सरल करने के बाद (5(2x-3)-3(3x+1)) कौन सा बहुपद बनेगा?
After simplifying (5(2x-3)-3(3x+1)), which polynomial is obtained?
#polynomial
#linear
#simplification
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A (x-18)
B (19x-18)
C (x-12)
D (10x-18)
Explanation opens after your attempt
Step 1
Concept
(10x-15-9x-3=x-18). After opening brackets, combine like terms.
Step 2
Why this answer is correct
The correct answer is A. (x-18). (10x-15-9x-3=x-18). After opening brackets, combine like terms.
Step 3
Exam Tip
(10x-15-9x-3=x-18) है। कोष्ठक खोलने के बाद समान पद मिलाएं।
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किस मान पर (\(a^2-16\)x+7) रेखीय बहुपद नहीं रहेगा?
For which value will (\(a^2-16\)x+7) not remain a linear polynomial?
#polynomial
#linear
#parameter
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A (a=0)
B (a=4) या (a=-4) / (a=4) or (a=-4)
C (a=16)
D (a=1)
Explanation opens after your attempt
Correct Answer
B. (a=4) या (a=-4) / (a=4) or (a=-4)
Step 1
Concept
For it not to be linear, the coefficient of (x) must be (0). From \(a^2-16=0\), \(a=\pm4\).
Step 2
Why this answer is correct
The correct answer is B. (a=4) या (a=-4) / (a=4) or (a=-4). For it not to be linear, the coefficient of (x) must be (0). From \(a^2-16=0\), \(a=\pm4\).
Step 3
Exam Tip
रेखीय न रहने के लिए (x) का गुणांक (0) होना चाहिए। \(a^2-16=0\) से \(a=\pm4\) मिलता है।
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यदि (p(x)=(k-2)x+9) का शून्यक (-3) है, तो (k) का मान क्या है?
If the zero of (p(x)=(k-2)x+9) is (-3), what is the value of (k)?
#polynomial
#linear
#zero_parameter
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A (5)
B (-1)
C (2)
D (9)
Explanation opens after your attempt
Step 1
Concept
From (-3(k-2)+9=0), we get (k=5). Substitute the zero into the polynomial and set it to (0).
Step 2
Why this answer is correct
The correct answer is A. (5). From (-3(k-2)+9=0), we get (k=5). Substitute the zero into the polynomial and set it to (0).
Step 3
Exam Tip
(-3(k-2)+9=0) से (k=5) मिलता है। शून्यक को बहुपद में रखकर (0) करें।
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यदि (p(x)=3x-2) और (q(x)=x+5), तो (2p(x)-3q(x)) क्या है?
If (p(x)=3x-2) and (q(x)=x+5), what is (2p(x)-3q(x))?
#polynomial
#linear
#combination
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A (3x-19)
B (9x+11)
C (3x+11)
D (x-19)
Explanation opens after your attempt
Correct Answer
A. (3x-19)
Step 1
Concept
(2(3x-2)-3(x+5)=3x-19). Multiply and then combine like terms.
Step 2
Why this answer is correct
The correct answer is A. (3x-19). (2(3x-2)-3(x+5)=3x-19). Multiply and then combine like terms.
Step 3
Exam Tip
(2(3x-2)-3(x+5)=3x-19) है। गुणा करके समान पदों को मिलाएं।
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किस मान पर ((2m-5)x+10) का शून्यक (4) होगा?
For which value will the zero of ((2m-5)x+10) be (4)?
#polynomial
#linear
#fraction_parameter
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A \(m=\frac{5}{2}\)
B \(m=\frac{5}{4}\)
C \(m=\frac{9}{4}\)
D \(m=-\frac{5}{4}\)
Explanation opens after your attempt
Correct Answer
B. \(m=\frac{5}{4}\)
Step 1
Concept
If the zero is (4), then (4(2m-5)+10=0). This gives \(m=\frac{5}{4}\).
Step 2
Why this answer is correct
The correct answer is B. \(m=\frac{5}{4}\). If the zero is (4), then (4(2m-5)+10=0). This gives \(m=\frac{5}{4}\).
Step 3
Exam Tip
शून्यक (4) होने पर (4(2m-5)+10=0) होगा। इससे \(m=\frac{5}{4}\) मिलता है।
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यदि (p(x)=ax+b) का शून्यक (2) है और (a=5), तो (b) क्या है?
If the zero of (p(x)=ax+b) is (2) and (a=5), what is (b)?
#polynomial
#linear
#general_form
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A (10)
B (-10)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
From (p(2)=0), (2a+b=0). Substituting (a=5) gives (b=-10).
Step 2
Why this answer is correct
The correct answer is B. (-10). From (p(2)=0), (2a+b=0). Substituting (a=5) gives (b=-10).
Step 3
Exam Tip
(p(2)=0) से (2a+b=0) होगा। (a=5) रखने पर (b=-10) मिलता है।
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किस विकल्प में दो रेखीय बहुपदों का योग शून्य बहुपद है?
In which option is the sum of two linear polynomials the zero polynomial?
#polynomial
#linear
#zero_polynomial
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A (2x+3) और (-2x+3) / (2x+3) and (-2x+3)
B (x-4) और (x+4) / (x-4) and (x+4)
C (5x-7) और (-5x+7) / (5x-7) and (-5x+7)
D (3x+1) और (-3x-2) / (3x+1) and (-3x-2)
Explanation opens after your attempt
Correct Answer
C. (5x-7) और (-5x+7) / (5x-7) and (-5x+7)
Step 1
Concept
(5x-7+(-5x+7)=0). The sum of opposite polynomials is the zero polynomial.
Step 2
Why this answer is correct
The correct answer is C. (5x-7) और (-5x+7) / (5x-7) and (-5x+7). (5x-7+(-5x+7)=0). The sum of opposite polynomials is the zero polynomial.
Step 3
Exam Tip
(5x-7+(-5x+7)=0) है। विपरीत बहुपदों का योग शून्य बहुपद होता है।
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यदि (p(x)=4x+c) और (p(3)=p(1)+10), तो (c) के बारे में क्या सही है?
If (p(x)=4x+c) and (p(3)=p(1)+10), what is correct about (c)?
#polynomial
#linear
#condition_check
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A (c=2) ही / Only (c=2)
B हर (c) सही है / Every (c) is valid
C ऐसा कोई (c) नहीं / No such (c)
D (c=10) ही / Only (c=10)
Explanation opens after your attempt
Correct Answer
C. ऐसा कोई (c) नहीं / No such (c)
Step 1
Concept
(p(3)-p(1)=(12+c)-(4+c)=8). So the condition with (10) is not satisfied for any (c).
Step 2
Why this answer is correct
The correct answer is C. ऐसा कोई (c) नहीं / No such (c). (p(3)-p(1)=(12+c)-(4+c)=8). So the condition with (10) is not satisfied for any (c).
Step 3
Exam Tip
(p(3)-p(1)=(12+c)-(4+c)=8) होता है। इसलिए (10) वाली शर्त किसी (c) पर पूरी नहीं होती।
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किस विकल्प में रेखीय बहुपद का शून्यक \(-\frac{3}{7}\) है?
Which option has zero \(-\frac{3}{7}\) for a linear polynomial?
#polynomial
#linear
#fraction_zero
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A (7x-3)
B (3x+7)
C (7x+3)
D \(x+\frac{7}{3}\)
Explanation opens after your attempt
Step 1
Concept
From (7x+3=0), we get \(x=-\frac{3}{7}\). Pay attention to the sign and denominator in fractional zeros.
Step 2
Why this answer is correct
The correct answer is C. (7x+3). From (7x+3=0), we get \(x=-\frac{3}{7}\). Pay attention to the sign and denominator in fractional zeros.
Step 3
Exam Tip
(7x+3=0) से \(x=-\frac{3}{7}\) मिलता है। भिन्न शून्यक में चिन्ह और हर ध्यान रखें।
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यदि (p(x)=\frac{2}{5}x-6), तो किस मान पर (p(x)=0) होगा?
If (p(x)=\frac{2}{5}x-6), for which value will (p(x)=0)?
#polynomial
#linear
#fraction_equation
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A (x=10)
B (x=12)
C (x=15)
D (x=20)
Explanation opens after your attempt
Step 1
Concept
From \(\frac{2}{5}x-6=0\), \(\frac{2}{5}x=6\) and (x=15). With a fractional coefficient, multiply by the reciprocal.
Step 2
Why this answer is correct
The correct answer is C. (x=15). From \(\frac{2}{5}x-6=0\), \(\frac{2}{5}x=6\) and (x=15). With a fractional coefficient, multiply by the reciprocal.
Step 3
Exam Tip
\(\frac{2}{5}x-6=0\) से \(\frac{2}{5}x=6\) और (x=15) मिलता है। भिन्न गुणांक में उलटा गुणा करें।
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यदि (p(x)=x+2) और (q(x)=x-5), तो (p(x)q(x)) की डिग्री क्या है?
If (p(x)=x+2) and (q(x)=x-5), what is the degree of (p(x)q(x))?
#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+2)(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+2)(x-5)), the highest term is \(x^2\). Therefore the product has degree (2).
Step 3
Exam Tip
((x+2)(x-5)) में उच्चतम पद \(x^2\) है। इसलिए गुणनफल की डिग्री (2) है।
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यदि (p(x)=2x-1), तो (p(x+3)) क्या है?
If (p(x)=2x-1), what is (p(x+3))?
#polynomial
#linear
#composition
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A (2x+5)
B (2x+2)
C (2x-4)
D (x+5)
Explanation opens after your attempt
Step 1
Concept
(p(x+3)=2(x+3)-1=2x+5). Substitute the whole (x+3) in place of (x).
Step 2
Why this answer is correct
The correct answer is A. (2x+5). (p(x+3)=2(x+3)-1=2x+5). Substitute the whole (x+3) in place of (x).
Step 3
Exam Tip
(p(x+3)=2(x+3)-1=2x+5) है। (x) की जगह पूरा (x+3) रखें।
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यदि (p(x)=5-3x), तो (p(2x)) कौन सा है?
If (p(x)=5-3x), which is (p(2x))?
#polynomial
#linear
#substitution
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A (5-3x)
B (10-3x)
C (5-6x)
D (10-6x)
Explanation opens after your attempt
Step 1
Concept
(p(2x)=5-3(2x)=5-6x). While substituting, use the whole (2x).
Step 2
Why this answer is correct
The correct answer is C. (5-6x). (p(2x)=5-3(2x)=5-6x). While substituting, use the whole (2x).
Step 3
Exam Tip
(p(2x)=5-3(2x)=5-6x) है। प्रतिस्थापन करते समय पूरे (2x) को रखें।
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किस मान पर (\(t^2-9\)x+(t-3)) रेखीय बहुपद नहीं रहेगा?
For which value will (\(t^2-9\)x+(t-3)) not remain a linear polynomial?
#polynomial
#linear
#parameter_condition
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A (t=3) या (t=-3) / (t=3) or (t=-3)
B (t=0)
C (t=9)
D (t=1)
Explanation opens after your attempt
Correct Answer
A. (t=3) या (t=-3) / (t=3) or (t=-3)
Step 1
Concept
For it to be linear, \(t^2-9\neq0\) is needed. At \(t=\pm3\), the coefficient of (x) becomes (0).
Step 2
Why this answer is correct
The correct answer is A. (t=3) या (t=-3) / (t=3) or (t=-3). For it to be linear, \(t^2-9\neq0\) is needed. At \(t=\pm3\), the coefficient of (x) becomes (0).
Step 3
Exam Tip
रेखीय होने के लिए \(t^2-9\neq0\) चाहिए। \(t=\pm3\) पर (x) का गुणांक (0) हो जाता है।
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यदि (p(x)=kx+4) और (p(2)=p(-2)), तो (p(x)) रेखीय कब रहेगा?
If (p(x)=kx+4) and (p(2)=p(-2)), when will (p(x)) remain linear?
#polynomial
#linear
#condition_check
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A जब (k=0) / When (k=0)
B जब (k=4) / When (k=4)
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(2)=p(-2)), (2k+4=-2k+4), 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(2)=p(-2)), (2k+4=-2k+4), so (k=0). At (k=0), the polynomial is not linear.
Step 3
Exam Tip
(p(2)=p(-2)) से (2k+4=-2k+4) 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, तो कौन सी शर्त सही है?
If the zero of (p(x)=ax+b) is (0), which condition is correct?
#polynomial
#linear
#general_condition
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A (a=0)
B (b=0) और \(a\neq0\) / (b=0) and \(a\neq0\)
C (a=b)
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)=2x+3) और (q(x)=5x-1), तो (q(x)-2p(x)) की डिग्री क्या है?
If (p(x)=2x+3) and (q(x)=5x-1), what is the degree of (q(x)-2p(x))?
#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)=5x-1-2(2x+3)=x-7). Its degree is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). (q(x)-2p(x)=5x-1-2(2x+3)=x-7). Its degree is (1).
Step 3
Exam Tip
(q(x)-2p(x)=5x-1-2(2x+3)=x-7) है। इसकी डिग्री (1) है।
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किस विकल्प में रेखीय बहुपद का शून्यक \(\frac{11}{5}\) है?
Which option has zero \(\frac{11}{5}\) for a linear polynomial?
#polynomial
#linear
#fraction_zero
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A (5x-11)
B (11x-5)
C (5x+11)
D \(x-\frac{5}{11}\)
Explanation opens after your attempt
Correct Answer
A. (5x-11)
Step 1
Concept
From (5x-11=0), we get \(x=\frac{11}{5}\). Set the polynomial equal to (0) to find the zero.
Step 2
Why this answer is correct
The correct answer is A. (5x-11). From (5x-11=0), we get \(x=\frac{11}{5}\). Set the polynomial equal to (0) to find the zero.
Step 3
Exam Tip
(5x-11=0) से \(x=\frac{11}{5}\) मिलता है। शून्यक के लिए बहुपद को (0) के बराबर रखें।
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यदि (p(x)=3x-8), तो (p(x+1)-p(x)) क्या है?
If (p(x)=3x-8), what is (p(x+1)-p(x))?
#polynomial
#linear
#difference_value
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A (1)
B (3)
C (x+1)
D (3x)
Explanation opens after your attempt
Step 1
Concept
(p(x+1)=3x-5) and (p(x)=3x-8). The difference is (3).
Step 2
Why this answer is correct
The correct answer is B. (3). (p(x+1)=3x-5) and (p(x)=3x-8). The difference is (3).
Step 3
Exam Tip
(p(x+1)=3x-5) और (p(x)=3x-8) है। अंतर (3) मिलता है।
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यदि (p(x)=\lambda x+6) और इसका शून्यक (-2) से बड़ा है, तो \(\lambda>0\) होने पर कौन सी शर्त सही है?
If (p(x)=\lambda x+6) and its zero is greater than (-2), which condition is correct when \(\lambda>0\)?
#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 \(-\frac{6}{\lambda}\). From \(-\frac{6}{\lambda}>-2\) and \(\lambda>0\), we get \(\lambda>3\).
Step 2
Why this answer is correct
The correct answer is C. \(\lambda>3\). The zero is \(-\frac{6}{\lambda}\). From \(-\frac{6}{\lambda}>-2\) and \(\lambda>0\), we get \(\lambda>3\).
Step 3
Exam Tip
शून्यक \(-\frac{6}{\lambda}\) है। \(-\frac{6}{\lambda}>-2\) और \(\lambda>0\) से \(\lambda>3\) मिलता है।
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किस विकल्प में (p(x)=ax+b) का शून्यक (-2) होगा?
In which option will (p(x)=ax+b) have zero (-2)?
#polynomial
#linear
#general_condition
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A (b=2a) और \(a\neq0\) / (b=2a) and \(a\neq0\)
B (b=-2a) और \(a\neq0\) / (b=-2a) and \(a\neq0\)
C (a=0)
D (b=0)
Explanation opens after your attempt
Correct Answer
A. (b=2a) और \(a\neq0\) / (b=2a) and \(a\neq0\)
Step 1
Concept
If the zero is (-2), then (-2a+b=0). So (b=2a) and \(a\neq0\) are needed.
Step 2
Why this answer is correct
The correct answer is A. (b=2a) और \(a\neq0\) / (b=2a) and \(a\neq0\). If the zero is (-2), then (-2a+b=0). So (b=2a) and \(a\neq0\) are needed.
Step 3
Exam Tip
शून्यक (-2) होने पर (-2a+b=0) होगा। इसलिए (b=2a) और \(a\neq0\) चाहिए।
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यदि (p(x)=x+r) और (q(x)=x-r), तो (p(x)+q(x)) क्या है?
If (p(x)=x+r) and (q(x)=x-r), what is (p(x)+q(x))?
#polynomial
#linear
#parameter_sum
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A (2x)
B (2r)
C \(x^2-r^2\)
D (0)
Explanation opens after your attempt
Step 1
Concept
On adding, (x+r+x-r=2x). The terms containing (r) cancel.
Step 2
Why this answer is correct
The correct answer is A. (2x). On adding, (x+r+x-r=2x). The terms containing (r) cancel.
Step 3
Exam Tip
जोड़ने पर (x+r+x-r=2x) मिलता है। (r) वाले पद कट जाते हैं।
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यदि (p(x)=x+r) और (q(x)=x-r), तो (p(x)-q(x)) किस प्रकार का बहुपद है?
If (p(x)=x+r) and (q(x)=x-r), what type of polynomial is (p(x)-q(x))?
#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)=2r). 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)=2r). With respect to (x), it is a constant polynomial.
Step 3
Exam Tip
(p(x)-q(x)=2r) है। (x) के संदर्भ में यह नियतांक बहुपद है।
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यदि (p(x)=2x-5), तो (p(p(3))) का मान क्या है?
If (p(x)=2x-5), what is the value of (p(p(3)))?
#polynomial
#linear
#composition_value
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(3)=1) and (p(1)=2(1)-5=-3). The correct value is (-3), which is not in the options.
Step 2
Why this answer is correct
The correct answer is A. (1). (p(3)=1) and (p(1)=2(1)-5=-3). The correct value is (-3), which is not in the options.
Step 3
Exam Tip
(p(3)=1) और (p(1)=-3) नहीं बल्कि (2(1)-5=-3) है। इसलिए सही मान (-3) नहीं दिए विकल्पों में नहीं है।
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यदि (p(x)=3x+1), तो (p(p(2))) का मान क्या है?
If (p(x)=3x+1), what is the value of (p(p(2)))?
#polynomial
#linear
#composition_value
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A (7)
B (21)
C (22)
D (23)
Explanation opens after your attempt
Step 1
Concept
(p(2)=7) and (p(7)=22). Find the inner value first.
Step 2
Why this answer is correct
The correct answer is C. (22). (p(2)=7) and (p(7)=22). Find the inner value first.
Step 3
Exam Tip
(p(2)=7) और (p(7)=22) है। अंदर वाला मान पहले निकालें।
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किस मान पर ((n-1)x+n+2) का शून्यक (1) होगा?
For which value will the zero of ((n-1)x+n+2) be (1)?
#polynomial
#linear
#parameter_zero
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A \(n=-\frac{1}{2}\)
B (n=1)
C (n=-1)
D (n=2)
Explanation opens after your attempt
Correct Answer
A. \(n=-\frac{1}{2}\)
Step 1
Concept
If the zero is (1), then (n-1+n+2=0). Thus (2n+1=0) and \(n=-\frac{1}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(n=-\frac{1}{2}\). If the zero is (1), then (n-1+n+2=0). Thus (2n+1=0) and \(n=-\frac{1}{2}\).
Step 3
Exam Tip
शून्यक (1) होने पर (n-1+n+2=0) होगा। इससे (2n+1=0) और \(n=-\frac{1}{2}\) मिलता है।
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यदि (p(x)=\frac{x}{3}+a) और (p(6)=5), तो (a) का मान क्या है?
If (p(x)=\frac{x}{3}+a) and (p(6)=5), what is the value of (a)?
#polynomial
#linear
#fraction_parameter
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A (1)
B (2)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (p(6)=2+a=5), we get (a=3). In fractional form, substitute the value of (x) first.
Step 2
Why this answer is correct
The correct answer is C. (3). From (p(6)=2+a=5), we get (a=3). In fractional form, substitute the value of (x) first.
Step 3
Exam Tip
(p(6)=2+a=5) से (a=3) मिलता है। भिन्न रूप में पहले (x) का मान रखें।
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किस विकल्प में (p(x)-q(x)) रेखीय बहुपद है?
In which option is (p(x)-q(x)) a linear polynomial?
#polynomial
#linear
#difference_degree
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A (p(x)=4x+1), (q(x)=4x-2)
B (p(x)=2x+3), (q(x)=x-5)
C (p(x)=x+7), (q(x)=x+7)
D (p(x)=5), (q(x)=2)
Explanation opens after your attempt
Correct Answer
B. (p(x)=2x+3), (q(x)=x-5)
Step 1
Concept
In the second option, the difference is (x+8), whose degree is (1). In the others, the difference is constant or zero.
Step 2
Why this answer is correct
The correct answer is B. (p(x)=2x+3), (q(x)=x-5). In the second option, the difference is (x+8), whose degree is (1). In the others, the difference is constant or zero.
Step 3
Exam Tip
दूसरे विकल्प में अंतर (x+8) है जिसकी डिग्री (1) है। बाकी में अंतर नियतांक या शून्य है।
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यदि (p(x)=2x+a) और (q(x)=x-3), तो (p(x)+q(x)) का शून्यक (1) होने पर (a) क्या है?
If (p(x)=2x+a) and (q(x)=x-3), what is (a) if the zero of (p(x)+q(x)) is (1)?
#polynomial
#linear
#sum_zero_parameter
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A (0)
B (-1)
C (1)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(x)+q(x)=3x+a-3). Substituting (x=1) gives (3+a-3=0), so (a=0).
Step 2
Why this answer is correct
The correct answer is A. (0). (p(x)+q(x)=3x+a-3). Substituting (x=1) gives (3+a-3=0), so (a=0).
Step 3
Exam Tip
(p(x)+q(x)=3x+a-3) है। (x=1) रखने पर (3+a-3=0) से (a=0) मिलता है।
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किस मान पर (p(x)=(c+1)x+2c) का शून्यक (-4) होगा?
For which value will the zero of (p(x)=(c+1)x+2c) be (-4)?
#polynomial
#linear
#parameter_zero
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A (c=1)
B (c=2)
C (c=-2)
D (c=-1)
Explanation opens after your attempt
Step 1
Concept
From (-4(c+1)+2c=0), we get (-2c-4=0). Therefore (c=-2) is required.
Step 2
Why this answer is correct
The correct answer is B. (c=2). From (-4(c+1)+2c=0), we get (-2c-4=0). Therefore (c=-2) is required.
Step 3
Exam Tip
(-4(c+1)+2c=0) से (-2c-4=0) मिलता है। इसलिए (c=-2) होना चाहिए।
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यदि (p(x)=(c+1)x+2c) का शून्यक (-4) है, तो (c) का सही मान क्या है?
If the zero of (p(x)=(c+1)x+2c) is (-4), what is the correct value of (c)?
#polynomial
#linear
#parameter_zero
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A (c=1)
B (c=2)
C (c=-2)
D (c=-1)
Explanation opens after your attempt
Step 1
Concept
From (-4(c+1)+2c=0), we get (-2c-4=0). Hence (c=-2).
Step 2
Why this answer is correct
The correct answer is C. (c=-2). From (-4(c+1)+2c=0), we get (-2c-4=0). Hence (c=-2).
Step 3
Exam Tip
(-4(c+1)+2c=0) से (-2c-4=0) मिलता है। अतः (c=-2) है।
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यदि (p(x)=rx+5) और (p(2)=15), तो (p(-1)) का मान क्या है?
If (p(x)=rx+5) and (p(2)=15), what is the value of (p(-1))?
#polynomial
#linear
#two_step
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A (0)
B (5)
C (-5)
D (10)
Explanation opens after your attempt
Step 1
Concept
From (2r+5=15), we get (r=5). Therefore (p(-1)=5(-1)+5=0).
Step 2
Why this answer is correct
The correct answer is A. (0). From (2r+5=15), we get (r=5). Therefore (p(-1)=5(-1)+5=0).
Step 3
Exam Tip
(2r+5=15) से (r=5) मिलता है। इसलिए (p(-1)=5(-1)+5=0) है।
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यदि (p(x)=ax-6) और (p(2)=p(5)-9), तो (a) क्या है?
If (p(x)=ax-6) and (p(2)=p(5)-9), what is (a)?
#polynomial
#linear
#parameter_equation
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A (1)
B (2)
C (3)
D (6)
Explanation opens after your attempt
Step 1
Concept
From (2a-6=(5a-6)-9), we get (2a=5a-9). Therefore (a=3).
Step 2
Why this answer is correct
The correct answer is C. (3). From (2a-6=(5a-6)-9), we get (2a=5a-9). Therefore (a=3).
Step 3
Exam Tip
(2a-6=(5a-6)-9) से (2a=5a-9) मिलता है। इसलिए (a=3) है।
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किस विकल्प में (x) का गुणांक (0) होकर भी बहुपद रेखीय बताया गया है?
In which option is a polynomial called linear even though the coefficient of (x) is (0)?
#polynomial
#linear
#error_identification
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A (6x+1) रेखीय है / (6x+1) is linear
B (0x+8) रेखीय है / (0x+8) is linear
C (x-9) रेखीय है / (x-9) is linear
D (3-2x) रेखीय है / (3-2x) is linear
Explanation opens after your attempt
Correct Answer
B. (0x+8) रेखीय है / (0x+8) is linear
Step 1
Concept
(0x+8) simplifies to (8). It is a constant polynomial, not linear.
Step 2
Why this answer is correct
The correct answer is B. (0x+8) रेखीय है / (0x+8) is linear. (0x+8) simplifies to (8). It is a constant polynomial, not linear.
Step 3
Exam Tip
(0x+8) सरल होकर (8) बनता है। यह नियतांक बहुपद है रेखीय नहीं।
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यदि (p(x)=2x-7), तो (p(a)=a) होने पर (a) क्या है?
If (p(x)=2x-7), what is (a) when (p(a)=a)?
#polynomial
#linear
#fixed_value
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A (5)
B (7)
C (-7)
D (0)
Explanation opens after your attempt
Step 1
Concept
(p(a)=2a-7). From (2a-7=a), we get (a=7).
Step 2
Why this answer is correct
The correct answer is B. (7). (p(a)=2a-7). From (2a-7=a), we get (a=7).
Step 3
Exam Tip
(p(a)=2a-7) है। (2a-7=a) से (a=7) मिलता है।
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यदि (p(x)=mx+n), (p(0)=4) और (p(2)=10), तो (m+n) क्या है?
If (p(x)=mx+n), (p(0)=4) and (p(2)=10), what is (m+n)?
#polynomial
#linear
#coefficients
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A (3)
B (4)
C (7)
D (10)
Explanation opens after your attempt
Step 1
Concept
(p(0)=n=4) and (2m+4=10) gives (m=3). Therefore (m+n=7).
Step 2
Why this answer is correct
The correct answer is C. (7). (p(0)=n=4) and (2m+4=10) gives (m=3). Therefore (m+n=7).
Step 3
Exam Tip
(p(0)=n=4) और (2m+4=10) से (m=3) मिलता है। इसलिए (m+n=7) है।
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यदि (p(x)=mx+n), (p(1)=5) और (p(3)=13), तो (m) क्या है?
If (p(x)=mx+n), (p(1)=5) and (p(3)=13), what is (m)?
#polynomial
#linear
#slope_parameter
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A (2)
B (4)
C (5)
D (8)
Explanation opens after your attempt
Step 1
Concept
Subtracting the two values gives (p(3)-p(1)=2m=8). Therefore (m=4).
Step 2
Why this answer is correct
The correct answer is B. (4). Subtracting the two values gives (p(3)-p(1)=2m=8). Therefore (m=4).
Step 3
Exam Tip
दोनों मान घटाने पर (p(3)-p(1)=2m=8) मिलता है। इसलिए (m=4) है।
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किस विकल्प में (p(2)=0) और (p(x)) रेखीय है?
Which option has (p(2)=0) and (p(x)) is linear?
#polynomial
#linear
#zero_identification
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A (p(x)=x+2)
B (p(x)=2x+2)
C (p(x)=x-2)
D (p(x)=x-2 -4)
Explanation opens after your attempt
Correct Answer
C. (p(x)=x-2)
Step 1
Concept
Substituting (x=2) in (x-2) 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-2). Substituting (x=2) in (x-2) gives (0). It is a linear polynomial of degree (1).
Step 3
Exam Tip
(x-2) में (x=2) रखने पर (0) मिलता है। यह डिग्री (1) वाला रेखीय बहुपद है।
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यदि (p(x)=3x-4), तो (p(x)+p(-x)) क्या है?
If (p(x)=3x-4), what is (p(x)+p(-x))?
#polynomial
#linear
#symmetry
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A (6x-8)
B (-8)
C (0)
D (3x-8)
Explanation opens after your attempt
Step 1
Concept
(p(-x)=-3x-4). Adding gives (3x-4-3x-4=-8).
Step 2
Why this answer is correct
The correct answer is B. (-8). (p(-x)=-3x-4). Adding gives (3x-4-3x-4=-8).
Step 3
Exam Tip
(p(-x)=-3x-4) है। जोड़ने पर (3x-4-3x-4=-8) मिलता है।
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यदि (p(x)=3x-4), तो (p(x)-p(-x)) क्या है?
If (p(x)=3x-4), what is (p(x)-p(-x))?
#polynomial
#linear
#symmetry
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A (6x)
B (0)
C (-8)
D (3x)
Explanation opens after your attempt
Step 1
Concept
(p(-x)=-3x-4). Subtracting gives (3x-4-(-3x-4)=6x).
Step 2
Why this answer is correct
The correct answer is A. (6x). (p(-x)=-3x-4). Subtracting gives (3x-4-(-3x-4)=6x).
Step 3
Exam Tip
(p(-x)=-3x-4) है। घटाने पर (3x-4-(-3x-4)=6x) मिलता है।
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किस मान पर ((s-2 )x+s) का शून्यक (0) होगा?
For which value will the zero of ((s-2 )x+s) be (0)?
#polynomial
#linear
#zero_at_origin
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A (s=0)
B (s=2)
C (s=-2)
D कोई मान नहीं / No value
Explanation opens after your attempt
Step 1
Concept
For the zero to be (0), the constant term (s) must be (0). At (s=0), the coefficient of (x) is (-2), so the polynomial is linear.
Step 2
Why this answer is correct
The correct answer is A. (s=0). For the zero to be (0), the constant term (s) must be (0). At (s=0), the coefficient of (x) is (-2), so the polynomial is linear.
Step 3
Exam Tip
शून्यक (0) होने के लिए नियतांक पद (s=0) होना चाहिए। (s=0) पर (x) का गुणांक (-2) है इसलिए बहुपद रेखीय है।
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यदि (p(x)=2x+a) और (q(x)=4x-a), तो (p(x)+q(x)) का शून्यक (-1) होने पर (a) क्या है?
If (p(x)=2x+a) and (q(x)=4x-a), what is (a) if the zero of (p(x)+q(x)) is (-1)?
#polynomial
#linear
#no_solution
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A कोई मान नहीं / No value
B (0)
C (1)
D (6)
Explanation opens after your attempt
Correct Answer
A. कोई मान नहीं / No value
Step 1
Concept
(p(x)+q(x)=6x), 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)=6x), whose zero is (0). Therefore the zero cannot be (-1) for any (a).
Step 3
Exam Tip
(p(x)+q(x)=6x) है जिसका शून्यक (0) है। इसलिए शून्यक (-1) किसी (a) पर नहीं हो सकता।
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यदि (p(x)=2x+a) और (q(x)=4x-a), तो (p(x)-q(x)) क्या है?
If (p(x)=2x+a) and (q(x)=4x-a), what is (p(x)-q(x))?
#polynomial
#linear
#parameter_difference
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A (6x)
B (-2x+2a)
C (2x)
D (2a)
Explanation opens after your attempt
Correct Answer
B. (-2x+2a)
Step 1
Concept
(2x+a-(4x-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). (2x+a-(4x-a)=-2x+2a). Change the signs inside the bracket while subtracting.
Step 3
Exam Tip
(2x+a-(4x-a)=-2x+2a) है। घटाते समय कोष्ठक के चिन्ह बदलें।
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किस विकल्प में ((x+3)) और ((2x-1)) का गुणनफल रेखीय नहीं है?
Which option correctly says that the product of ((x+3)) and ((2x-1)) is not linear?
#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 ((x+3)(2x-1)), 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 ((x+3)(2x-1)), the highest term is \(2x^2\). So the product has degree (2) and is not linear.
Step 3
Exam Tip
((x+3)(2x-1)) 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+1) और (p(p(0))=7), तो (a) क्या है?
If (p(x)=ax+1) and (p(p(0))=7), what is (a)?
#polynomial
#linear
#composition_parameter
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A (3)
B (5)
C (6)
D (7)
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Step 1
Concept
(p(0)=1) and (p(1)=a+1). From (a+1=7), we get (a=6).
Step 2
Why this answer is correct
The correct answer is C. (6). (p(0)=1) and (p(1)=a+1). From (a+1=7), we get (a=6).
Step 3
Exam Tip
(p(0)=1) और (p(1)=a+1) है। (a+1=7) से (a=6) मिलता है।
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यदि (p(x)=x+a) और (p(p(0))=0), तो (a) का मान क्या है?
If (p(x)=x+a) and (p(p(0))=0), what is the value of (a)?
#polynomial
#linear
#composition_parameter
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A (0)
B (1)
C कोई वास्तविक मान नहीं / No real value
D हर मान / Every value
Explanation opens after your attempt
Step 1
Concept
(p(0)=a) and (p(a)=2a). From (2a=0), we get (a=0).
Step 2
Why this answer is correct
The correct answer is A. (0). (p(0)=a) and (p(a)=2a). From (2a=0), we get (a=0).
Step 3
Exam Tip
(p(0)=a) और (p(a)=2a) है। (2a=0) से (a=0) मिलता है।
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यदि (p(x)=mx+n) और (p(1)=p(2)), तो (p(x)) रेखीय कब हो सकता है?
If (p(x)=mx+n) and (p(1)=p(2)), when can (p(x)) be linear?
#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(1)=p(2)), (m+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(1)=p(2)), (m+n=2m+n), so (m=0). At (m=0), the polynomial is not linear.
Step 3
Exam Tip
(p(1)=p(2)) से (m+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 (3) होगा?
In which option will (p(x)=ax+b) have zero (3)?
#polynomial
#linear
#general_condition
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A (b=-3a) और \(a\neq0\) / (b=-3a) and \(a\neq0\)
B (b=3a) और \(a\neq0\) / (b=3a) and \(a\neq0\)
C (a=0)
D (b=0)
Explanation opens after your attempt
Correct Answer
A. (b=-3a) और \(a\neq0\) / (b=-3a) and \(a\neq0\)
Step 1
Concept
If the zero is (3), then (3a+b=0). So (b=-3a) and \(a\neq0\) are needed.
Step 2
Why this answer is correct
The correct answer is A. (b=-3a) और \(a\neq0\) / (b=-3a) and \(a\neq0\). If the zero is (3), then (3a+b=0). So (b=-3a) and \(a\neq0\) are needed.
Step 3
Exam Tip
शून्यक (3) होने पर (3a+b=0) होगा। इसलिए (b=-3a) और \(a\neq0\) चाहिए।
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यदि (p(x)=7x-2), तो (p(x+2)-p(x-1)) क्या है?
If (p(x)=7x-2), what is (p(x+2)-p(x-1))?
#polynomial
#linear
#shift_difference
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A (7)
B (14)
C (21)
D (28)
Explanation opens after your attempt
Step 1
Concept
(p(x+2)=7x+12) and (p(x-1)=7x-9). The difference is (21).
Step 2
Why this answer is correct
The correct answer is C. (21). (p(x+2)=7x+12) and (p(x-1)=7x-9). The difference is (21).
Step 3
Exam Tip
(p(x+2)=7x+12) और (p(x-1)=7x-9) है। अंतर (21) है।
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यदि (p(x)=2x-5), तो (p(p(3))) का सही मान क्या है?
If (p(x)=2x-5), what is the correct value of (p(p(3)))?
#polynomial
#linear
#composition_value
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A (3)
B (1)
C (-3)
D (-1)
Explanation opens after your attempt
Step 1
Concept
(p(3)=1) and (p(1)=2-5=-3). Find the inner value first.
Step 2
Why this answer is correct
The correct answer is C. (-3). (p(3)=1) and (p(1)=2-5=-3). Find the inner value first.
Step 3
Exam Tip
(p(3)=1) है और (p(1)=2-5=-3) है। अंदर वाले मान को पहले निकालें।
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