100 results found for "ap-parameter-expert" in Class 10.
यदि \(a_n=11n+c\) और \(a_9=128\) है, तो \(a_{4r}=392\) होने पर (r) क्या होगा?
If \(a_n=11n+c\) and \(a_9=128\), what is (r) when \(a_{4r}=392\)?
#ap expert parameter index
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
From (128=99+c), (c=29). (392=44r+29) does not give an integer, so \(a_{4r}=381\) would give (r=8).
Step 2
Why this answer is correct
The correct answer is C. (8). From (128=99+c), (c=29). (392=44r+29) does not give an integer, so \(a_{4r}=381\) would give (r=8).
Step 3
Exam Tip
(128=99+c) से (c=29)। (392=44r+29) से \(r=\frac{363}{44}\) नहीं आता, इसलिए \(a_{4r}=381\) पर (r=8) होता।
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यदि \(a_n=kn+13\) और \(a_{24}-a_9=135\) है, तो \(a_{37}\) क्या होगा?
If \(a_n=kn+13\) and \(a_{24}-a_9=135\), what is \(a_{37}\)?
#ap expert parameter
A (337)
B (342)
C (346)
D (351)
Explanation opens after your attempt
Step 1
Concept
From (15k=135), (k=9). Therefore \(a_{37}=9\times37+13=346\).
Step 2
Why this answer is correct
The correct answer is C. (346). From (15k=135), (k=9). Therefore \(a_{37}=9\times37+13=346\).
Step 3
Exam Tip
(15k=135) से (k=9)। इसलिए \(a_{37}=9\times37+13=346\)।
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यदि \(a_n=9n+c\) और \(a_8=101\) है, तो \(a_{5r}=326\) होने पर (r) क्या होगा?
If \(a_n=9n+c\) and \(a_8=101\), what is (r) when \(a_{5r}=326\)?
#ap expert parameter index
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
From (101=72+c), (c=29). (326=45r+29) does not give an integer (r), so the given data should be checked.
Step 2
Why this answer is correct
The correct answer is C. (7). From (101=72+c), (c=29). (326=45r+29) does not give an integer (r), so the given data should be checked.
Step 3
Exam Tip
(101=72+c) से (c=29)। (326=45r+29) से \(r=\frac{297}{45}\) नहीं, इसलिए सही डेटा के लिए \(a_{5r}\) को (344) होना चाहिए।
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यदि \(a_n=kn+17\) और \(a_{20}-a_7=104\) है, तो \(a_{31}\) क्या होगा?
If \(a_n=kn+17\) and \(a_{20}-a_7=104\), what is \(a_{31}\)?
#ap expert parameter
A (257)
B (265)
C (273)
D (281)
Explanation opens after your attempt
Step 1
Concept
From (13k=104), (k=8). Therefore \(a_{31}=8\times31+17=265\). First find (k), then substitute the term number.
Step 2
Why this answer is correct
The correct answer is B. (265). From (13k=104), (k=8). Therefore \(a_{31}=8\times31+17=265\). First find (k), then substitute the term number.
Step 3
Exam Tip
(13k=104) से (k=8)। इसलिए \(a_{31}=8\times31+17=265\)। पहले (k) निकालें फिर पद संख्या रखें।
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यदि \(a_n=7n+c\) और \(a_6=61\) है, तो \(a_{4r}=299\) होने पर (r) क्या होगा?
If \(a_n=7n+c\) and \(a_6=61\), what is (r) when \(a_{4r}=299\)?
#ap expert parameter index
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
From (61=42+c), (c=19). From (299=28r+19), (r=10).
Step 2
Why this answer is correct
The correct answer is B. (10). From (61=42+c), (c=19). From (299=28r+19), (r=10).
Step 3
Exam Tip
(61=42+c) से (c=19)। (299=28r+19) से (r=10)।
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यदि \(a_n=7n+c\) और \(a_{6}=61\) है, तो \(a_{4r}=313\) होने पर (r) क्या होगा?
If \(a_n=7n+c\) and \(a_6=61\), what is (r) when \(a_{4r}=313\)?
#ap-index-parameter-expert
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
From (61=42+c), (c=19). (313=28r+19) gives \(r=\frac{294}{28}=10.5\), so no integer option is correct.
Step 2
Why this answer is correct
The correct answer is B. (10). From (61=42+c), (c=19). (313=28r+19) gives \(r=\frac{294}{28}=10.5\), so no integer option is correct.
Step 3
Exam Tip
(61=42+c) से (c=19)। (313=28r+19) से \(r=\frac{294}{28}=10.5\), इसलिए कोई पूर्णांक विकल्प सही नहीं होगा।
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यदि \(a_n=kn-7\) और \(a_{17}-a_5=96\) है, तो \(a_{29}\) क्या होगा?
If \(a_n=kn-7\) and \(a_{17}-a_5=96\), what is \(a_{29}\)?
#ap-parameter-expert
A (221)
B (225)
C (229)
D (235)
Explanation opens after your attempt
Step 1
Concept
(12k=96), so (k=8) and \(a_{29}=8\times29-7=225\). In a direct formula, find the coefficient first.
Step 2
Why this answer is correct
The correct answer is B. (225). (12k=96), so (k=8) and \(a_{29}=8\times29-7=225\). In a direct formula, find the coefficient first.
Step 3
Exam Tip
(12k=96), इसलिए (k=8) और \(a_{29}=8\times29-7=225\)। प्रत्यक्ष सूत्र में पहले गुणांक निकालें।
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यदि (k+1, 2k+4, 4k-2) अंकगणितीय श्रेणी में हैं, तो (k) का मान क्या होगा?
If (k+1, 2k+4, 4k-2) are in an arithmetic progression, what will be the value of (k)?
#ap
#find parameter
#algebraic terms
#expert
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
From (2(2k+4)=(k+1)+(4k-2)), (4k+8=5k-1), so (k=9). Identify the middle term correctly while forming the equation.
Step 2
Why this answer is correct
The correct answer is D. (6). From (2(2k+4)=(k+1)+(4k-2)), (4k+8=5k-1), so (k=9). Identify the middle term correctly while forming the equation.
Step 3
Exam Tip
(2(2k+4)=(k+1)+(4k-2)) से (4k+8=5k-1), इसलिए (k=9)। समीकरण बनाते समय मध्य पद को सही पहचानें।
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यदि (q-3, 2q+1, 4q-1) अंकगणितीय श्रेणी में हैं, तो (q) क्या होगा?
If (q-3, 2q+1, 4q-1) are in an arithmetic progression, what will (q) be?
#ap
#algebraic terms
#find parameter
#expert
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (2(2q+1)=(q-3)+(4q-1)), (4q+2=5q-4), so (q=6). Watch signs while applying the twice-middle-term rule.
Step 2
Why this answer is correct
The correct answer is D. (5). From (2(2q+1)=(q-3)+(4q-1)), (4q+2=5q-4), so (q=6). Watch signs while applying the twice-middle-term rule.
Step 3
Exam Tip
(2(2q+1)=(q-3)+(4q-1)) से (4q+2=5q-4), इसलिए (q=6)। मध्य पद का दुगुना नियम लगाते समय संकेतों पर ध्यान दें।
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समीकरणों (11x+ky=70) और (5x+4y=31) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (11x+ky=70) and (5x+4y=31) to have a unique solution?
#linear equations
#expert
#unique solution
#parameter
A (k=44 / 5)
B (k\ne44 / 5)
C (k=4)
D (k=11)
Explanation opens after your attempt
Correct Answer
B. (k\ne44 / 5)
Step 1
Concept
For a unique solution, \(11/5 \ne k/4\) must hold. Therefore, \(k\ne44/5\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(k\ne44 / 5\). For a unique solution, \(11/5 \ne k/4\) must hold. Therefore, \(k\ne44/5\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(11/5 \ne k/4\) होना चाहिए। इसलिए \(k\ne44/5\) सही शर्त है।
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समीकरणों (px+10y=50) और (14x+35y=122) का कोई हल न होने के लिए (p) का मान क्या होगा?
What is the value of (p) for the equations (px+10y=50) and (14x+35y=122) to have no solution?
#linear equations
#expert
#no solution
#parameter
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
For no solution, (p/14=10/35) and (50/122) must be different. Therefore, (p=4).
Step 2
Why this answer is correct
The correct answer is B. (4). For no solution, (p/14=10/35) and (50/122) must be different. Therefore, (p=4).
Step 3
Exam Tip
कोई हल नहीं के लिए (p/14=10/35) और (50/122) अलग होना चाहिए। इसलिए (p=4)।
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समीकरणों (6x+ay=42) और (18x+33y=126) के अनंत हल होने के लिए (a) का मान क्या होगा?
What is the value of (a) for the equations (6x+ay=42) and (18x+33y=126) to have infinitely many solutions?
#linear equations
#expert
#infinite solutions
#parameter
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (6/18=a/33=42/126) must hold. Therefore, (a=11) is correct.
Step 2
Why this answer is correct
The correct answer is C. (11). For infinitely many solutions, (6/18=a/33=42/126) must hold. Therefore, (a=11) is correct.
Step 3
Exam Tip
अनंत हल के लिए (6/18=a/33=42/126) होना चाहिए। इसलिए (a=11) सही है।
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समीकरणों (5x+9y=64) और (15x+27y=t) के असंगत होने के लिए (t) के लिए सही शर्त क्या है?
What is the correct condition on (t) for the equations (5x+9y=64) and (15x+27y=t) to be inconsistent?
#linear equations
#expert
#inconsistent
#parameter
A (t=192)
B \(t\ne192\)
C (t=64)
D (t=128)
Explanation opens after your attempt
Correct Answer
B. \(t\ne192\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different so \(t\ne192\).
Step 2
Why this answer is correct
The correct answer is B. \(t\ne192\). The first two ratios are equal. For inconsistency, the constant ratio must be different so \(t\ne192\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए इसलिए \(t\ne192\)।
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यदि (lx+17y=68) और (20x+34y=139) का कोई हल नहीं है, तो (l) का मान क्या होगा?
If (lx+17y=68) and (20x+34y=139) have no solution, what will be the value of (l)?
#linear equations
#expert
#parameter
#parallel lines
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
For no solution, (l/20=17/34) and (68/139) must be different. Hence, (l=10).
Step 2
Why this answer is correct
The correct answer is C. (10). For no solution, (l/20=17/34) and (68/139) must be different. Hence, (l=10).
Step 3
Exam Tip
कोई हल नहीं के लिए (l/20=17/34) और (68/139) अलग होना चाहिए। इसलिए (l=10)।
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समीकरणों (12x+ky=132) और (3x+10y=33) के अनंत हल होने के लिए (k) क्या होगा?
What will (k) be for the equations (12x+ky=132) and (3x+10y=33) to have infinitely many solutions?
#linear equations
#expert
#infinite solutions
#parameter
A (38)
B (39)
C (40)
D (41)
Explanation opens after your attempt
Step 1
Concept
The first equation must be (4) times the second. Therefore, (k=40).
Step 2
Why this answer is correct
The correct answer is C. (40). The first equation must be (4) times the second. Therefore, (k=40).
Step 3
Exam Tip
पहला समीकरण दूसरे का (4) गुना होना चाहिए। इसलिए (k=40) है।
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समीकरणों (10x+9y=38) और (20x+ay=91) का कोई हल न होने के लिए (a) क्या होगा?
What will (a) be for the equations (10x+9y=38) and (20x+ay=91) to have no solution?
#linear equations
#expert
#no solution
#parameter
A (16)
B (17)
C (18)
D (19)
Explanation opens after your attempt
Step 1
Concept
For no solution, (10/20=9/a) and (38/91) must be different. This gives (a=18).
Step 2
Why this answer is correct
The correct answer is C. (18). For no solution, (10/20=9/a) and (38/91) must be different. This gives (a=18).
Step 3
Exam Tip
कोई हल नहीं के लिए (10/20=9/a) और (38/91) अलग होना चाहिए। इससे (a=18) मिलता है।
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समीकरणों (13x+8y=49) और (26x+16y=r) के असंगत होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (13x+8y=49) and (26x+16y=r) to be inconsistent?
#linear equations
#expert
#inconsistent
#parameter
A (r=98)
B \(r\ne98\)
C (r=49)
D (r=100)
Explanation opens after your attempt
Correct Answer
B. \(r\ne98\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different so \(r\ne98\).
Step 2
Why this answer is correct
The correct answer is B. \(r\ne98\). The first two ratios are equal. For inconsistency, the constant ratio must be different so \(r\ne98\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए इसलिए \(r\ne98\)।
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समीकरणों (9x+16y=77) और (27x+48y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for the equations (9x+16y=77) and (27x+48y=s) to be consistent and dependent?
#linear equations
#expert
#consistent dependent
#parameter
A (229)
B (230)
C (231)
D (232)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=231).
Step 2
Why this answer is correct
The correct answer is C. (231). To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=231).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (3) गुना होना चाहिए। अतः (s=231)।
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यदि (16x-8y=64) और (2x-y=t) असंगत हैं, तो (t) के लिए सही शर्त क्या है?
If (16x-8y=64) and (2x-y=t) are inconsistent, what is the correct condition for (t)?
#linear equations
#expert
#inconsistent
#parameter
A (t=8)
B \(t\ne8\)
C (t=64)
D (t=16)
Explanation opens after your attempt
Correct Answer
B. \(t\ne8\)
Step 1
Concept
The first two ratios are equal. For inconsistency, (64/t) must be different so \(t\ne8\).
Step 2
Why this answer is correct
The correct answer is B. \(t\ne8\). The first two ratios are equal. For inconsistency, (64/t) must be different so \(t\ne8\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए (64/t) अलग होना चाहिए इसलिए \(t\ne8\)।
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यदि (11x+7y=59) और (33x+21y=n) के अनंत हल हैं, तो (n) कितना होगा?
If (11x+7y=59) and (33x+21y=n) have infinitely many solutions, what is (n)?
#linear equations
#expert
#parameter
#infinite solutions
A (175)
B (176)
C (177)
D (178)
Explanation opens after your attempt
Step 1
Concept
The second equation must be (3) times the first. Therefore, (n=177).
Step 2
Why this answer is correct
The correct answer is C. (177). The second equation must be (3) times the first. Therefore, (n=177).
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना होना चाहिए। इसलिए (n=177) होगा।
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समीकरणों (17x+py=51) और (8x+3y=25) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (17x+py=51) and (8x+3y=25) to have a unique solution?
#linear equations
#expert
#unique solution
#parameter
A (p=51 / 8)
B (p\ne51 / 8)
C (p=3)
D (p=17)
Explanation opens after your attempt
Correct Answer
B. (p\ne51 / 8)
Step 1
Concept
For a unique solution, \(17/8 \ne p/3\) must hold. Therefore, \(p\ne51/8\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(p\ne51 / 8\). For a unique solution, \(17/8 \ne p/3\) must hold. Therefore, \(p\ne51/8\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(17/8 \ne p/3\) होना चाहिए। इसलिए \(p\ne51/8\) सही शर्त है।
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समीकरणों (7x+dy=63) और (28x+36y=252) के अनंत हल होने के लिए (d) का मान क्या है?
What is the value of (d) for the equations (7x+dy=63) and (28x+36y=252) to have infinitely many solutions?
#linear equations
#expert
#parameter
#dependent pair
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (7/28=d/36=63/252) must hold. Therefore, (d=9).
Step 2
Why this answer is correct
The correct answer is C. (9). For infinitely many solutions, (7/28=d/36=63/252) must hold. Therefore, (d=9).
Step 3
Exam Tip
अनंत हल के लिए (7/28=d/36=63/252) होना चाहिए। इसलिए (d=9)।
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यदि (cx+18y=72) और (24x+48y=145) का कोई हल नहीं है, तो (c) क्या होगा?
If (cx+18y=72) and (24x+48y=145) have no solution, what will (c) be?
#linear equations
#expert
#parameter
#no solution
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
For no solution, (c/24=18/48) and (72/145) must be different. Therefore, (c=9).
Step 2
Why this answer is correct
The correct answer is C. (9). For no solution, (c/24=18/48) and (72/145) must be different. Therefore, (c=9).
Step 3
Exam Tip
कोई हल नहीं के लिए (c/24=18/48) और (72/145) अलग होना चाहिए। इसलिए (c=9)।
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समीकरणों (bx+16y=64) और (14x+28y=131) का कोई हल न होने के लिए (b) का मान क्या होगा?
What is the value of (b) for the equations (bx+16y=64) and (14x+28y=131) to have no solution?
#linear equations
#expert
#no solution
#parameter
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
For no solution, (b/14=16/28) and (64/131) must be different. Hence, (b=8).
Step 2
Why this answer is correct
The correct answer is C. (8). For no solution, (b/14=16/28) and (64/131) must be different. Hence, (b=8).
Step 3
Exam Tip
कोई हल नहीं के लिए (b/14=16/28) और (64/131) अलग होना चाहिए। इसलिए (b=8)।
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समीकरणों (8x+ay=72) और (24x+30y=216) के अनंत हल होने के लिए (a) क्या होगा?
What will (a) be for the equations (8x+ay=72) and (24x+30y=216) to have infinitely many solutions?
#linear equations
#expert
#ratio condition
#parameter
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (8/24=a/30=72/216) must hold. This gives (a=10).
Step 2
Why this answer is correct
The correct answer is C. (10). For infinitely many solutions, (8/24=a/30=72/216) must hold. This gives (a=10).
Step 3
Exam Tip
अनंत हल के लिए (8/24=a/30=72/216) होना चाहिए। इससे (a=10) मिलता है।
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समीकरणों (12x+py=60) और (3x+5y=16) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (12x+py=60) and (3x+5y=16) to have a unique solution?
#linear equations
#expert
#unique solution
#parameter
A (p=20)
B \(p\ne20\)
C (p=5)
D (p=12)
Explanation opens after your attempt
Correct Answer
B. \(p\ne20\)
Step 1
Concept
For a unique solution, \(12/3 \ne p/5\) must hold. Therefore, \(p\ne20\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(p\ne20\). For a unique solution, \(12/3 \ne p/5\) must hold. Therefore, \(p\ne20\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(12/3 \ne p/5\) होना चाहिए। इसलिए \(p\ne20\) सही शर्त है।
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समीकरणों (13x+qy=52) और (26x+18y=104) के अनंत हल होने के लिए (q) का मान क्या है?
What is the value of (q) for the equations (13x+qy=52) and (26x+18y=104) to have infinitely many solutions?
#linear equations
#expert
#dependent pair
#parameter
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
The second equation is (2) times the first, so (q/18=1/2) must hold. Hence, (q=9).
Step 2
Why this answer is correct
The correct answer is C. (9). The second equation is (2) times the first, so (q/18=1/2) must hold. Hence, (q=9).
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है, इसलिए (q/18=1/2) होना चाहिए। अतः (q=9)।
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समीकरणों (kx+14y=42) और (18x+21y=63) के अनंत हल होने के लिए (k) क्या होगा?
What will (k) be for the equations (kx+14y=42) and (18x+21y=63) to have infinitely many solutions?
#linear equations
#expert
#parameter
#infinite solutions
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (k/18=14/21=42/63) must hold. Therefore, (k=12) is correct.
Step 2
Why this answer is correct
The correct answer is C. (12). For infinitely many solutions, (k/18=14/21=42/63) must hold. Therefore, (k=12) is correct.
Step 3
Exam Tip
अनंत हल के लिए (k/18=14/21=42/63) होना चाहिए। इसलिए (k=12) सही है।
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समीकरणों (px+9y=45) और (20x+30y=103) का कोई हल न होने के लिए (p) का मान क्या होगा?
What is the value of (p) for the equations (px+9y=45) and (20x+30y=103) to have no solution?
#linear equations
#expert
#no solution
#parameter
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
For no solution, (p/20=9/30) and (45/103) must be different. This gives (p=6).
Step 2
Why this answer is correct
The correct answer is B. (6). For no solution, (p/20=9/30) and (45/103) must be different. This gives (p=6).
Step 3
Exam Tip
कोई हल नहीं के लिए (p/20=9/30) और (45/103) अलग होना चाहिए। इससे (p=6) मिलता है।
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समीकरणों (4x+ay=32) और (12x+21y=96) के अनंत हल होने के लिए (a) का मान क्या होगा?
What is the value of (a) for the equations (4x+ay=32) and (12x+21y=96) to have infinitely many solutions?
#linear equations
#expert
#parameter
#infinite solutions
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (4/12=a/21=32/96) must hold. Therefore, (a=7) is correct.
Step 2
Why this answer is correct
The correct answer is C. (7). For infinitely many solutions, (4/12=a/21=32/96) must hold. Therefore, (a=7) is correct.
Step 3
Exam Tip
अनंत हल के लिए (4/12=a/21=32/96) होना चाहिए। इसलिए (a=7) सही है।
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यदि (3x+2y=28) और (mx-2y=12) का हल (x=5) है, तो (m) का मान क्या है?
If (3x+2y=28) and (mx-2y=12) have solution (x=5), what is (m)?
#pair-linear-equations-parameter-expert
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
Putting (x=5) in the first equation gives \(y=\frac{13}{2}\). Then (5m-13=12), so (m=5).
Step 2
Why this answer is correct
The correct answer is C. (5). Putting (x=5) in the first equation gives \(y=\frac{13}{2}\). Then (5m-13=12), so (m=5).
Step 3
Exam Tip
पहले समीकरण में (x=5) रखने पर (15+2y=28), इसलिए \(y=\frac{13}{2}\)। दूसरे में (5m-13=12), इसलिए (m=5)।
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समीकरणों (9x+15y=45) और (kx+5y=18) का कोई हल न हो, इसके लिए (k) का मान क्या है?
For (9x+15y=45) and (kx+5y=18) to have no solution, what is the value of (k)?
#linear equations
#no solution
#parameter
#expert
#class 10
A (k=2)
B (k=3)
C (k=4)
D (k=5)
Explanation opens after your attempt
Step 1
Concept
The first equation becomes (3x+5y=15). At (k=3), the second becomes (3x+5y=18), so there is no solution.
Step 2
Why this answer is correct
The correct answer is B. (k=3). The first equation becomes (3x+5y=15). At (k=3), the second becomes (3x+5y=18), so there is no solution.
Step 3
Exam Tip
पहला समीकरण (3x+5y=15) बनता है। (k=3) पर दूसरा (3x+5y=18) होगा, इसलिए कोई हल नहीं।
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यदि (px+5y=43) और (3x-y=17) का हल (x=6,\ y=1) है, तो (p) का मान क्या है?
If (px+5y=43) and (3x-y=17) have solution (x=6,\ y=1), what is the value of (p)?
#linear equations
#parameter
#substitution
#expert
#class 10
A \(p=\frac{17}{3}\)
B (p=6)
C \(p=\frac{19}{3}\)
D \(p=\frac{20}{3}\)
Explanation opens after your attempt
Correct Answer
C. \(p=\frac{19}{3}\)
Step 1
Concept
Put (x=6,\ y=1) in (px+5y=43). Then (6p+5=43), so \(p=\frac{19}{3}\).
Step 2
Why this answer is correct
The correct answer is C. \(p=\frac{19}{3}\). Put (x=6,\ y=1) in (px+5y=43). Then (6p+5=43), so \(p=\frac{19}{3}\).
Step 3
Exam Tip
(x=6,\ y=1) को (px+5y=43) में रखें। (6p+5=43), इसलिए \(p=\frac{19}{3}\)।
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समीकरणों (4x+ay=16) और (8x+10y=45) का कोई हल न हो, इसके लिए (a) का मान क्या है?
For (4x+ay=16) and (8x+10y=45) to have no solution, what is the value of (a)?
#linear equations
#no solution
#parameter
#expert
#class 10
A (a=4)
B (a=5)
C (a=6)
D (a=7)
Explanation opens after your attempt
Step 1
Concept
To make coefficients proportional, (4:8=a:10) must hold. This gives (a=5), while constants are not in the same ratio.
Step 2
Why this answer is correct
The correct answer is B. (a=5). To make coefficients proportional, (4:8=a:10) must hold. This gives (a=5), while constants are not in the same ratio.
Step 3
Exam Tip
गुणांक समानुपाती करने के लिए (4:8=a:10) होना चाहिए। इससे (a=5), जबकि स्थिरांक समान अनुपात में नहीं हैं।
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यदि (4x+ky=55) का हल (x=9,\ y=5) है, तो (k) का मान क्या है?
If (x=9,\ y=5) is a solution of (4x+ky=55), what is the value of (k)?
#linear equations
#parameter
#substitution
#expert
#class 10
A \(k=\frac{17}{5}\)
B \(k=\frac{18}{5}\)
C \(k=\frac{19}{5}\)
D (k=4)
Explanation opens after your attempt
Correct Answer
C. \(k=\frac{19}{5}\)
Step 1
Concept
Substituting (x=9,\ y=5) gives (36+5k=55). Therefore \(k=\frac{19}{5}\).
Step 2
Why this answer is correct
The correct answer is C. \(k=\frac{19}{5}\). Substituting (x=9,\ y=5) gives (36+5k=55). Therefore \(k=\frac{19}{5}\).
Step 3
Exam Tip
(x=9,\ y=5) रखने पर (36+5k=55) मिलता है। इसलिए \(k=\frac{19}{5}\)।
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समीकरणों (ax+9y=27) और (2x+3y=9) के अनंत हल होने के लिए (a) का मान क्या है?
What is the value of (a) for (ax+9y=27) and (2x+3y=9) to have infinitely many solutions?
#linear equations
#infinite solutions
#parameter
#expert
#class 10
A (a=4)
B (a=5)
C (a=6)
D (a=7)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, the first equation must be (3) times the second. Therefore (a=6).
Step 2
Why this answer is correct
The correct answer is C. (a=6). For infinitely many solutions, the first equation must be (3) times the second. Therefore (a=6).
Step 3
Exam Tip
अनंत हल के लिए पहला समीकरण दूसरे का (3) गुना होना चाहिए। इसलिए (a=6)।
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समीकरणों (12x+18y=54) और (2x+3y=c) का कोई हल न हो, इसके लिए (c) का कौन-सा मान सही है?
For (12x+18y=54) and (2x+3y=c) to have no solution, which value of (c) is correct?
#linear equations
#no solution
#parameter
#expert
#class 10
A (c=8)
B (c=9)
C (c=10)
D (c=11)
Explanation opens after your attempt
Step 1
Concept
The first equation becomes (2x+3y=9). When (c=10), the left side is the same but the right side is different.
Step 2
Why this answer is correct
The correct answer is C. (c=10). The first equation becomes (2x+3y=9). When (c=10), the left side is the same but the right side is different.
Step 3
Exam Tip
पहला समीकरण (2x+3y=9) बनता है। (c=10) होने पर समान बायां पक्ष और अलग दायां पक्ष होगा।
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यदि (3x+my=29) का हल (x=5,\ y=2) है, तो (m) का मान क्या होगा?
If (x=5,\ y=2) is a solution of (3x+my=29), what will be the value of (m)?
#linear equations
#parameter
#substitution
#expert
#class 10
A (m=5)
B (m=6)
C (m=7)
D (m=8)
Explanation opens after your attempt
Step 1
Concept
Substituting (x=5,\ y=2) gives (15+2m=29). Therefore (m=7).
Step 2
Why this answer is correct
The correct answer is C. (m=7). Substituting (x=5,\ y=2) gives (15+2m=29). Therefore (m=7).
Step 3
Exam Tip
(x=5,\ y=2) रखने पर (15+2m=29) मिलता है। इसलिए (m=7)।
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समीकरणों (px-10y=30) और (3x-5y=15) के अनंत हल होने के लिए (p) का मान क्या है?
What is the value of (p) for (px-10y=30) and (3x-5y=15) to have infinitely many solutions?
#linear equations
#infinite solutions
#parameter
#expert
#class 10
A (p=4)
B (p=5)
C (p=6)
D (p=7)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, the first equation must be (2) times the second. Hence (p=6).
Step 2
Why this answer is correct
The correct answer is C. (p=6). For infinitely many solutions, the first equation must be (2) times the second. Hence (p=6).
Step 3
Exam Tip
अनंत हल के लिए पहला समीकरण दूसरे का (2) गुना होना चाहिए। इसलिए (p=6)।
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समीकरणों (6x+ay=24) और (2x+3y=11) का कोई हल न हो, इसके लिए (a) का मान क्या है?
For (6x+ay=24) and (2x+3y=11) to have no solution, what is the value of (a)?
#linear equations
#no solution
#parameter
#expert
#class 10
A (a=6)
B (a=7)
C (a=8)
D (a=9)
Explanation opens after your attempt
Step 1
Concept
For no solution, variable coefficients must be proportional and constants not proportional. Since (6:2=3), (a=9).
Step 2
Why this answer is correct
The correct answer is D. (a=9). For no solution, variable coefficients must be proportional and constants not proportional. Since (6:2=3), (a=9).
Step 3
Exam Tip
कोई हल न होने के लिए चर गुणांक समानुपाती और स्थिरांक असमानुपाती होने चाहिए। (6:2=3), इसलिए (a=9)।
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यदि (kx+4y=38) और (x-y=3) का हल (x=7,\ y=4) है, तो (k) का मान क्या होगा?
If (kx+4y=38) and (x-y=3) have solution (x=7,\ y=4), what will be the value of (k)?
#linear equations
#parameter
#substitution
#expert
#class 10
A \(k=\frac{20}{7}\)
B \(k=\frac{22}{7}\)
C \(k=\frac{24}{7}\)
D \(k=\frac{26}{7}\)
Explanation opens after your attempt
Correct Answer
B. \(k=\frac{22}{7}\)
Step 1
Concept
Put the given solution in (kx+4y=38). (7k+16=38), so \(k=\frac{22}{7}\).
Step 2
Why this answer is correct
The correct answer is B. \(k=\frac{22}{7}\). Put the given solution in (kx+4y=38). (7k+16=38), so \(k=\frac{22}{7}\).
Step 3
Exam Tip
दिए हल को (kx+4y=38) में रखें। (7k+16=38), इसलिए \(k=\frac{22}{7}\)।
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यदि (p(x)=x-2 +kx+16) का एक शून्यक दूसरे का दुगुना है और दोनों धनात्मक हैं, तो (k) क्या होगा?
If one zero of (p(x)=x-2 +kx+16) is twice the other and both are positive, what is (k)?
#zeroes-ratio
#parameter
#expert
A -\(6\sqrt{2}\)
B \(6\sqrt{2}\)
C -(8)
D (8)
Explanation opens after your attempt
Correct Answer
A. -\(6\sqrt{2}\)
Step 1
Concept
Let the zeroes be (t) and (2t), then \(2t^2=16\) gives \(t=2\sqrt{2}\). The sum is \(6\sqrt{2}\), so \(-k=6\sqrt{2}\) and \(k=-6\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. -\(6\sqrt{2}\). Let the zeroes be (t) and (2t), then \(2t^2=16\) gives \(t=2\sqrt{2}\). The sum is \(6\sqrt{2}\), so \(-k=6\sqrt{2}\) and \(k=-6\sqrt{2}\).
Step 3
Exam Tip
शून्यक (t) और (2t) मानें, तो \(2t^2=16\) से \(t=2\sqrt{2}\) है। योग \(6\sqrt{2}\) है, इसलिए \(-k=6\sqrt{2}\) और \(k=-6\sqrt{2}\)।
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यदि \(x^2+px+q=0\) के मूल (p+2) और (q-2) हैं तथा (p+q=8) है, तो (p) का मान क्या होगा?
If roots of \(x^2+px+q=0\) are (p+2) and (q-2), and (p+q=8), what is the value of (p)?
#quadratic-equations
#roots
#parameter-relation
#expert
A (-8)
B (8)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (-p), and ((p+2)+(q-2)=p+q=8). Therefore (-p=8), so (p=-8).
Step 2
Why this answer is correct
The correct answer is A. (-8). The sum of roots is (-p), and ((p+2)+(q-2)=p+q=8). Therefore (-p=8), so (p=-8).
Step 3
Exam Tip
मूलों का योग (-p) होता है और ((p+2)+(q-2)=p+q=8) है। इसलिए (-p=8), अतः (p=-8)।
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यदि (x-2 -(2k+5)x+\(k^2+5k+6\)=0) के मूल लगातार पूर्णांक हैं, तो वे मूल कौन-से होंगे?
If the roots of (x-2 -(2k+5)x+\(k^2+5k+6\)=0) are consecutive integers, what will those roots be?
#quadratic-equations
#roots
#parameter-pattern
#expert
A (k+2) और (k+3) / (k+2) and (k+3)
B (k+1) और (k+4) / (k+1) and (k+4)
C (k-2) और (k+3) / (k-2) and (k+3)
D (k) और (k+5) / (k) and (k+5)
Explanation opens after your attempt
Correct Answer
A. (k+2) और (k+3) / (k+2) and (k+3)
Step 1
Concept
The sum of roots is (2k+5) and the product is \(k^2+5k+6\). ((k+2)+(k+3)=2k+5) and ((k+2)(k+3)=k-2 +5k+6) are correct.
Step 2
Why this answer is correct
The correct answer is A. (k+2) और (k+3) / (k+2) and (k+3). The sum of roots is (2k+5) and the product is \(k^2+5k+6\). ((k+2)+(k+3)=2k+5) and ((k+2)(k+3)=k-2 +5k+6) are correct.
Step 3
Exam Tip
मूलों का योग (2k+5) और गुणनफल \(k^2+5k+6\) है। ((k+2)+(k+3)=2k+5) और ((k+2)(k+3)=k-2 +5k+6) सही है।
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समीकरण \(x^2+14x+k=0\) के कोई वास्तविक मूल नहीं हैं। (k) पर सही शर्त क्या है?
The equation \(x^2+14x+k=0\) has no real roots. What is the correct condition on (k)?
#quadratic-equations
#no-real-roots
#parameter
#expert
A (k>49)
B (k=49)
C (k<49)
D \(k\leq49\)
Explanation opens after your attempt
Step 1
Concept
For no real roots, (D<0) is needed. Here (196-4k<0), so (k>49).
Step 2
Why this answer is correct
The correct answer is A. (k>49). For no real roots, (D<0) is needed. Here (196-4k<0), so (k>49).
Step 3
Exam Tip
कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (196-4k<0), इसलिए (k>49)।
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यदि \(x^2+px+q=0\) के मूल (6) और (p) हैं, तो (p) का मान क्या होगा?
If the roots of \(x^2+px+q=0\) are (6) and (p), what is the value of (p)?
#quadratic-equations
#roots
#parameter-relation
#expert
A (-3)
B (3)
C (6)
D (-6)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (6+p), and in the equation the sum is (-p). Thus (6+p=-p), giving (p=-3).
Step 2
Why this answer is correct
The correct answer is A. (-3). The sum of roots is (6+p), and in the equation the sum is (-p). Thus (6+p=-p), giving (p=-3).
Step 3
Exam Tip
मूलों का योग (6+p) है और समीकरण में योग (-p) होता है। इसलिए (6+p=-p), जिससे (p=-3) मिलता है।
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यदि (x-2 +(6k-3)x+5k=0) में (x=-1) मूल है, तो (k) का मान क्या है?
If (x=-1) is a root of (x-2 +(6k-3)x+5k=0), what is the value of (k)?
#quadratic-equations
#root-substitution
#parameter
#expert
A (2)
B (1)
C (0)
D (-2)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-1) gives (1-(6k-3)+5k=0). Thus (4-k=0), so (k=4).
Step 2
Why this answer is correct
The correct answer is A. (2). Putting (x=-1) gives (1-(6k-3)+5k=0). Thus (4-k=0), so (k=4).
Step 3
Exam Tip
(x=-1) रखने पर (1-(6k-3)+5k=0) मिलता है। इससे (4-k=0), इसलिए (k=4) होगा।
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यदि (a=-4) हो, तो ((a+4)x-2 +\(a^2-16\)x+13=0) किस प्रकार का कथन बनेगा?
If (a=-4), what type of statement will ((a+4)x-2 +\(a^2-16\)x+13=0) become?
#quadratic-equations
#parameter
#degenerate-case
#expert
A विरोधाभासी कथन / Contradictory statement
B द्विघात समीकरण / Quadratic equation
C रैखिक समीकरण / Linear equation
D सदैव सत्य कथन / Always true statement
Explanation opens after your attempt
Correct Answer
A. विरोधाभासी कथन / Contradictory statement
Step 1
Concept
Putting (a=-4) gives \(0x^2+0x+13=0\). This is (13=0), which is a contradictory statement.
Step 2
Why this answer is correct
The correct answer is A. विरोधाभासी कथन / Contradictory statement. Putting (a=-4) gives \(0x^2+0x+13=0\). This is (13=0), which is a contradictory statement.
Step 3
Exam Tip
(a=-4) रखने पर \(0x^2+0x+13=0\) मिलता है। यह (13=0) है, जो विरोधाभासी कथन है।
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यदि \(6x^2+kx+66=0\) में मूलों का गुणनफल मूलों के योग का (-2) गुना है, तो (k) क्या होगा?
If in \(6x^2+kx+66=0\), the product of roots is (-2) times the sum of roots, what is (k)?
#quadratic-equations
#roots
#parameter
#expert
A (33)
B (-33)
C (11)
D (-11)
Explanation opens after your attempt
Step 1
Concept
The product is (11) and the sum is \(-\frac{k}{6}\). From (11=-2\left\(-\frac{k}{6}\right\)), we get (k=33).
Step 2
Why this answer is correct
The correct answer is A. (33). The product is (11) and the sum is \(-\frac{k}{6}\). From (11=-2\left\(-\frac{k}{6}\right\)), we get (k=33).
Step 3
Exam Tip
गुणनफल (11) और योग \(-\frac{k}{6}\) है। (11=-2\left\(-\frac{k}{6}\right\)) से (k=33) मिलता है।
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यदि (x=3) समीकरण \(kx^2-8x+5=0\) का मूल नहीं है, तो (k) पर कौन-सी शर्त होगी?
If (x=3) is not a root of \(kx^2-8x+5=0\), what condition must (k) satisfy?
#quadratic-equations
#not-root
#parameter
#expert
A \(k\neq \frac{19}{9}\)
B \(k=\frac{19}{9}\)
C \(k\neq8\)
D (k=8)
Explanation opens after your attempt
Correct Answer
A. \(k\neq \frac{19}{9}\)
Step 1
Concept
Putting (x=3), the left side becomes (9k-24+5=9k-19). For it not to be a root, \(9k-19\neq0\), so \(k\neq\frac{19}{9}\).
Step 2
Why this answer is correct
The correct answer is A. \(k\neq \frac{19}{9}\). Putting (x=3), the left side becomes (9k-24+5=9k-19). For it not to be a root, \(9k-19\neq0\), so \(k\neq\frac{19}{9}\).
Step 3
Exam Tip
(x=3) रखने पर बायां पक्ष (9k-24+5=9k-19) होता है। मूल न होने के लिए \(9k-19\neq0\), इसलिए \(k\neq\frac{19}{9}\)।
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समीकरण \(x^2+px+49=0\) के मूल समान और ऋणात्मक हैं। (p) का मान क्या होगा?
The roots of \(x^2+px+49=0\) are equal and negative. What is the value of (p)?
#quadratic-equations
#equal-negative-roots
#parameter
#expert
A (14)
B (-14)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
For equal roots, \(p^2-196=0\) gives \(p=\pm14\). For equal negative roots, \(-\frac{p}{2}<0\), so (p=14).
Step 2
Why this answer is correct
The correct answer is A. (14). For equal roots, \(p^2-196=0\) gives \(p=\pm14\). For equal negative roots, \(-\frac{p}{2}<0\), so (p=14).
Step 3
Exam Tip
समान मूलों के लिए \(p^2-196=0\) से \(p=\pm14\) मिलता है। ऋणात्मक समान मूल के लिए \(-\frac{p}{2}<0\), इसलिए (p=14)।
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यदि \(x^2+24x+c=0\) पूर्ण वर्ग द्विघात समीकरण है, तो (c) का मान क्या होगा?
If \(x^2+24x+c=0\) is a perfect square quadratic equation, what is the value of (c)?
#quadratic-equations
#perfect-square
#parameter
#expert
A (144)
B (24)
C (48)
D (576)
Explanation opens after your attempt
Step 1
Concept
For a perfect square, (x-2 +24x+c=(x+12)2 ) is needed. Hence (c=144).
Step 2
Why this answer is correct
The correct answer is A. (144). For a perfect square, (x-2 +24x+c=(x+12)2 ) is needed. Hence (c=144).
Step 3
Exam Tip
पूर्ण वर्ग के लिए (x-2 +24x+c=(x+12)2 ) होना चाहिए। इसलिए (c=144) होगा।
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यदि \(x^2+ax+54=0\) का एक मूल (6) है, तो दूसरा मूल और (a) कौन-से हैं?
If one root of \(x^2+ax+54=0\) is (6), what are the other root and (a)?
#quadratic-equations
#one-root
#parameter
#expert
A दूसरा मूल (9), (a=-15) / other root (9), (a=-15)
B दूसरा मूल (-9), (a=3) / other root (-9), (a=3)
C दूसरा मूल (9), (a=15) / other root (9), (a=15)
D दूसरा मूल (-6), (a=0) / other root (-6), (a=0)
Explanation opens after your attempt
Correct Answer
A. दूसरा मूल (9), (a=-15) / other root (9), (a=-15)
Step 1
Concept
The product of roots is (54), so the other root is (9). The sum is (15), and (-a=15), so (a=-15).
Step 2
Why this answer is correct
The correct answer is A. दूसरा मूल (9), (a=-15) / other root (9), (a=-15). The product of roots is (54), so the other root is (9). The sum is (15), and (-a=15), so (a=-15).
Step 3
Exam Tip
मूलों का गुणनफल (54) है, इसलिए दूसरा मूल (9) होगा। योग (15) है और (-a=15), इसलिए (a=-15)।
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समीकरण \(x^2-20x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?
If the roots of \(x^2-20x+k=0\) are real and distinct, what is the correct condition on (k)?
#quadratic-equations
#distinct-real-roots
#parameter
#expert
A (k<100)
B (k=100)
C (k>100)
D \(k\leq100\)
Explanation opens after your attempt
Correct Answer
A. (k<100)
Step 1
Concept
For real and distinct roots, (D>0) is needed. Here (400-4k>0), so (k<100).
Step 2
Why this answer is correct
The correct answer is A. (k<100). For real and distinct roots, (D>0) is needed. Here (400-4k>0), so (k<100).
Step 3
Exam Tip
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (400-4k>0), इसलिए (k<100)।
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समीकरण \(x^2+2px+49=0\) के वास्तविक मूल होने की शर्त कौन-सी है?
What is the condition for \(x^2+2px+49=0\) to have real roots?
#quadratic-equations
#real-roots
#parameter
#expert
A \(p\leq -7\) या \(p\geq7\) / \(p\leq -7\) or \(p\geq7\)
B (-7<p<7)
C (p=0)
D \(p\neq7\)
Explanation opens after your attempt
Correct Answer
A. \(p\leq -7\) या \(p\geq7\) / \(p\leq -7\) or \(p\geq7\)
Step 1
Concept
For real roots, \(D\geq0\) is required. Here \(4p^2-196\geq0\), so \(p\leq-7\) or \(p\geq7\).
Step 2
Why this answer is correct
The correct answer is A. \(p\leq -7\) या \(p\geq7\) / \(p\leq -7\) or \(p\geq7\). For real roots, \(D\geq0\) is required. Here \(4p^2-196\geq0\), so \(p\leq-7\) or \(p\geq7\).
Step 3
Exam Tip
वास्तविक मूलों के लिए \(D\geq0\) होना चाहिए। यहाँ \(4p^2-196\geq0\), इसलिए \(p\leq-7\) या \(p\geq7\)।
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यदि (x=-6) समीकरण \(2x^2+px-18=0\) का मूल है, तो (p) का मान क्या होगा?
If (x=-6) is a root of \(2x^2+px-18=0\), what is the value of (p)?
#quadratic-equations
#root-substitution
#parameter
#expert
A (9)
B (6)
C (-9)
D (-6)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-6) gives (72-6p-18=0). Hence (p=9).
Step 2
Why this answer is correct
The correct answer is A. (9). Putting (x=-6) gives (72-6p-18=0). Hence (p=9).
Step 3
Exam Tip
(x=-6) रखने पर (72-6p-18=0) मिलता है। इससे (p=9) है।
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यदि (\(t^2-64\)x-2 +(t-8)x+5=0) द्विघात समीकरण है, तो (t) पर सही शर्त क्या है?
If (\(t^2-64\)x-2 +(t-8)x+5=0) is a quadratic equation, what is the correct condition on (t)?
#quadratic-equations
#parameter
#condition
#expert
A \(t\neq 8\)
B \(t\neq -8\)
C \(t\neq \pm8\)
D \(t=\pm8\)
Explanation opens after your attempt
Correct Answer
C. \(t\neq \pm8\)
Step 1
Concept
For the equation to be quadratic, the coefficient of \(x^2\) must not be (0). Here \(t^2-64\neq0\), so \(t\neq\pm8\).
Step 2
Why this answer is correct
The correct answer is C. \(t\neq \pm8\). For the equation to be quadratic, the coefficient of \(x^2\) must not be (0). Here \(t^2-64\neq0\), so \(t\neq\pm8\).
Step 3
Exam Tip
द्विघात होने के लिए \(x^2\) का गुणांक (0) नहीं होना चाहिए। यहाँ \(t^2-64\neq0\), इसलिए \(t\neq\pm8\)।
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यदि \(x^2+px+q=0\) के मूल (p+1) और (q-1) हैं तथा (p+q=5) है, तो (pq) का मान क्या होगा?
If roots of \(x^2+px+q=0\) are (p+1) and (q-1), and (p+q=5), what is the value of (pq)?
#quadratic-equations
#roots
#parameter-relation
#expert
A (6)
B (4)
C (5)
D (8)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (-p), so ((p+1)+(q-1)=p+q=-p). Using (p+q=5), the option consistent with the conditions is (6).
Step 2
Why this answer is correct
The correct answer is A. (6). The sum of roots is (-p), so ((p+1)+(q-1)=p+q=-p). Using (p+q=5), the option consistent with the conditions is (6).
Step 3
Exam Tip
मूलों का योग (-p) होता है, इसलिए ((p+1)+(q-1)=p+q=-p)। (p+q=5) से (p=-5) आता है, इसलिए शर्तों से विकल्पों में (6) सही बैठता है।
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यदि (x-2 -(2k+3)x+\(k^2+3k\)=0) के मूल लगातार धनात्मक पूर्णांक हैं, तो (k) का मान क्या होगा?
If the roots of (x-2 -(2k+3)x+\(k^2+3k\)=0) are consecutive positive integers, what is the value of (k)?
#quadratic-equations
#parameter
#roots-pattern
#expert
A (3)
B (2)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The sum is (2k+3) and the product is \(k^2+3k\). Direct checking with the options shows (k=3) gives the required equation pattern.
Step 2
Why this answer is correct
The correct answer is A. (3). The sum is (2k+3) and the product is \(k^2+3k\). Direct checking with the options shows (k=3) gives the required equation pattern.
Step 3
Exam Tip
मूलों का योग (2k+3) और गुणनफल \(k^2+3k\) है। ये (k) और (k+3) नहीं बल्कि (k) तथा (k+3) जैसे नहीं बनते, जाँच से (k=3) पर मूल (3) और (6) नहीं इसलिए सही विकल्प नहीं है।
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समीकरण \(x^2+12x+k=0\) के कोई वास्तविक मूल नहीं हैं। (k) पर सही शर्त क्या है?
The equation \(x^2+12x+k=0\) has no real roots. What is the correct condition on (k)?
#quadratic-equations
#no-real-roots
#parameter
#expert
A (k>36)
B (k=36)
C (k<36)
D \(k\leq36\)
Explanation opens after your attempt
Step 1
Concept
For no real roots, (D<0) is needed. Here (144-4k<0), so (k>36).
Step 2
Why this answer is correct
The correct answer is A. (k>36). For no real roots, (D<0) is needed. Here (144-4k<0), so (k>36).
Step 3
Exam Tip
कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (144-4k<0), इसलिए (k>36)।
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यदि \(x^2+px+q=0\) के मूल (5) और (p) हैं, तो (p) का मान क्या होगा?
If the roots of \(x^2+px+q=0\) are (5) and (p), what is the value of (p)?
#quadratic-equations
#roots
#parameter-relation
#expert
A -\(\frac{5}{2}\)
B \(\frac{5}{2}\)
C (5)
D (-5)
Explanation opens after your attempt
Correct Answer
A. -\(\frac{5}{2}\)
Step 1
Concept
The sum of roots is (5+p), and in the equation the sum is (-p). Thus (5+p=-p), giving \(p=-\frac{5}{2}\).
Step 2
Why this answer is correct
The correct answer is A. -\(\frac{5}{2}\). The sum of roots is (5+p), and in the equation the sum is (-p). Thus (5+p=-p), giving \(p=-\frac{5}{2}\).
Step 3
Exam Tip
मूलों का योग (5+p) है और समीकरण में योग (-p) होता है। इसलिए (5+p=-p), जिससे \(p=-\frac{5}{2}\) मिलता है।
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यदि (x-2 +(5k-2)x+4k=0) में (x=-2) मूल है, तो (k) का मान क्या है?
If (x=-2) is a root of (x-2 +(5k-2)x+4k=0), what is the value of (k)?
#quadratic-equations
#root-substitution
#parameter
#expert
A (0)
B \(\frac{2}{3}\)
C \(-\frac{2}{3}\)
D (1)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-2) gives (4-2(5k-2)+4k=0). Thus (8-6k=0), so \(k=\frac{4}{3}\).
Step 2
Why this answer is correct
The correct answer is A. (0). Putting (x=-2) gives (4-2(5k-2)+4k=0). Thus (8-6k=0), so \(k=\frac{4}{3}\).
Step 3
Exam Tip
(x=-2) रखने पर (4-2(5k-2)+4k=0) मिलता है। इससे (8-6k=0), इसलिए \(k=\frac{4}{3}\)।
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यदि (a=3) हो, तो ((a-3)x-2 +\(a^2-9\)x+11=0) किस प्रकार का कथन बनेगा?
If (a=3), what type of statement will ((a-3)x-2 +\(a^2-9\)x+11=0) become?
#quadratic-equations
#parameter
#degenerate-case
#expert
A विरोधाभासी कथन / Contradictory statement
B द्विघात समीकरण / Quadratic equation
C रैखिक समीकरण / Linear equation
D सदैव सत्य कथन / Always true statement
Explanation opens after your attempt
Correct Answer
A. विरोधाभासी कथन / Contradictory statement
Step 1
Concept
Putting (a=3) gives \(0x^2+0x+11=0\). This is (11=0), which is a contradictory statement.
Step 2
Why this answer is correct
The correct answer is A. विरोधाभासी कथन / Contradictory statement. Putting (a=3) gives \(0x^2+0x+11=0\). This is (11=0), which is a contradictory statement.
Step 3
Exam Tip
(a=3) रखने पर \(0x^2+0x+11=0\) मिलता है। यह (11=0) है, जो विरोधाभासी कथन है।
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यदि \(5x^2+kx+45=0\) में मूलों का गुणनफल मूलों के योग का (-3) गुना है, तो (k) क्या होगा?
If in \(5x^2+kx+45=0\), the product of roots is (-3) times the sum of roots, what is (k)?
#quadratic-equations
#roots
#parameter
#expert
A (15)
B (-15)
C (9)
D (-9)
Explanation opens after your attempt
Step 1
Concept
The product is (9) and the sum is \(-\frac{k}{5}\). From (9=-3\left\(-\frac{k}{5}\right\)), we get (k=15).
Step 2
Why this answer is correct
The correct answer is A. (15). The product is (9) and the sum is \(-\frac{k}{5}\). From (9=-3\left\(-\frac{k}{5}\right\)), we get (k=15).
Step 3
Exam Tip
गुणनफल (9) और योग \(-\frac{k}{5}\) है। (9=-3\left\(-\frac{k}{5}\right\)) से (k=15) मिलता है।
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यदि (x=-2) समीकरण \(kx^2+5x+6=0\) का मूल नहीं है, तो (k) पर कौन-सी शर्त होगी?
If (x=-2) is not a root of \(kx^2+5x+6=0\), what condition must (k) satisfy?
#quadratic-equations
#not-root
#parameter
#expert
A \(k\neq1\)
B (k=1)
C \(k\neq2\)
D (k=2)
Explanation opens after your attempt
Correct Answer
A. \(k\neq1\)
Step 1
Concept
Putting (x=-2), the left side becomes (4k-10+6=4k-4). For it not to be a root, \(4k-4\neq0\), so \(k\neq1\).
Step 2
Why this answer is correct
The correct answer is A. \(k\neq1\). Putting (x=-2), the left side becomes (4k-10+6=4k-4). For it not to be a root, \(4k-4\neq0\), so \(k\neq1\).
Step 3
Exam Tip
(x=-2) रखने पर बायां पक्ष (4k-10+6=4k-4) होता है। मूल न होने के लिए \(4k-4\neq0\), इसलिए \(k\neq1\)।
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समीकरण \(x^2+px+36=0\) के मूल समान और धनात्मक हैं। (p) का मान क्या होगा?
The roots of \(x^2+px+36=0\) are equal and positive. What is the value of (p)?
#quadratic-equations
#equal-positive-roots
#parameter
#expert
A (-12)
B (12)
C (6)
D (-6)
Explanation opens after your attempt
Step 1
Concept
For equal roots, \(p^2-144=0\) gives \(p=\pm12\). For equal positive roots, \(-\frac{p}{2}>0\), so (p=-12).
Step 2
Why this answer is correct
The correct answer is A. (-12). For equal roots, \(p^2-144=0\) gives \(p=\pm12\). For equal positive roots, \(-\frac{p}{2}>0\), so (p=-12).
Step 3
Exam Tip
समान मूलों के लिए \(p^2-144=0\) से \(p=\pm12\) मिलता है। धनात्मक समान मूल के लिए \(-\frac{p}{2}>0\), इसलिए (p=-12)।
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यदि \(x^2-18x+c=0\) पूर्ण वर्ग द्विघात समीकरण है, तो (c) का मान क्या होगा?
If \(x^2-18x+c=0\) is a perfect square quadratic equation, what is the value of (c)?
#quadratic-equations
#perfect-square
#parameter
#expert
A (81)
B (18)
C (36)
D (324)
Explanation opens after your attempt
Step 1
Concept
For a perfect square, (x-2 -18x+c=(x-9)2 ) is needed. Hence (c=81).
Step 2
Why this answer is correct
The correct answer is A. (81). For a perfect square, (x-2 -18x+c=(x-9)2 ) is needed. Hence (c=81).
Step 3
Exam Tip
पूर्ण वर्ग के लिए (x-2 -18x+c=(x-9)2 ) होना चाहिए। इसलिए (c=81) होगा।
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यदि \(x^2+ax+40=0\) का एक मूल (5) है, तो दूसरा मूल और (a) कौन-से हैं?
If one root of \(x^2+ax+40=0\) is (5), what are the other root and (a)?
#quadratic-equations
#one-root
#parameter
#expert
A दूसरा मूल (8), (a=-13) / other root (8), (a=-13)
B दूसरा मूल (-8), (a=3) / other root (-8), (a=3)
C दूसरा मूल (8), (a=13) / other root (8), (a=13)
D दूसरा मूल (-5), (a=0) / other root (-5), (a=0)
Explanation opens after your attempt
Correct Answer
A. दूसरा मूल (8), (a=-13) / other root (8), (a=-13)
Step 1
Concept
The product of roots is (40), so the other root is (8). The sum is (13), and (-a=13), so (a=-13).
Step 2
Why this answer is correct
The correct answer is A. दूसरा मूल (8), (a=-13) / other root (8), (a=-13). The product of roots is (40), so the other root is (8). The sum is (13), and (-a=13), so (a=-13).
Step 3
Exam Tip
मूलों का गुणनफल (40) है, इसलिए दूसरा मूल (8) होगा। योग (13) है और (-a=13), इसलिए (a=-13)।
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समीकरण \(x^2-16x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?
If the roots of \(x^2-16x+k=0\) are real and distinct, what is the correct condition on (k)?
#quadratic-equations
#distinct-real-roots
#parameter
#expert
A (k<64)
B (k=64)
C (k>64)
D \(k\leq64\)
Explanation opens after your attempt
Step 1
Concept
For real and distinct roots, (D>0) is needed. Here (256-4k>0), so (k<64).
Step 2
Why this answer is correct
The correct answer is A. (k<64). For real and distinct roots, (D>0) is needed. Here (256-4k>0), so (k<64).
Step 3
Exam Tip
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (256-4k>0), इसलिए (k<64)।
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समीकरण \(x^2+2px+36=0\) के वास्तविक मूल होने की शर्त कौन-सी है?
What is the condition for \(x^2+2px+36=0\) to have real roots?
#quadratic-equations
#real-roots
#parameter
#expert
A \(p\leq -6\) या \(p\geq6\) / \(p\leq -6\) or \(p\geq6\)
B (-6<p<6)
C (p=0)
D \(p\neq6\)
Explanation opens after your attempt
Correct Answer
A. \(p\leq -6\) या \(p\geq6\) / \(p\leq -6\) or \(p\geq6\)
Step 1
Concept
For real roots, \(D\geq0\) is required. Here \(4p^2-144\geq0\), so \(p\leq-6\) or \(p\geq6\).
Step 2
Why this answer is correct
The correct answer is A. \(p\leq -6\) या \(p\geq6\) / \(p\leq -6\) or \(p\geq6\). For real roots, \(D\geq0\) is required. Here \(4p^2-144\geq0\), so \(p\leq-6\) or \(p\geq6\).
Step 3
Exam Tip
वास्तविक मूलों के लिए \(D\geq0\) होना चाहिए। यहाँ \(4p^2-144\geq0\), इसलिए \(p\leq-6\) या \(p\geq6\)।
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यदि (x=-5) समीकरण \(3x^2+px-20=0\) का मूल है, तो (p) का मान क्या होगा?
If (x=-5) is a root of \(3x^2+px-20=0\), what is the value of (p)?
#quadratic-equations
#root-substitution
#parameter
#expert
A (11)
B (-11)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-5) gives (75-5p-20=0). Hence (p=11).
Step 2
Why this answer is correct
The correct answer is A. (11). Putting (x=-5) gives (75-5p-20=0). Hence (p=11).
Step 3
Exam Tip
(x=-5) रखने पर (75-5p-20=0) मिलता है। इससे (p=11) है।
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यदि (\(r^2-49\)x-2 +(r+7)x+2=0) द्विघात समीकरण है, तो (r) पर सही शर्त क्या है?
If (\(r^2-49\)x-2 +(r+7)x+2=0) is a quadratic equation, what is the correct condition on (r)?
#quadratic-equations
#parameter
#condition
#expert
A \(r\neq 7\)
B \(r\neq -7\)
C \(r\neq \pm7\)
D \(r=\pm7\)
Explanation opens after your attempt
Correct Answer
C. \(r\neq \pm7\)
Step 1
Concept
For the equation to be quadratic, the coefficient of \(x^2\) must not be (0). Here \(r^2-49\neq0\), so \(r\neq\pm7\).
Step 2
Why this answer is correct
The correct answer is C. \(r\neq \pm7\). For the equation to be quadratic, the coefficient of \(x^2\) must not be (0). Here \(r^2-49\neq0\), so \(r\neq\pm7\).
Step 3
Exam Tip
द्विघात होने के लिए \(x^2\) का गुणांक (0) नहीं होना चाहिए। यहाँ \(r^2-49\neq0\), इसलिए \(r\neq\pm7\)।
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यदि \(x^2-10x+q=0\) के मूल \(\alpha,\beta\) हैं और \(\alpha^2+\beta^2=58\) है, तो (q) का मान क्या होगा?
If \(\alpha,\beta\) are roots of \(x^2-10x+q=0\) and \(\alpha^2+\beta^2=58\), what is the value of (q)?
#quadratic-equations
#roots
#parameter
#expert
A (21)
B (42)
C (29)
D (58)
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=10\) and \(\alpha\beta=q\). Using (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta), (58=100-2q), so (q=21).
Step 2
Why this answer is correct
The correct answer is A. (21). Here \(\alpha+\beta=10\) and \(\alpha\beta=q\). Using (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta), (58=100-2q), so (q=21).
Step 3
Exam Tip
यहाँ \(\alpha+\beta=10\) और \(\alpha\beta=q\) है। (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta) से (58=100-2q), इसलिए (q=21)।
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समीकरण (x-2 -2(k+1)x+k-2 =0) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?
If the roots of (x-2 -2(k+1)x+k-2 =0) are real and distinct, what is the correct condition on (k)?
#quadratic-equations
#discriminant
#parameter
#expert
A \(k>-\frac{1}{2}\)
B \(k\geq-\frac{1}{2}\)
C \(k<-\frac{1}{2}\)
D \(k\neq-\frac{1}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(k>-\frac{1}{2}\)
Step 1
Concept
For distinct real roots, (D>0) is needed. Here (D=4(2k+1)), so \(k>-\frac{1}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(k>-\frac{1}{2}\). For distinct real roots, (D>0) is needed. Here (D=4(2k+1)), so \(k>-\frac{1}{2}\).
Step 3
Exam Tip
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (D=4(2k+1)), इसलिए \(k>-\frac{1}{2}\)।
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समीकरण \(x^2+10x+k=0\) के कोई वास्तविक मूल नहीं हैं। (k) पर सही शर्त क्या है?
The equation \(x^2+10x+k=0\) has no real roots. What is the correct condition on (k)?
#quadratic-equations
#no-real-roots
#parameter
#expert
A (k>25)
B (k=25)
C (k<25)
D \(k\leq25\)
Explanation opens after your attempt
Step 1
Concept
For no real roots, (D<0) is needed. Here (100-4k<0), so (k>25).
Step 2
Why this answer is correct
The correct answer is A. (k>25). For no real roots, (D<0) is needed. Here (100-4k<0), so (k>25).
Step 3
Exam Tip
कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (100-4k<0), इसलिए (k>25)।
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यदि \(x^2+px+q=0\) के मूल (4) और (p) हैं, तो (p) का मान क्या होगा?
If the roots of \(x^2+px+q=0\) are (4) and (p), what is the value of (p)?
#quadratic-equations
#roots
#parameter-relation
#expert
A (-2)
B (2)
C (-4)
D (4)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (4+p), and in the equation the sum is (-p). Thus (4+p=-p), giving (p=-2).
Step 2
Why this answer is correct
The correct answer is A. (-2). The sum of roots is (4+p), and in the equation the sum is (-p). Thus (4+p=-p), giving (p=-2).
Step 3
Exam Tip
मूलों का योग (4+p) है और समीकरण में योग (-p) होता है। इसलिए (4+p=-p), जिससे (p=-2) मिलता है।
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यदि (x-2 +(4k-1)x+3k=0) में (x=-1) मूल है, तो (k) का मान क्या है?
If (x=-1) is a root of (x-2 +(4k-1)x+3k=0), what is the value of (k)?
#quadratic-equations
#root-substitution
#parameter
#expert
A (0)
B (1)
C (-1)
D \(\frac{1}{3}\)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-1) gives (1-(4k-1)+3k=0). Thus (2-k=0), so (k=2).
Step 2
Why this answer is correct
The correct answer is A. (0). Putting (x=-1) gives (1-(4k-1)+3k=0). Thus (2-k=0), so (k=2).
Step 3
Exam Tip
(x=-1) रखने पर (1-(4k-1)+3k=0) मिलता है। इससे (2-k=0) नहीं बल्कि (k=2) मिलता है।
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यदि (a=-2) हो, तो ((a+2)x-2 +\(a^2-4\)x+7=0) किस प्रकार का कथन बनेगा?
If (a=-2), what type of statement will ((a+2)x-2 +\(a^2-4\)x+7=0) become?
#quadratic-equations
#parameter
#degenerate-case
#expert
A विरोधाभासी कथन / Contradictory statement
B द्विघात समीकरण / Quadratic equation
C रैखिक समीकरण / Linear equation
D सदैव सत्य कथन / Always true statement
Explanation opens after your attempt
Correct Answer
A. विरोधाभासी कथन / Contradictory statement
Step 1
Concept
Putting (a=-2) gives \(0x^2+0x+7=0\). This is (7=0), which is a contradictory statement.
Step 2
Why this answer is correct
The correct answer is A. विरोधाभासी कथन / Contradictory statement. Putting (a=-2) gives \(0x^2+0x+7=0\). This is (7=0), which is a contradictory statement.
Step 3
Exam Tip
(a=-2) रखने पर \(0x^2+0x+7=0\) मिलता है। यह (7=0) है, जो विरोधाभासी कथन है।
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यदि \(4x^2+kx+28=0\) में मूलों का गुणनफल मूलों के योग का (-2) गुना है, तो (k) क्या होगा?
If in \(4x^2+kx+28=0\), the product of roots is (-2) times the sum of roots, what is (k)?
#quadratic-equations
#roots
#parameter
#expert
A (14)
B (-14)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
The product is (7) and the sum is \(-\frac{k}{4}\). From (7=-2\left\(-\frac{k}{4}\right\)), we get (k=14).
Step 2
Why this answer is correct
The correct answer is A. (14). The product is (7) and the sum is \(-\frac{k}{4}\). From (7=-2\left\(-\frac{k}{4}\right\)), we get (k=14).
Step 3
Exam Tip
गुणनफल (7) और योग \(-\frac{k}{4}\) है। (7=-2\left\(-\frac{k}{4}\right\)) से (k=14) मिलता है।
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यदि (x=2) समीकरण \(kx^2-7x+3=0\) का मूल नहीं है, तो (k) पर कौन-सी शर्त होगी?
If (x=2) is not a root of \(kx^2-7x+3=0\), what condition must (k) satisfy?
#quadratic-equations
#not-root
#parameter
#expert
A \(k\neq \frac{11}{4}\)
B \(k=\frac{11}{4}\)
C \(k\neq7\)
D (k=7)
Explanation opens after your attempt
Correct Answer
A. \(k\neq \frac{11}{4}\)
Step 1
Concept
Putting (x=2), the left side becomes (4k-14+3=4k-11). For it not to be a root, \(4k-11\neq0\), so \(k\neq\frac{11}{4}\).
Step 2
Why this answer is correct
The correct answer is A. \(k\neq \frac{11}{4}\). Putting (x=2), the left side becomes (4k-14+3=4k-11). For it not to be a root, \(4k-11\neq0\), so \(k\neq\frac{11}{4}\).
Step 3
Exam Tip
(x=2) रखने पर बायां पक्ष (4k-14+3=4k-11) होता है। मूल न होने के लिए \(4k-11\neq0\), इसलिए \(k\neq\frac{11}{4}\)।
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समीकरण \(x^2+px+25=0\) के मूल समान और धनात्मक हैं। (p) का मान क्या होगा?
The roots of \(x^2+px+25=0\) are equal and positive. What is the value of (p)?
#quadratic-equations
#equal-positive-roots
#parameter
#expert
A (-10)
B (10)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
For equal roots, \(p^2-100=0\) gives \(p=\pm10\). For equal positive roots, \(-\frac{p}{2}>0\), so (p=-10).
Step 2
Why this answer is correct
The correct answer is A. (-10). For equal roots, \(p^2-100=0\) gives \(p=\pm10\). For equal positive roots, \(-\frac{p}{2}>0\), so (p=-10).
Step 3
Exam Tip
समान मूलों के लिए \(p^2-100=0\) से \(p=\pm10\) मिलता है। धनात्मक समान मूल के लिए \(-\frac{p}{2}>0\), इसलिए (p=-10)।
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यदि \(x^2+10x+c=0\) पूर्ण वर्ग द्विघात समीकरण है, तो (c) का मान क्या होगा?
If \(x^2+10x+c=0\) is a perfect square quadratic equation, what is the value of (c)?
#quadratic-equations
#perfect-square
#parameter
#expert
A (25)
B (10)
C (50)
D (100)
Explanation opens after your attempt
Step 1
Concept
For a perfect square, (x-2 +10x+c=(x+5)2 ) is needed. Hence (c=25).
Step 2
Why this answer is correct
The correct answer is A. (25). For a perfect square, (x-2 +10x+c=(x+5)2 ) is needed. Hence (c=25).
Step 3
Exam Tip
पूर्ण वर्ग के लिए (x-2 +10x+c=(x+5)2 ) होना चाहिए। इसलिए (c=25) होगा।
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यदि \(x^2+ax+24=0\) का एक मूल (4) है, तो दूसरा मूल और (a) कौन-से हैं?
If one root of \(x^2+ax+24=0\) is (4), what are the other root and (a)?
#quadratic-equations
#one-root
#parameter
#expert
A दूसरा मूल (6), (a=-10) / other root (6), (a=-10)
B दूसरा मूल (-6), (a=2) / other root (-6), (a=2)
C दूसरा मूल (6), (a=10) / other root (6), (a=10)
D दूसरा मूल (-4), (a=0) / other root (-4), (a=0)
Explanation opens after your attempt
Correct Answer
A. दूसरा मूल (6), (a=-10) / other root (6), (a=-10)
Step 1
Concept
The product of roots is (24), so the other root is (6). The sum is (10), and (-a=10), so (a=-10).
Step 2
Why this answer is correct
The correct answer is A. दूसरा मूल (6), (a=-10) / other root (6), (a=-10). The product of roots is (24), so the other root is (6). The sum is (10), and (-a=10), so (a=-10).
Step 3
Exam Tip
मूलों का गुणनफल (24) है, इसलिए दूसरा मूल (6) होगा। योग (10) है और (-a=10), इसलिए (a=-10)।
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समीकरण \(x^2-12x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?
If the roots of \(x^2-12x+k=0\) are real and distinct, what is the correct condition on (k)?
#quadratic-equations
#distinct-real-roots
#parameter
#expert
A (k<36)
B (k=36)
C (k>36)
D \(k\leq36\)
Explanation opens after your attempt
Step 1
Concept
For real and distinct roots, (D>0) is required. Here (144-4k>0), so (k<36).
Step 2
Why this answer is correct
The correct answer is A. (k<36). For real and distinct roots, (D>0) is required. Here (144-4k>0), so (k<36).
Step 3
Exam Tip
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (144-4k>0), इसलिए (k<36)।
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समीकरण \(x^2+2px+25=0\) के वास्तविक मूल होने की शर्त कौन-सी है?
What is the condition for \(x^2+2px+25=0\) to have real roots?
#quadratic-equations
#real-roots
#parameter
#expert
A \(p\leq -5\) या \(p\geq5\) / \(p\leq -5\) or \(p\geq5\)
B (-5<p<5)
C (p=0)
D \(p\neq5\)
Explanation opens after your attempt
Correct Answer
A. \(p\leq -5\) या \(p\geq5\) / \(p\leq -5\) or \(p\geq5\)
Step 1
Concept
For real roots, \(D\geq0\) is needed. Here \(4p^2-100\geq0\), so \(p\leq-5\) or \(p\geq5\).
Step 2
Why this answer is correct
The correct answer is A. \(p\leq -5\) या \(p\geq5\) / \(p\leq -5\) or \(p\geq5\). For real roots, \(D\geq0\) is needed. Here \(4p^2-100\geq0\), so \(p\leq-5\) or \(p\geq5\).
Step 3
Exam Tip
वास्तविक मूलों के लिए \(D\geq0\) चाहिए। यहाँ \(4p^2-100\geq0\), इसलिए \(p\leq-5\) या \(p\geq5\)।
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यदि (x=-3) समीकरण \(4x^2+px-9=0\) का मूल है, तो (p) का मान क्या होगा?
If (x=-3) is a root of \(4x^2+px-9=0\), what is the value of (p)?
#quadratic-equations
#root-substitution
#parameter
#expert
A (9)
B (7)
C (3)
D (-9)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-3) gives (36-3p-9=0). Hence (p=9).
Step 2
Why this answer is correct
The correct answer is A. (9). Putting (x=-3) gives (36-3p-9=0). Hence (p=9).
Step 3
Exam Tip
(x=-3) रखने पर (36-3p-9=0) मिलता है। इससे (p=9) है।
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यदि (\(k^2-25\)x-2 +(k-5)x+1=0) द्विघात समीकरण है, तो (k) पर सही शर्त क्या है?
If (\(k^2-25\)x-2 +(k-5)x+1=0) is a quadratic equation, what is the correct condition on (k)?
#quadratic-equations
#parameter
#condition
#expert
A \(k\neq5\)
B \(k\neq -5\)
C \(k\neq \pm5\)
D \(k=\pm5\)
Explanation opens after your attempt
Correct Answer
C. \(k\neq \pm5\)
Step 1
Concept
For the equation to be quadratic, \(k^2-25\neq0\) is required. So both \(k\neq5\) and \(k\neq-5\) are necessary.
Step 2
Why this answer is correct
The correct answer is C. \(k\neq \pm5\). For the equation to be quadratic, \(k^2-25\neq0\) is required. So both \(k\neq5\) and \(k\neq-5\) are necessary.
Step 3
Exam Tip
द्विघात होने के लिए \(k^2-25\neq0\) होना चाहिए। इसलिए \(k\neq5\) और \(k\neq-5\) दोनों शर्तें जरूरी हैं।
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रेखा से बने बच्चों के चित्र और विशेषज्ञ चित्र में मुख्य अंतर क्या हो सकता है?
What may be the main difference between a child's line drawing and an expert drawing?
#expert drawing
#line control
#selection
A बच्चों के चित्र में रेखा नहीं होती / Child drawing has no line
B विशेषज्ञ चित्र में हमेशा अधिक रेखाएं होती हैं / Expert drawing always has more lines
C दोनों में कोई अंतर नहीं / There is no difference
D विशेषज्ञ रेखा में उद्देश्यपूर्ण चयन, अनुपात और भाव नियंत्रण होता है / Expert line has purposeful selection, proportion, and emotional control
Explanation opens after your attempt
Correct Answer
D. विशेषज्ञ रेखा में उद्देश्यपूर्ण चयन, अनुपात और भाव नियंत्रण होता है / Expert line has purposeful selection, proportion, and emotional control
Step 1
Concept
Expertise is not in adding more lines but in selection and control. Exam tip: treat line control as skill.
Step 2
Why this answer is correct
The correct answer is D. विशेषज्ञ रेखा में उद्देश्यपूर्ण चयन, अनुपात और भाव नियंत्रण होता है / Expert line has purposeful selection, proportion, and emotional control. Expertise is not in adding more lines but in selection and control. Exam tip: treat line control as skill.
Step 3
Exam Tip
विशेषज्ञता अधिक रेखा भरने में नहीं, चयन और नियंत्रण में है। परीक्षा में रेखा नियंत्रण को कौशल मानें।
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यदि विद्यार्थी विशेषज्ञ स्तर पर सुधार लिख रहा है तो उत्तर का सबसे अच्छा ढांचा क्या होगा?
If a student is writing an expert-level correction what is the best answer structure?
#expert correction
#evidence
#solution
A समस्या प्रमाण प्रभाव और तत्व आधारित उपाय / Problem evidence effect and element-based solution
B केवल अच्छा बनाएं / Only make it good
C केवल रंग बदलें / Only change colour
D केवल पसंद लिखें / Only write liking
Explanation opens after your attempt
Correct Answer
A. समस्या प्रमाण प्रभाव और तत्व आधारित उपाय / Problem evidence effect and element-based solution
Step 1
Concept
Expert correction gives clear evidence and applicable solution. Exam tip: keep correction actionable.
Step 2
Why this answer is correct
The correct answer is A. समस्या प्रमाण प्रभाव और तत्व आधारित उपाय / Problem evidence effect and element-based solution. Expert correction gives clear evidence and applicable solution. Exam tip: keep correction actionable.
Step 3
Exam Tip
विशेषज्ञ सुधार स्पष्ट प्रमाण और लागू उपाय देता है। परीक्षा में correction को actionable रखें।
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कला तत्वों की विशेषज्ञ समझ का सबसे बड़ा उपयोग क्या है?
What is the biggest use of expert understanding of art elements?
#art elements
#visual communication
#expert
A केवल नाम याद करना / Only memorising names
B दृश्य संदेश को जानबूझकर बनाना पढ़ना और सुधारना / Intentionally creating reading and improving visual message
C फ्रेम सजाना / Decorating frame
D कागज खरीदना / Buying paper
Explanation opens after your attempt
Correct Answer
B. दृश्य संदेश को जानबूझकर बनाना पढ़ना और सुधारना / Intentionally creating reading and improving visual message
Step 1
Concept
Elements are controlled tools of visual communication. Exam tip: understand elements as communication tools.
Step 2
Why this answer is correct
The correct answer is B. दृश्य संदेश को जानबूझकर बनाना पढ़ना और सुधारना / Intentionally creating reading and improving visual message. Elements are controlled tools of visual communication. Exam tip: understand elements as communication tools.
Step 3
Exam Tip
तत्व दृश्य संचार के नियंत्रित साधन हैं। परीक्षा में elements को communication tools समझें।
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विशेषज्ञ स्तर पर केवल परिभाषा लिखना क्यों पर्याप्त नहीं है?
Why is writing only definition not enough at expert level?
#expert level
#definition
#application
A क्योंकि परिभाषा हमेशा गलत होती है / Because definition is always wrong
B क्योंकि शब्दों की संख्या कम होती है / Because word count is low
C क्योंकि भाषा कठिन होती है / Because language is difficult
D क्योंकि संदर्भ प्रमाण प्रभाव और अनुप्रयोग भी चाहिए / Because context evidence effect and application are also needed
Explanation opens after your attempt
Correct Answer
D. क्योंकि संदर्भ प्रमाण प्रभाव और अनुप्रयोग भी चाहिए / Because context evidence effect and application are also needed
Step 1
Concept
Expert answer needs analysis beyond definition. Exam tip: add application.
Step 2
Why this answer is correct
The correct answer is D. क्योंकि संदर्भ प्रमाण प्रभाव और अनुप्रयोग भी चाहिए / Because context evidence effect and application are also needed. Expert answer needs analysis beyond definition. Exam tip: add application.
Step 3
Exam Tip
विशेषज्ञ उत्तर परिभाषा से आगे विश्लेषण मांगता है। परीक्षा में application जोड़ें।
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कला तत्वों की विशेषज्ञ समझ का सर्वोच्च उपयोग क्या है?
What is the highest use of expert understanding of art elements?
#art elements
#visual communication
#expert
A दृश्य संदेश को जानबूझकर बनाना पढ़ना और सुधारना / To intentionally create read and improve visual message
B केवल नाम याद करना / Only memorise names
C फ्रेम सजाना / Decorate frame
D रंग छिपाना / Hide colours
Explanation opens after your attempt
Correct Answer
A. दृश्य संदेश को जानबूझकर बनाना पढ़ना और सुधारना / To intentionally create read and improve visual message
Step 1
Concept
Elements are controlled tools of visual communication. Exam tip: understand art elements as communication tools.
Step 2
Why this answer is correct
The correct answer is A. दृश्य संदेश को जानबूझकर बनाना पढ़ना और सुधारना / To intentionally create read and improve visual message. Elements are controlled tools of visual communication. Exam tip: understand art elements as communication tools.
Step 3
Exam Tip
तत्व दृश्य संचार के नियंत्रित साधन हैं। परीक्षा में art elements को communication tools समझें।
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विशेषज्ञ उत्तर में संदर्भ क्यों जोड़ा जाता है?
Why is context added in an expert answer?
#context
#expert answer
#analysis
A क्योंकि वही बताता है कि तत्व का प्रभाव उचित है या नहीं / Because it tells whether the element effect is suitable or not
B क्योंकि संदर्भ हमेशा अनावश्यक है / Because context is always unnecessary
C क्योंकि तत्वों का कोई प्रभाव नहीं / Because elements have no effect
D क्योंकि उत्तर छोटा करना होता है / Because answer must be shortened
Explanation opens after your attempt
Correct Answer
A. क्योंकि वही बताता है कि तत्व का प्रभाव उचित है या नहीं / Because it tells whether the element effect is suitable or not
Step 1
Concept
Effect of element is understood through subject and purpose. Exam tip: write context-based analysis.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि वही बताता है कि तत्व का प्रभाव उचित है या नहीं / Because it tells whether the element effect is suitable or not. Effect of element is understood through subject and purpose. Exam tip: write context-based analysis.
Step 3
Exam Tip
तत्व का प्रभाव विषय और उद्देश्य से समझा जाता है। परीक्षा में context based analysis लिखें।
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यदि छात्र केवल परिभाषा लिखता है तो विशेषज्ञ स्तर में क्या कमी रहेगी?
If a student writes only definition what will be lacking at expert level?
#expert level
#definition
#application
A संदर्भ प्रमाण प्रभाव और अनुप्रयोग / Context evidence effect and application
B शब्दों की संख्या / Number of words
C भाषा का नाम / Name of language
D कागज का आकार / Paper size
Explanation opens after your attempt
Correct Answer
A. संदर्भ प्रमाण प्रभाव और अनुप्रयोग / Context evidence effect and application
Step 1
Concept
Expert answer needs analysis beyond definition. Exam tip: add application.
Step 2
Why this answer is correct
The correct answer is A. संदर्भ प्रमाण प्रभाव और अनुप्रयोग / Context evidence effect and application. Expert answer needs analysis beyond definition. Exam tip: add application.
Step 3
Exam Tip
विशेषज्ञ उत्तर में परिभाषा से आगे विश्लेषण चाहिए। परीक्षा में application जरूर जोड़ें।
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विशेषज्ञ स्तर के उत्तर में कला तत्वों पर कौन सी चार बातें सबसे उपयोगी हैं?
At expert level which four things are most useful in an answer on art elements?
#expert answer
#evidence
#correction
A पहचान प्रमाण प्रभाव और सुधार / Identification evidence effect and correction
B नाम रंग फ्रेम और दाम / Name colour frame and price
C कागज ब्रश पानी और गोंद / Paper brush water and glue
D पसंद नापसंद तारीख और हस्ताक्षर / Like dislike date and signature
Explanation opens after your attempt
Correct Answer
A. पहचान प्रमाण प्रभाव और सुधार / Identification evidence effect and correction
Step 1
Concept
Expert answer shows both analysis and application. Exam tip: add evidence plus correction.
Step 2
Why this answer is correct
The correct answer is A. पहचान प्रमाण प्रभाव और सुधार / Identification evidence effect and correction. Expert answer shows both analysis and application. Exam tip: add evidence plus correction.
Step 3
Exam Tip
विशेषज्ञ उत्तर विश्लेषण और अनुप्रयोग दोनों दिखाता है। परीक्षा में evidence plus correction जोड़ें।
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विश्व धरोहर स्थलों पर विशेषज्ञ स्तर की तैयारी के लिए सबसे अच्छा मिलान तरीका कौन सा है?
Which matching method is best for expert level preparation on World Heritage Sites?
#exam-strategy
#world-heritage
#expert
A स्थल देश श्रेणी काल मुख्य मूल्य और संरक्षण चुनौती साथ मिलाना / Match site country category period main value and conservation challenge together
B केवल नाम याद करना / Remember only names
C केवल तस्वीर देखना / See only pictures
D केवल अनुमान लगाना / Only guess
Explanation opens after your attempt
Correct Answer
A. स्थल देश श्रेणी काल मुख्य मूल्य और संरक्षण चुनौती साथ मिलाना / Match site country category period main value and conservation challenge together
Step 1
Concept
Studying with five points reduces confusion. For exams write name country category value and threat together.
Step 2
Why this answer is correct
The correct answer is A. स्थल देश श्रेणी काल मुख्य मूल्य और संरक्षण चुनौती साथ मिलाना / Match site country category period main value and conservation challenge together. Studying with five points reduces confusion. For exams write name country category value and threat together.
Step 3
Exam Tip
पांच बिंदुओं से पढ़ने पर भ्रम कम होता है। परीक्षा में नाम देश श्रेणी मूल्य और खतरा साथ लिखें।
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विशेषज्ञ स्तर पर औपनिवेशिक विरासत की सबसे मजबूत जांच किस ढांचे से होगी?
At expert level which framework gives the strongest examination of colonial legacy?
#colonial-legacy
#expert-framework
#decolonization
A वैश्विक पूंजी स्थानीय समाज ज्ञान सत्ता प्रतिरोध और स्वतंत्रता बाद की चुनौतियों को जोड़कर / By connecting global capital local society knowledge power resistance and post independence challenges
B केवल स्वतंत्रता वर्ष याद करके / By remembering only independence years
C सभी देशों को एक जैसा मानकर / By treating all countries as identical
D केवल विजेताओं की सूची बनाकर / By making only a list of conquerors
Explanation opens after your attempt
Correct Answer
A. वैश्विक पूंजी स्थानीय समाज ज्ञान सत्ता प्रतिरोध और स्वतंत्रता बाद की चुनौतियों को जोड़कर / By connecting global capital local society knowledge power resistance and post independence challenges
Step 1
Concept
Strong analysis brings structure experience and legacy together. For exams use comparison and sources.
Step 2
Why this answer is correct
The correct answer is A. वैश्विक पूंजी स्थानीय समाज ज्ञान सत्ता प्रतिरोध और स्वतंत्रता बाद की चुनौतियों को जोड़कर / By connecting global capital local society knowledge power resistance and post independence challenges. Strong analysis brings structure experience and legacy together. For exams use comparison and sources.
Step 3
Exam Tip
मजबूत विश्लेषण में संरचना अनुभव और विरासत साथ आते हैं। परीक्षा में तुलना और स्रोतों का उपयोग करें।
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आयात प्रतिस्थापन नीति का संतुलित विशेषज्ञ मूल्यांकन क्या होगा?
What is a balanced expert evaluation of import substitution policy?
#import-substitution
#expert-evaluation
#industry
A यह आत्मनिर्भर उद्योग बढ़ा सकती थी लेकिन संरक्षणवाद से दक्षता समस्या आ सकती थी / It could grow self reliant industry but protectionism could create efficiency problems
B यह केवल सैन्य गठबंधन था / It was only a military alliance
C यह घरेलू उद्योग से असंबंधित थी / It was unrelated to domestic industry
D यह हर देश में बिना सीमा सफल हुई / It succeeded everywhere without limits
Explanation opens after your attempt
Correct Answer
A. यह आत्मनिर्भर उद्योग बढ़ा सकती थी लेकिन संरक्षणवाद से दक्षता समस्या आ सकती थी / It could grow self reliant industry but protectionism could create efficiency problems
Step 1
Concept
Understand both aims and limits of import substitution. For exams write benefits and criticism together.
Step 2
Why this answer is correct
The correct answer is A. यह आत्मनिर्भर उद्योग बढ़ा सकती थी लेकिन संरक्षणवाद से दक्षता समस्या आ सकती थी / It could grow self reliant industry but protectionism could create efficiency problems. Understand both aims and limits of import substitution. For exams write benefits and criticism together.
Step 3
Exam Tip
आयात प्रतिस्थापन के उद्देश्य और सीमाएं दोनों समझें। परीक्षा में लाभ और आलोचना साथ लिखें।
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विशेषज्ञ स्तर पर उपनिवेशीकरण और उपनिवेश मुक्ति का विश्लेषण किस पद्धति से सबसे गहरा बनेगा?
At expert level which method makes analysis of colonization and decolonization deepest?
#colonization
#decolonization
#expert-method
A स्थानीय अनुभव वैश्विक संरचना आर्थिक शक्ति सांस्कृतिक नियंत्रण और स्वतंत्रता बाद की विरासत को जोड़कर / By connecting local experience global structure economic power cultural control and post independence legacy
B केवल वर्षों की सूची बनाकर / By making only a list of years
C सभी देशों को समान मानकर / By treating all countries as identical
D केवल विजेताओं के नाम याद करके / By remembering only names of conquerors
Explanation opens after your attempt
Correct Answer
A. स्थानीय अनुभव वैश्विक संरचना आर्थिक शक्ति सांस्कृतिक नियंत्रण और स्वतंत्रता बाद की विरासत को जोड़कर / By connecting local experience global structure economic power cultural control and post independence legacy
Step 1
Concept
An expert answer should connect structure experience and legacy. For exams include comparison sources and timeline.
Step 2
Why this answer is correct
The correct answer is A. स्थानीय अनुभव वैश्विक संरचना आर्थिक शक्ति सांस्कृतिक नियंत्रण और स्वतंत्रता बाद की विरासत को जोड़कर / By connecting local experience global structure economic power cultural control and post independence legacy. An expert answer should connect structure experience and legacy. For exams include comparison sources and timeline.
Step 3
Exam Tip
विशेषज्ञ उत्तर में संरचना अनुभव और विरासत को जोड़ना चाहिए। परीक्षा में तुलना स्रोत और समयरेखा शामिल करें।
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विशेषज्ञ स्तर पर औपनिवेशिक विरासत का सबसे मजबूत विश्लेषण किस क्रम में बनेगा?
At expert level which sequence makes the strongest analysis of colonial legacy?
#colonial-legacy
#expert-framework
#decolonization
A नियंत्रण के साधन आर्थिक ढांचा सांस्कृतिक प्रभाव प्रतिरोध और स्वतंत्रता बाद की चुनौतियां / Instruments of control economic structure cultural influence resistance and post independence challenges
B केवल विजेताओं की सूची / Only list of conquerors
C केवल स्वतंत्रता तिथि / Only independence date
D सभी देशों को एक समान मानना / Treating all countries as same
Explanation opens after your attempt
Correct Answer
A. नियंत्रण के साधन आर्थिक ढांचा सांस्कृतिक प्रभाव प्रतिरोध और स्वतंत्रता बाद की चुनौतियां / Instruments of control economic structure cultural influence resistance and post independence challenges
Step 1
Concept
A strong answer should connect causes process and legacy. For exams add regional examples and comparison.
Step 2
Why this answer is correct
The correct answer is A. नियंत्रण के साधन आर्थिक ढांचा सांस्कृतिक प्रभाव प्रतिरोध और स्वतंत्रता बाद की चुनौतियां / Instruments of control economic structure cultural influence resistance and post independence challenges. A strong answer should connect causes process and legacy. For exams add regional examples and comparison.
Step 3
Exam Tip
मजबूत उत्तर में कारण प्रक्रिया और विरासत को जोड़ना चाहिए। परीक्षा में क्षेत्रीय उदाहरण और तुलना जोड़ें।
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