रेखा (2x-y=4) के लिए (x=3) होने पर (y) क्या होगा?
For the line (2x-y=4), what is (y) when (x=3)?
#linear equations
#substitution
#graphical method
#easy
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(2(3)-y=4), so (6-y=4) and (y=2). Be careful with negative signs.
Step 2
Why this answer is correct
The correct answer is A. (2). (2(3)-y=4), so (6-y=4) and (y=2). Be careful with negative signs.
Step 3
Exam Tip
(2(3)-y=4), इसलिए (6-y=4) और (y=2)। ऋण चिह्न वाले पदों में सावधानी रखें।
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समीकरण (y=2x) के लिए कौन-सा बिंदु सही है?
Which point is correct for the equation (y=2x)?
#linear equations
#point on graph
#substitution
#easy
A ( (2,4) )
B ( (3,5) )
C ( (1,3) )
D ( (4,2) )
Explanation opens after your attempt
Correct Answer
A. ( (2,4) )
Step 1
Concept
For (x=2), (y=2(2)=4), so ( (2,4) ) is correct. To check a point on a line, substitute its values in the equation.
Step 2
Why this answer is correct
The correct answer is A. ( (2,4) ). For (x=2), (y=2(2)=4), so ( (2,4) ) is correct. To check a point on a line, substitute its values in the equation.
Step 3
Exam Tip
(x=2) पर (y=2(2)=4), इसलिए ( (2,4) ) सही है। रेखा पर बिंदु जाँचने के लिए समीकरण में मान रखें।
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यदि (p(x)=x-2 -8x+16) है, तो (p(4+t)) का मान क्या है?
If (p(x)=x-2 -8x+16), what is the value of (p(4+t))?
#substitution
#perfect-square
#polynomial
A \(t^2\)
B \(t^2+4\)
C (4t)
D \(t^2-16\)
Explanation opens after your attempt
Correct Answer
A. \(t^2\)
Step 1
Concept
(p(x)=(x-4)2 ), so (p(4+t)=t-2 ). In such questions, first form a perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(t^2\). (p(x)=(x-4)2 ), so (p(4+t)=t-2 ). In such questions, first form a perfect square.
Step 3
Exam Tip
(p(x)=(x-4)2 ), इसलिए (p(4+t)=t-2 )। ऐसे प्रश्नों में पहले पूर्ण वर्ग बनाना आसान होता है।
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यदि (p(x)=x-2 +4x+4), तो (p(-2+h)) का मान क्या है?
If (p(x)=x-2 +4x+4), what is the value of (p(-2+h))?
#substitution
#identity
#polynomial
A \(h^2\)
B (h)
C \(h^2+4\)
D (2h)
Explanation opens after your attempt
Correct Answer
A. \(h^2\)
Step 1
Concept
(p(x)=(x+2)2 ), so (p(-2+h)=h-2 ). Perfect square form makes substitution easier.
Step 2
Why this answer is correct
The correct answer is A. \(h^2\). (p(x)=(x+2)2 ), so (p(-2+h)=h-2 ). Perfect square form makes substitution easier.
Step 3
Exam Tip
(p(x)=(x+2)2 ), इसलिए (p(-2+h)=h-2 )। पूर्ण वर्ग रूप से प्रतिस्थापन आसान हो जाता है।
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यदि (p(x)=2x-2 -7x+3), तो (p(x+1)-p(x-1)) क्या होगा?
If (p(x)=2x-2 -7x+3), what will (p(x+1)-p(x-1)) be?
#composition
#substitution
#polynomial
A (8x-14)
B (8x+14)
C (4x-14)
D (4x+14)
Explanation opens after your attempt
Correct Answer
A. (8x-14)
Step 1
Concept
(p(x+1)=2x-2 -3x-2) and (p(x-1)=2x-2 -11x+12), so the difference is (8x-14). Substitute the whole expression in place of (x).
Step 2
Why this answer is correct
The correct answer is A. (8x-14). (p(x+1)=2x-2 -3x-2) and (p(x-1)=2x-2 -11x+12), so the difference is (8x-14). Substitute the whole expression in place of (x).
Step 3
Exam Tip
(p(x+1)=2x-2 -3x-2) और (p(x-1)=2x-2 -11x+12), इसलिए अंतर (8x-14) है। पूरे व्यंजक को (x) की जगह रखें।
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यदि (p(x)=4x-2 -3x+2), तो (p(3x)) क्या है?
If (p(x)=4x-2 -3x+2), what is (p(3x))?
#substitution
#composition
#polynomial
A \(36x^2-9x+2\)
B \(12x^2-9x+2\)
C \(36x^2-3x+2\)
D \(4x^2-9x+2\)
Explanation opens after your attempt
Correct Answer
A. \(36x^2-9x+2\)
Step 1
Concept
(p(3x)=4(3x)2 -3(3x)+2=36x-2 -9x+2). Square the whole (3x).
Step 2
Why this answer is correct
The correct answer is A. \(36x^2-9x+2\). (p(3x)=4(3x)2 -3(3x)+2=36x-2 -9x+2). Square the whole (3x).
Step 3
Exam Tip
(p(3x)=4(3x)2 -3(3x)+2=36x-2 -9x+2)। पूरे (3x) का वर्ग करें।
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यदि (p(x)=x-2 -2x+4), तो (p(x+3)) क्या होगा?
If (p(x)=x-2 -2x+4), what is (p(x+3))?
#composition
#substitution
#polynomial
A \(x^2+4x+7\)
B \(x^2+4x+9\)
C \(x^2+6x+7\)
D \(x^2+6x+9\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+4x+7\)
Step 1
Concept
(p(x+3)=(x+3)2 -2(x+3)+4=x-2 +4x+7). Substitute the whole (x+3) in place of (x).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+4x+7\). (p(x+3)=(x+3)2 -2(x+3)+4=x-2 +4x+7). Substitute the whole (x+3) in place of (x).
Step 3
Exam Tip
(p(x+3)=(x+3)2 -2(x+3)+4=x-2 +4x+7)। (x) की जगह पूरा (x+3) रखें।
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(p(x)=x-4 -x-3 +x-2 -x+1) के लिए (p(1)) क्या है?
What is (p(1)) for (p(x)=x-4 -x-3 +x-2 -x+1)?
#evaluation
#quartic
#substitution
A (0)
B (1)
C (2)
D (5)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-1+1-1+1=1). Add alternating signs in order.
Step 2
Why this answer is correct
The correct answer is B. (1). (p(1)=1-1+1-1+1=1). Add alternating signs in order.
Step 3
Exam Tip
(p(1)=1-1+1-1+1=1)। वैकल्पिक संकेतों को क्रम से जोड़ें।
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(p(x)=4x-3 -11x-2 +6x+2) के लिए (p(2)) का मान क्या है?
What is the value of (p(2)) for (p(x)=4x-3 -11x-2 +6x+2)?
#evaluation
#cubic
#substitution
A (0)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
(p(2)=32-44+12+2=2). Evaluate each term separately and then add.
Step 2
Why this answer is correct
The correct answer is B. (2). (p(2)=32-44+12+2=2). Evaluate each term separately and then add.
Step 3
Exam Tip
(p(2)=32-44+12+2=2)। हर पद का मान अलग निकालकर जोड़ें।
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यदि (p(x)=2x-2 -5x+3), तो (p(x+2)-p(x)) क्या होगा?
If (p(x)=2x-2 -5x+3), what will (p(x+2)-p(x)) be?
#composition
#substitution
#polynomial
A (8x-2)
B (8x+2)
C (4x-2)
D (4x+2)
Explanation opens after your attempt
Step 1
Concept
(p(x+2)=2(x+2)2 -5(x+2)+3=2x-2 +3x+1), so the difference is (8x+2). Substitute the whole (x+2) correctly.
Step 2
Why this answer is correct
The correct answer is B. (8x+2). (p(x+2)=2(x+2)2 -5(x+2)+3=2x-2 +3x+1), so the difference is (8x+2). Substitute the whole (x+2) correctly.
Step 3
Exam Tip
(p(x+2)=2(x+2)2 -5(x+2)+3=2x-2 +3x+1), इसलिए अंतर (8x+2) है। पूरे (x+2) को सही जगह रखें।
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यदि (p(x)=3x-2 -2x+5), तो (p(2x)) क्या है?
If (p(x)=3x-2 -2x+5), what is (p(2x))?
#substitution
#composition
#polynomial
A \(12x^2-4x+5\)
B \(6x^2-4x+5\)
C \(12x^2-2x+5\)
D \(3x^2-4x+5\)
Explanation opens after your attempt
Correct Answer
A. \(12x^2-4x+5\)
Step 1
Concept
(p(2x)=3(2x)2 -2(2x)+5=12x-2 -4x+5). Square the whole (2x).
Step 2
Why this answer is correct
The correct answer is A. \(12x^2-4x+5\). (p(2x)=3(2x)2 -2(2x)+5=12x-2 -4x+5). Square the whole (2x).
Step 3
Exam Tip
(p(2x)=3(2x)2 -2(2x)+5=12x-2 -4x+5)। पूरे (2x) का वर्ग करें।
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यदि (p(x)=x-2 +4x+6), तो (p(x-1)) क्या होगा?
If (p(x)=x-2 +4x+6), what is (p(x-1))?
#composition
#substitution
#polynomial
A \(x^2+2x+3\)
B \(x^2+2x+1\)
C \(x^2+4x+3\)
D \(x^2-2x+3\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+2x+3\)
Step 1
Concept
(p(x-1)=(x-1)2 +4(x-1)+6=x-2 +2x+3). Substitute the whole (x-1) in place of (x).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+2x+3\). (p(x-1)=(x-1)2 +4(x-1)+6=x-2 +2x+3). Substitute the whole (x-1) in place of (x).
Step 3
Exam Tip
(p(x-1)=(x-1)2 +4(x-1)+6=x-2 +2x+3)। (x) की जगह पूरा (x-1) रखें।
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(p(x)=3x-3 -8x-2 +7x-2) के लिए (p(2)) का मान क्या है?
What is the value of (p(2)) for (p(x)=3x-3 -8x-2 +7x-2)?
#evaluation
#cubic
#substitution
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(p(2)=24-32+14-2=4). Evaluate each term separately and then add.
Step 2
Why this answer is correct
The correct answer is B. (4). (p(2)=24-32+14-2=4). Evaluate each term separately and then add.
Step 3
Exam Tip
(p(2)=24-32+14-2=4)। हर पद का मान अलग निकालकर जोड़ें।
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\(3x^3-2x^2+x+7\) को (x+2) से भाग देने पर शेषफल क्या है?
What is the remainder when \(3x^3-2x^2+x+7\) is divided by (x+2)?
#polynomials
#remainder
#substitution
#hard
A (-27)
B (-25)
C (25)
D (27)
Explanation opens after your attempt
Step 1
Concept
The remainder is (p(-2)). (3(-8)-2(4)-2+7=-27).
Step 2
Why this answer is correct
The correct answer is A. (-27). The remainder is (p(-2)). (3(-8)-2(4)-2+7=-27).
Step 3
Exam Tip
शेषफल (p(-2)) होगा। (3(-8)-2(4)-2+7=-27) है।
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बहुपद \(x^3-4x^2+x+6\) में (x=2) रखने पर क्या निष्कर्ष निकलेगा?
What conclusion follows when (x=2) is substituted in \(x^3-4x^2+x+6\)?
#polynomials
#zero
#substitution
#hard
A (2) शून्यक है / (2) is a zero
B (2) शून्यक नहीं है / (2) is not a zero
C बहुपद रैखिक है / The polynomial is linear
D बहुपद स्थिर है / The polynomial is constant
Explanation opens after your attempt
Correct Answer
A. (2) शून्यक है / (2) is a zero
Step 1
Concept
(p(2)=8-16+2+6=0), so (2) is a zero. Direct substitution is the quickest check.
Step 2
Why this answer is correct
The correct answer is A. (2) शून्यक है / (2) is a zero. (p(2)=8-16+2+6=0), so (2) is a zero. Direct substitution is the quickest check.
Step 3
Exam Tip
(p(2)=8-16+2+6=0) है इसलिए (2) शून्यक है। सीधे प्रतिस्थापन से जल्दी जांच होती है।
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यदि (p(x)=2x-2 +3x-4), तो (p(2x)) क्या है?
If (p(x)=2x-2 +3x-4), what is (p(2x))?
#substitution
#composition
#polynomial
A \(8x^2+6x-4\)
B \(4x^2+6x-4\)
C \(8x^2+3x-4\)
D \(2x^2+6x-4\)
Explanation opens after your attempt
Correct Answer
A. \(8x^2+6x-4\)
Step 1
Concept
(p(2x)=2(2x)2 +3(2x)-4=8x-2 +6x-4). Square the whole (2x).
Step 2
Why this answer is correct
The correct answer is A. \(8x^2+6x-4\). (p(2x)=2(2x)2 +3(2x)-4=8x-2 +6x-4). Square the whole (2x).
Step 3
Exam Tip
(p(2x)=2(2x)2 +3(2x)-4=8x-2 +6x-4)। पूरे (2x) का वर्ग करें।
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यदि (p(x)=x-2 -2x+3), तो (p(x+1)) क्या होगा?
If (p(x)=x-2 -2x+3), what is (p(x+1))?
#composition
#substitution
#polynomial
A \(x^2+2\)
B \(x^2+1\)
C \(x^2-1\)
D \(x^2+2x+3\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+2\)
Step 1
Concept
(p(x+1)=(x+1)2 -2(x+1)+3=x-2 +2). Substitute the whole (x+1) in place of (x).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+2\). (p(x+1)=(x+1)2 -2(x+1)+3=x-2 +2). Substitute the whole (x+1) in place of (x).
Step 3
Exam Tip
(p(x+1)=(x+1)2 -2(x+1)+3=x-2 +2)। (x) की जगह पूरा (x+1) रखें।
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(p(x)=2x-3 -9x-2 +12x-5) के लिए (p(2)) का मान क्या है?
What is the value of (p(2)) for (p(x)=2x-3 -9x-2 +12x-5)?
#evaluation
#cubic
#substitution
A (-1)
B (0)
C (1)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(2)=16-36+24-5=-1). Evaluate each term separately and then add.
Step 2
Why this answer is correct
The correct answer is A. (-1). (p(2)=16-36+24-5=-1). Evaluate each term separately and then add.
Step 3
Exam Tip
(p(2)=16-36+24-5=-1)। प्रत्येक पद का मान अलग निकालकर जोड़ें।
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यदि (p(x)=x-2 -16), तो (p(4)) का मान क्या है?
If (p(x)=x-2 -16), what is the value of (p(4))?
#zero
#evaluation
#substitution
A (0)
B (4)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
(p(4)=42 -16=0). Hence (4) is a zero of this polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(4)=42 -16=0). Hence (4) is a zero of this polynomial.
Step 3
Exam Tip
(p(4)=42 -16=0)। इसलिए (4) इस बहुपद का शून्य है।
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यदि (p(x)=2x-2 +3x-11), तो (p(2)) का मान क्या है?
If (p(x)=2x-2 +3x-11), what is the value of (p(2))?
#evaluation
#substitution
#polynomial
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(2)=2(2)2 +3(2)-11=3). While evaluating, calculate the power first.
Step 2
Why this answer is correct
The correct answer is C. (3). (p(2)=2(2)2 +3(2)-11=3). While evaluating, calculate the power first.
Step 3
Exam Tip
(p(2)=2(2)2 +3(2)-11=3)। मान निकालते समय पहले घात का मान निकालें।
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यदि (p(x)=2x-2 +3x+4), तो (p(-1)) और (p(0)) का अंतर (p(-1)-p(0)) क्या है?
If (p(x)=2x-2 +3x+4), what is the difference (p(-1)-p(0))?
#polynomial-value
#difference
#substitution
A (-1)
B (0)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
(p(-1)=3) and (p(0)=4). Therefore (p(-1)-p(0)=-1).
Step 2
Why this answer is correct
The correct answer is A. (-1). (p(-1)=3) and (p(0)=4). Therefore (p(-1)-p(0)=-1).
Step 3
Exam Tip
(p(-1)=3) और (p(0)=4) है। इसलिए (p(-1)-p(0)=-1) है।
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यदि (p(x)=x-3 -2x-2 +x), तो (p(1)) का मान क्या है?
If (p(x)=x-3 -2x-2 +x), what is the value of (p(1))?
#cubic-polynomial
#zero
#substitution
A (0)
B (1)
C (2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-2+1=0). Therefore (1) is a zero of this polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(1)=1-2+1=0). Therefore (1) is a zero of this polynomial.
Step 3
Exam Tip
(p(1)=1-2+1=0) है। इसलिए (1) इस बहुपद का शून्य है।
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यदि (p(x)=x-2 -2x+3), तो (p(2)+p(-1)) का मान क्या है?
If (p(x)=x-2 -2x+3), what is the value of (p(2)+p(-1))?
#polynomial-value
#sum
#substitution
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
(p(2)=3) and (p(-1)=6). Therefore the sum is (9).
Step 2
Why this answer is correct
The correct answer is B. (9). (p(2)=3) and (p(-1)=6). Therefore the sum is (9).
Step 3
Exam Tip
(p(2)=3) और (p(-1)=6) है। इसलिए योग (9) है।
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यदि (p(x)=x-2 -3x+2), तो (p(1)) और (p(2)) के बारे में सही कथन कौन सा है?
If (p(x)=x-2 -3x+2), which statement about (p(1)) and (p(2)) is correct?
#zeros
#quadratic
#substitution
A दोनों (0) हैं / Both are (0)
B केवल (p(1)=0) है / Only (p(1)=0)
C केवल (p(2)=0) है / Only (p(2)=0)
D दोनों (0) नहीं हैं / Both are not (0)
Explanation opens after your attempt
Correct Answer
A. दोनों (0) हैं / Both are (0)
Step 1
Concept
(p(1)=1-3+2=0) and (p(2)=4-6+2=0). So both are zeros.
Step 2
Why this answer is correct
The correct answer is A. दोनों (0) हैं / Both are (0). (p(1)=1-3+2=0) and (p(2)=4-6+2=0). So both are zeros.
Step 3
Exam Tip
(p(1)=1-3+2=0) और (p(2)=4-6+2=0) है। इसलिए दोनों शून्य हैं।
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यदि (p(x)=x-2 +x+1), तो (p(-1)) का मान क्या है?
If (p(x)=x-2 +x+1), what is the value of (p(-1))?
#substitution
#negative-value
#quadratic
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(-1)=(-1)2 +(-1)+1=1). Add the signs carefully.
Step 2
Why this answer is correct
The correct answer is B. (1). (p(-1)=(-1)2 +(-1)+1=1). Add the signs carefully.
Step 3
Exam Tip
(p(-1)=(-1)2 +(-1)+1=1) है। चिह्नों को सावधानी से जोड़ें।
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यदि (p(x)=x-3 +ax-2 +bx+1) में (a=0) और (b=-2), तो बहुपद क्या होगा?
If (a=0) and (b=-2) in (p(x)=x-3 +ax-2 +bx+1), what will the polynomial be?
#parameter
#substitution
#polynomial-form
A \(x^3-2x+1\)
B \(x^3+2x+1\)
C \(x^3-2x^2+1\)
D \(x^3+x^2-2x\)
Explanation opens after your attempt
Correct Answer
A. \(x^3-2x+1\)
Step 1
Concept
With (a=0), the \(x^2\) term vanishes, and with (b=-2), we get (-2x). So the polynomial is \(x^3-2x+1\).
Step 2
Why this answer is correct
The correct answer is A. \(x^3-2x+1\). With (a=0), the \(x^2\) term vanishes, and with (b=-2), we get (-2x). So the polynomial is \(x^3-2x+1\).
Step 3
Exam Tip
(a=0) से \(x^2\) पद हटता है और (b=-2) से (-2x) मिलता है। इसलिए बहुपद \(x^3-2x+1\) है।
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यदि (p(x)=5x-2 -3x+2), तो (p(0)+p(1)) का मान क्या है?
If (p(x)=5x-2 -3x+2), what is the value of (p(0)+p(1))?
#polynomial-value
#sum
#substitution
A (4)
B (5)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(p(0)=2) and (p(1)=4). Therefore the sum is (6).
Step 2
Why this answer is correct
The correct answer is C. (6). (p(0)=2) and (p(1)=4). Therefore the sum is (6).
Step 3
Exam Tip
(p(0)=2) और (p(1)=4) है। इसलिए योग (6) है।
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(p(x)=x-2 +4x+4) के लिए निम्न में से कौन सा सत्य है?
Which of the following is true for (p(x)=x-2 +4x+4)?
#zero-of-polynomial
#perfect-square
#substitution
A (p(-2)=0)
B (p(0)=0)
C (p(2)=0)
D (p(4)=0)
Explanation opens after your attempt
Correct Answer
A. (p(-2)=0)
Step 1
Concept
(p(-2)=4-8+4=0). Therefore (-2) is a zero of this polynomial.
Step 2
Why this answer is correct
The correct answer is A. (p(-2)=0). (p(-2)=4-8+4=0). Therefore (-2) is a zero of this polynomial.
Step 3
Exam Tip
(p(-2)=4-8+4=0) है। इसलिए (-2) इस बहुपद का शून्य है।
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यदि (p(x)=2x-2 -7x+3), तो (p(3)) का मान क्या है?
If (p(x)=2x-2 -7x+3), what is the value of (p(3))?
#substitution
#zero
#quadratic
A (0)
B (3)
C (6)
D (9)
Explanation opens after your attempt
Step 1
Concept
(p(3)=2(3)2 -7(3)+3=18-21+3=0). Hence (3) is its zero.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(3)=2(3)2 -7(3)+3=18-21+3=0). Hence (3) is its zero.
Step 3
Exam Tip
(p(3)=2(3)2 -7(3)+3=18-21+3=0) है। अतः (3) इसका शून्य है।
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यदि (p(x)=x-2 +ax+a) और (p(1)=5), तो (a) का मान क्या है?
If (p(x)=x-2 +ax+a) and (p(1)=5), what is the value of (a)?
#parameter
#polynomial-value
#substitution
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1+a+a=5) gives (1+2a=5). Therefore (a=2).
Step 2
Why this answer is correct
The correct answer is B. (2). (p(1)=1+a+a=5) gives (1+2a=5). Therefore (a=2).
Step 3
Exam Tip
(p(1)=1+a+a=5) से (1+2a=5) मिलता है। इसलिए (a=2) है।
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