\)
Step 1
Concept
If the zero is (-9), then (-9a+b=0). So (b=9a) and \(a\neq0\) are needed.
Step 2
Why this answer is correct
The correct answer is A. (b=9a) और \(a\neq0\) / (b=9a) and \(a\neq0\). If the zero is (-9), then (-9a+b=0). So (b=9a) and \(a\neq0\) are needed.
Step 3
Exam Tip
शून्यक (-9) होने पर (-9a+b=0) होगा। इसलिए (b=9a) और \(a\neq0\) चाहिए।
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यदि (p(x)=x+4r) और (q(x)=x-7r), तो (p(x)+q(x)) क्या है?
If (p(x)=x+4r) and (q(x)=x-7r), what is (p(x)+q(x))?
#polynomial
#linear
#parameter_sum
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A (2x-3r)
B (2x+11r)
C (x-3r)
D (11r)
Explanation opens after your attempt
Correct Answer
A. (2x-3r)
Step 1
Concept
On adding, (x+4r+x-7r=2x-3r). Combine the parameter terms too.
Step 2
Why this answer is correct
The correct answer is A. (2x-3r). On adding, (x+4r+x-7r=2x-3r). Combine the parameter terms too.
Step 3
Exam Tip
जोड़ने पर (x+4r+x-7r=2x-3r) मिलता है। पैरामीटर वाले पदों को भी मिलाएं।
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यदि (p(x)=x+4r) और (q(x)=x-7r), तो (p(x)-q(x)) किस प्रकार का बहुपद है?
If (p(x)=x+4r) and (q(x)=x-7r), 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)=11r). 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)=11r). With respect to (x), it is a constant polynomial.
Step 3
Exam Tip
(p(x)-q(x)=11r) है। (x) के संदर्भ में यह नियतांक बहुपद है।
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यदि (p(x)=8x-23), तो (p(p(3))) का सही मान क्या है?
If (p(x)=8x-23), what is the correct value of (p(p(3)))?
#polynomial
#linear
#composition_value
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A (1)
B (-15)
C (3)
D (8)
Explanation opens after your attempt
Step 1
Concept
(p(3)=1) and (p(1)=8-23=-15). Find the inner value first.
Step 2
Why this answer is correct
The correct answer is B. (-15). (p(3)=1) and (p(1)=8-23=-15). Find the inner value first.
Step 3
Exam Tip
(p(3)=1) और (p(1)=8-23=-15) है। अंदर वाले मान को पहले निकालें।
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यदि (p(x)=5x+4), तो (p(p(0))) का मान क्या है?
If (p(x)=5x+4), what is the value of (p(p(0)))?
#polynomial
#linear
#composition_value
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A (4)
B (20)
C (24)
D (25)
Explanation opens after your attempt
Step 1
Concept
(p(0)=4) and (p(4)=24). In composition, find the inner value first.
Step 2
Why this answer is correct
The correct answer is C. (24). (p(0)=4) and (p(4)=24). In composition, find the inner value first.
Step 3
Exam Tip
(p(0)=4) और (p(4)=24) है। रचना में अंदर वाला मान पहले निकालें।
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किस मान पर ((n-5)x+3n+2) का शून्यक (1) होगा?
For which value will the zero of ((n-5)x+3n+2) be (1)?
#polynomial
#linear
#parameter_zero
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A \(n=\frac{3}{4}\)
B (n=1)
C (n=-1)
D (n=5)
Explanation opens after your attempt
Correct Answer
A. \(n=\frac{3}{4}\)
Step 1
Concept
If the zero is (1), then (n-5+3n+2=0). Thus (4n-3=0) and \(n=\frac{3}{4}\).
Step 2
Why this answer is correct
The correct answer is A. \(n=\frac{3}{4}\). If the zero is (1), then (n-5+3n+2=0). Thus (4n-3=0) and \(n=\frac{3}{4}\).
Step 3
Exam Tip
शून्यक (1) होने पर (n-5+3n+2=0) होगा। इससे (4n-3=0) और \(n=\frac{3}{4}\) मिलता है।
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यदि (p(x)=\frac{x}{7}+a) और (p(21)=16), तो (a) का मान क्या है?
If (p(x)=\frac{x}{7}+a) and (p(21)=16), what is the value of (a)?
#polynomial
#linear
#fraction_parameter
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A (10)
B (12)
C (13)
D (16)
Explanation opens after your attempt
Step 1
Concept
From (p(21)=3+a=16), we get (a=13). In fractional form, substitute the value of (x) first.
Step 2
Why this answer is correct
The correct answer is C. (13). From (p(21)=3+a=16), we get (a=13). In fractional form, substitute the value of (x) first.
Step 3
Exam Tip
(p(21)=3+a=16) से (a=13) मिलता है। भिन्न रूप में पहले (x) का मान रखें।
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यदि (p(x)=6x+a) और (q(x)=3x-10), तो (p(x)+q(x)) का शून्यक (2) होने पर (a) क्या है?
If (p(x)=6x+a) and (q(x)=3x-10), what is (a) if the zero of (p(x)+q(x)) is (2)?
#polynomial
#linear
#sum_zero_parameter
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A (-8)
B (-6)
C (0)
D (8)
Explanation opens after your attempt
Step 1
Concept
(p(x)+q(x)=9x+a-10). Substituting (x=2) gives (18+a-10=0), so (a=-8).
Step 2
Why this answer is correct
The correct answer is A. (-8). (p(x)+q(x)=9x+a-10). Substituting (x=2) gives (18+a-10=0), so (a=-8).
Step 3
Exam Tip
(p(x)+q(x)=9x+a-10) है। (x=2) रखने पर (18+a-10=0) से (a=-8) मिलता है।
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किस मान पर (p(x)=(c-5)x+6c) का शून्यक (-3) होगा?
For which value will the zero of (p(x)=(c-5)x+6c) be (-3)?
#polynomial
#linear
#parameter_zero
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A (c=-5)
B (c=5)
C (c=1)
D कोई मान नहीं / No value
Explanation opens after your attempt
Step 1
Concept
From (-3(c-5)+6c=0), we get (3c+15=0). Therefore (c=-5).
Step 2
Why this answer is correct
The correct answer is A. (c=-5). From (-3(c-5)+6c=0), we get (3c+15=0). Therefore (c=-5).
Step 3
Exam Tip
(-3(c-5)+6c=0) से (3c+15=0) मिलता है। इसलिए (c=-5) है।
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यदि (p(x)=(c-2)x+4c) का शून्यक (-4) है, तो कौन सा निष्कर्ष सही है?
If the zero of (p(x)=(c-2)x+4c) is (-4), which conclusion is correct?
#polynomial
#linear
#no_solution
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A (c=2)
B (c=-2)
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 (-4(c-2)+4c=0), we get the impossible result (8=0). Therefore no (c) exists.
Step 2
Why this answer is correct
The correct answer is C. कोई (c) नहीं / No (c). From (-4(c-2)+4c=0), we get the impossible result (8=0). Therefore no (c) exists.
Step 3
Exam Tip
(-4(c-2)+4c=0) से (8=0) जैसा असंभव परिणाम मिलता है। इसलिए कोई (c) नहीं है।
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यदि (p(x)=rx-9) और (p(5)=21), तो (p(-1)) का मान क्या है?
If (p(x)=rx-9) and (p(5)=21), what is the value of (p(-1))?
#polynomial
#linear
#two_step
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A (0)
B (-15)
C (-18)
D (6)
Explanation opens after your attempt
Step 1
Concept
From (5r-9=21), we get (r=6). Therefore (p(-1)=6(-1)-9=-15).
Step 2
Why this answer is correct
The correct answer is B. (-15). From (5r-9=21), we get (r=6). Therefore (p(-1)=6(-1)-9=-15).
Step 3
Exam Tip
(5r-9=21) से (r=6) मिलता है। इसलिए (p(-1)=6(-1)-9=-15) है।
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यदि (p(x)=ax+12) और (p(3)=p(7)-20), तो (a) क्या है?
If (p(x)=ax+12) and (p(3)=p(7)-20), what is (a)?
#polynomial
#linear
#parameter_equation
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A (3)
B (4)
C (5)
D (12)
Explanation opens after your attempt
Step 1
Concept
From (3a+12=(7a+12)-20), we get (3a=7a-20). Therefore (a=5).
Step 2
Why this answer is correct
The correct answer is C. (5). From (3a+12=(7a+12)-20), we get (3a=7a-20). Therefore (a=5).
Step 3
Exam Tip
(3a+12=(7a+12)-20) से (3a=7a-20) मिलता है। इसलिए (a=5) है।
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यदि (p(x)=6x-25), तो (p(a)=a) होने पर (a) क्या है?
If (p(x)=6x-25), what is (a) when (p(a)=a)?
#polynomial
#linear
#fixed_value
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A (4)
B (5)
C (6)
D (25)
Explanation opens after your attempt
Step 1
Concept
(p(a)=6a-25). From (6a-25=a), we get (a=5).
Step 2
Why this answer is correct
The correct answer is B. (5). (p(a)=6a-25). From (6a-25=a), we get (a=5).
Step 3
Exam Tip
(p(a)=6a-25) है। (6a-25=a) से (a=5) मिलता है।
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यदि (p(x)=mx+n), (p(0)=-6) और (p(4)=18), तो (m+n) क्या है?
If (p(x)=mx+n), (p(0)=-6) and (p(4)=18), what is (m+n)?
#polynomial
#linear
#coefficients
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A (0)
B (6)
C (12)
D (18)
Explanation opens after your attempt
Step 1
Concept
(p(0)=n=-6) and (4m-6=18) gives (m=6). Therefore (m+n=0).
Step 2
Why this answer is correct
The correct answer is A. (0). (p(0)=n=-6) and (4m-6=18) gives (m=6). Therefore (m+n=0).
Step 3
Exam Tip
(p(0)=n=-6) और (4m-6=18) से (m=6) मिलता है। इसलिए (m+n=0) है।
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यदि (p(x)=mx+n), (p(-3)=2) और (p(1)=18), तो (m) क्या है?
If (p(x)=mx+n), (p(-3)=2) and (p(1)=18), what is (m)?
#polynomial
#linear
#slope_parameter
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A (2)
B (4)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
Subtracting the two values gives (p(1)-p(-3)=4m=16). Therefore (m=4).
Step 2
Why this answer is correct
The correct answer is B. (4). Subtracting the two values gives (p(1)-p(-3)=4m=16). Therefore (m=4).
Step 3
Exam Tip
दोनों मान घटाने पर (p(1)-p(-3)=4m=16) मिलता है। इसलिए (m=4) है।
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किस विकल्प में (p(7)=0) और (p(x)) रेखीय है?
Which option has (p(7)=0) and (p(x)) is linear?
#polynomial
#linear
#zero_identification
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A (p(x)=x+7)
B (p(x)=7x+7)
C (p(x)=x-2 -49)
D (p(x)=x-7)
Explanation opens after your attempt
Correct Answer
D. (p(x)=x-7)
Step 1
Concept
Substituting (x=7) in (x-7) 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-7). Substituting (x=7) in (x-7) gives (0). It is a linear polynomial of degree (1).
Step 3
Exam Tip
(x-7) में (x=7) रखने पर (0) मिलता है। यह डिग्री (1) वाला रेखीय बहुपद है।
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यदि (p(x)=7x-13), तो (p(x)+p(-x)) क्या है?
If (p(x)=7x-13), what is (p(x)+p(-x))?
#polynomial
#linear
#symmetry
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A (14x-26)
B (-26)
C (0)
D (7x-26)
Explanation opens after your attempt
Step 1
Concept
(p(-x)=-7x-13). Adding gives (7x-13-7x-13=-26).
Step 2
Why this answer is correct
The correct answer is B. (-26). (p(-x)=-7x-13). Adding gives (7x-13-7x-13=-26).
Step 3
Exam Tip
(p(-x)=-7x-13) है। जोड़ने पर (7x-13-7x-13=-26) मिलता है।
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यदि (p(x)=7x-13), तो (p(x)-p(-x)) क्या है?
If (p(x)=7x-13), what is (p(x)-p(-x))?
#polynomial
#linear
#symmetry
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A (14x)
B (0)
C (-26)
D (7x)
Explanation opens after your attempt
Step 1
Concept
(p(-x)=-7x-13). Subtracting gives (7x-13-(-7x-13)=14x).
Step 2
Why this answer is correct
The correct answer is A. (14x). (p(-x)=-7x-13). Subtracting gives (7x-13-(-7x-13)=14x).
Step 3
Exam Tip
(p(-x)=-7x-13) है। घटाने पर (7x-13-(-7x-13)=14x) मिलता है।
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किस मान पर ((s-8 )x+5s) का शून्यक (0) होगा?
For which value will the zero of ((s-8 )x+5s) be (0)?
#polynomial
#linear
#zero_at_origin
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A (s=0)
B (s=8)
C (s=-8)
D कोई मान नहीं / No value
Explanation opens after your attempt
Step 1
Concept
For the zero to be (0), the constant term (5s=0). At (s=0), the coefficient of (x) is (-8), 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 (5s=0). At (s=0), the coefficient of (x) is (-8), so the polynomial is linear.
Step 3
Exam Tip
शून्यक (0) होने के लिए नियतांक पद (5s=0) होना चाहिए। (s=0) पर (x) का गुणांक (-8) है इसलिए बहुपद रेखीय है।
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यदि (p(x)=6x+a) और (q(x)=8x-a), तो (p(x)+q(x)) का शून्यक (-1) होने पर (a) क्या है?
If (p(x)=6x+a) and (q(x)=8x-a), what is (a) if the zero of (p(x)+q(x)) is (-1)?
#polynomial
#linear
#no_solution
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A कोई मान नहीं / No value
B (0)
C (1)
D (14)
Explanation opens after your attempt
Correct Answer
A. कोई मान नहीं / No value
Step 1
Concept
(p(x)+q(x)=14x), whose zero is (0). Therefore the zero cannot be (-1) for any (a).
Step 2
Why this answer is correct
The correct answer is A. कोई मान नहीं / No value. (p(x)+q(x)=14x), whose zero is (0). Therefore the zero cannot be (-1) for any (a).
Step 3
Exam Tip
(p(x)+q(x)=14x) है जिसका शून्यक (0) है। इसलिए शून्यक (-1) किसी (a) पर नहीं हो सकता।
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यदि (p(x)=6x+a) और (q(x)=8x-a), तो (q(x)-p(x)) क्या है?
If (p(x)=6x+a) and (q(x)=8x-a), what is (q(x)-p(x))?
#polynomial
#linear
#parameter_difference
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A (14x)
B (2x-2a)
C (2x)
D (2a)
Explanation opens after your attempt
Correct Answer
B. (2x-2a)
Step 1
Concept
(8x-a-(6x+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). (8x-a-(6x+a)=2x-2a). Change the signs inside the bracket while subtracting.
Step 3
Exam Tip
(8x-a-(6x+a)=2x-2a) है। घटाते समय कोष्ठक के चिन्ह बदलें।
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किस विकल्प में ((5x-2)) और ((x+7)) का गुणनफल रेखीय नहीं है?
Which option correctly says that the product of ((5x-2)) and ((x+7)) 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 ((5x-2)(x+7)), the highest term is \(5x^2\). 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 ((5x-2)(x+7)), the highest term is \(5x^2\). So the product has degree (2) and is not linear.
Step 3
Exam Tip
((5x-2)(x+7)) में उच्चतम पद \(5x^2\) है। इसलिए गुणनफल की डिग्री (2) है और यह रेखीय नहीं है।
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यदि (p(x)=ax+6) और (p(p(0))=48), तो (a) क्या है?
If (p(x)=ax+6) and (p(p(0))=48), what is (a)?
#polynomial
#linear
#composition_parameter
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A (6)
B (7)
C (8)
D (48)
Explanation opens after your attempt
Step 1
Concept
(p(0)=6) and (p(6)=6a+6). From (6a+6=48), we get (a=7).
Step 2
Why this answer is correct
The correct answer is B. (7). (p(0)=6) and (p(6)=6a+6). From (6a+6=48), we get (a=7).
Step 3
Exam Tip
(p(0)=6) और (p(6)=6a+6) है। (6a+6=48) से (a=7) मिलता है।
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यदि (p(x)=x+a) और (p(p(4))=16), तो (a) का मान क्या है?
If (p(x)=x+a) and (p(p(4))=16), what is the value of (a)?
#polynomial
#linear
#composition_parameter
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A (4)
B (5)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(p(4)=4+a) and (p(4+a)=4+2a). From (4+2a=16), we get (a=6).
Step 2
Why this answer is correct
The correct answer is C. (6). (p(4)=4+a) and (p(4+a)=4+2a). From (4+2a=16), we get (a=6).
Step 3
Exam Tip
(p(4)=4+a) और (p(4+a)=4+2a) है। (4+2a=16) से (a=6) मिलता है।
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यदि (p(x)=mx+n) और (p(-4)=p(2)), तो (p(x)) रेखीय कब हो सकता है?
If (p(x)=mx+n) and (p(-4)=p(2)), 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(-4)=p(2)), (-4m+n=2m+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(-4)=p(2)), (-4m+n=2m+n), so (m=0). At (m=0), the polynomial is not linear.
Step 3
Exam Tip
(p(-4)=p(2)) से (-4m+n=2m+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 (10) होगा?
In which option will (p(x)=ax+b) have zero (10)?
#polynomial
#linear
#general_condition
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A (b=10a) और \(a\neq0\) / (b=10a) and \(a\neq0\)
B (b=-10a) और \(a\neq0\) / (b=-10a) and \(a\neq0\)
C (a=0)
D (b=0)
Explanation opens after your attempt
Correct Answer
B. (b=-10a) और \(a\neq0\) / (b=-10a) and \(a\neq0\)
Step 1
Concept
If the zero is (10), then (10a+b=0). So (b=-10a) and \(a\neq0\) are needed.
Step 2
Why this answer is correct
The correct answer is B. (b=-10a) और \(a\neq0\) / (b=-10a) and \(a\neq0\). If the zero is (10), then (10a+b=0). So (b=-10a) and \(a\neq0\) are needed.
Step 3
Exam Tip
शून्यक (10) होने पर (10a+b=0) होगा। इसलिए (b=-10a) और \(a\neq0\) चाहिए।
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यदि (p(x)=12x-5), तो (p(x+2)-p(x-1)) क्या है?
If (p(x)=12x-5), what is (p(x+2)-p(x-1))?
#polynomial
#linear
#shift_difference
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A (12)
B (24)
C (36)
D (48)
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Step 1
Concept
(p(x+2)=12x+19) and (p(x-1)=12x-17). The difference is (36).
Step 2
Why this answer is correct
The correct answer is C. (36). (p(x+2)=12x+19) and (p(x-1)=12x-17). The difference is (36).
Step 3
Exam Tip
(p(x+2)=12x+19) और (p(x-1)=12x-17) है। अंतर (36) है।
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यदि (p(x)=9x-26), तो (p(p(3))) का सही मान क्या है?
If (p(x)=9x-26), what is the correct value of (p(p(3)))?
#polynomial
#linear
#composition_value
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A (1)
B (-17)
C (3)
D (9)
Explanation opens after your attempt
Step 1
Concept
(p(3)=1) and (p(1)=9-26=-17). Find the inner value first.
Step 2
Why this answer is correct
The correct answer is B. (-17). (p(3)=1) and (p(1)=9-26=-17). Find the inner value first.
Step 3
Exam Tip
(p(3)=1) और (p(1)=9-26=-17) है। अंदर वाले मान को पहले निकालें।
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यदि (p(x)=13x+a) और (p(p(0))=182), तो (a) का मान क्या है?
If (p(x)=13x+a) and (p(p(0))=182), what is the value of (a)?
#polynomial
#linear
#composition_parameter
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A (13)
B (14)
C (169)
D (182)
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Step 1
Concept
(p(0)=a) and (p(a)=13a+a=14a). From (14a=182), we get (a=13).
Step 2
Why this answer is correct
The correct answer is A. (13). (p(0)=a) and (p(a)=13a+a=14a). From (14a=182), we get (a=13).
Step 3
Exam Tip
(p(0)=a) और (p(a)=13a+a=14a) है। (14a=182) से (a=13) मिलता है।
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यदि (p(x)=mx+n), (p(-2)=5) और (p(3)=30), तो (m+n) क्या है?
If (p(x)=mx+n), (p(-2)=5) and (p(3)=30), what is (m+n)?
#polynomial
#linear
#coefficients
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A (10)
B (15)
C (20)
D (25)
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Step 1
Concept
Subtracting the two values gives (5m=25), so (m=5). From (-2m+n=5), (n=15), so (m+n=20), not (15).
Step 2
Why this answer is correct
The correct answer is B. (15). Subtracting the two values gives (5m=25), so (m=5). From (-2m+n=5), (n=15), so (m+n=20), not (15).
Step 3
Exam Tip
दोनों मान घटाने पर (5m=25) से (m=5) मिलता है। (-2m+n=5) से (n=15), इसलिए (m+n=20) नहीं बल्कि (20) है।
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यदि (p(x)=14x-9), तो (p(x+1)+p(x-3)) क्या है?
If (p(x)=14x-9), what is (p(x+1)+p(x-3))?
#polynomial
#linear
#shift_sum
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A (28x-46)
B (28x-18)
C (14x-46)
D (28x+46)
Explanation opens after your attempt
Correct Answer
A. (28x-46)
Step 1
Concept
(p(x+1)=14x+5) and (p(x-3)=14x-51). Adding gives (28x-46).
Step 2
Why this answer is correct
The correct answer is A. (28x-46). (p(x+1)=14x+5) and (p(x-3)=14x-51). Adding gives (28x-46).
Step 3
Exam Tip
(p(x+1)=14x+5) और (p(x-3)=14x-51) है। जोड़ने पर (28x-46) मिलता है।
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किस मान पर (\(r^2-9r+20\)x+6) रेखीय बहुपद नहीं रहेगा?
For which value will (\(r^2-9r+20\)x+6) not remain a linear polynomial?
#polynomial
#linear
#parameter_condition
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A (r=4) या (r=5) / (r=4) or (r=5)
B (r=0) या (r=20) / (r=0) or (r=20)
C (r=9) ही / (r=9) only
D कोई मान नहीं / No value
Explanation opens after your attempt
Correct Answer
A. (r=4) या (r=5) / (r=4) or (r=5)
Step 1
Concept
For it not to be linear, the coefficient of (x) must be (0). From \(r^2-9r+20=0\), (r=4) or (r=5).
Step 2
Why this answer is correct
The correct answer is A. (r=4) या (r=5) / (r=4) or (r=5). For it not to be linear, the coefficient of (x) must be (0). From \(r^2-9r+20=0\), (r=4) or (r=5).
Step 3
Exam Tip
रेखीय न रहने के लिए (x) का गुणांक (0) होना चाहिए। \(r^2-9r+20=0\) से (r=4) या (r=5) मिलता है।
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