100 results found for "nnp formula" in Class 10.
द्विघात सूत्र से \(ax^2+bx+c=0\) के मूल निकालने का सही सूत्र कौनसा है?
Which is the correct formula to find roots of \(ax^2+bx+c=0\) by quadratic formula?
#quadratic
#formula
#roots
A \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
B \(x=\frac{b\pm\sqrt{b^2+4ac}}{2a}\)
C \(x=\frac{-b\pm\sqrt{b^2-4ac}}{a}\)
D \(x=\frac{-c\pm\sqrt{c^2-4ab}}{2b}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
Step 1
Concept
The quadratic formula is \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\). In exams, identifying (a), (b), and (c) correctly is most important.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\). The quadratic formula is \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\). In exams, identifying (a), (b), and (c) correctly is most important.
Step 3
Exam Tip
द्विघात सूत्र \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) है। परीक्षा में (a), (b), (c) को सही पहचानना सबसे जरूरी है।
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सी राजगोपालाचारी ने सी आर योजना किस वर्ष प्रस्तुत की थी?
In which year did C Rajagopalachari present the C R Formula?
#indian history
#freedom fighters
#cr formula
A 1935 / 1935
B 1940 / 1940
C 1944 / 1944
D 1947 / 1947
Explanation opens after your attempt
Correct Answer
C. 1944 / 1944
Step 1
Concept
The C R Formula is associated with 1944. Remember it as an attempt at Congress-League settlement before independence.
Step 2
Why this answer is correct
The correct answer is C. 1944 / 1944. The C R Formula is associated with 1944. Remember it as an attempt at Congress-League settlement before independence.
Step 3
Exam Tip
सी आर योजना 1944 से जुड़ी है। इसे स्वतंत्रता से पहले कांग्रेस और लीग समझौते के प्रयास से याद रखें।
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समान्तर श्रेणी \(23,31,39,\ldots\) के (n)वें पद का सूत्र \(a_n=8n+15\) है। (36)वां पद क्या होगा?
The (n)th-term formula of the AP \(23,31,39,\ldots\) is \(a_n=8n+15\). What is the (36)th term?
#ap direct-formula nth-term class10
A (293)
B (301)
C (303)
D (311)
Explanation opens after your attempt
Step 1
Concept
\(a_{36}=8\times36+15=303\). Put (n=36) in the formed formula to get the answer directly.
Step 2
Why this answer is correct
The correct answer is C. (303). \(a_{36}=8\times36+15=303\). Put (n=36) in the formed formula to get the answer directly.
Step 3
Exam Tip
\(a_{36}=8\times36+15=303\)। बने हुए सूत्र में (n=36) रखकर सीधे उत्तर पाएं।
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समान्तर श्रेणी \(19,26,33,\ldots\) के (n)वें पद का सूत्र \(a_n=7n+12\) है। (41)वां पद क्या होगा?
The (n)th-term formula of the AP \(19,26,33,\ldots\) is \(a_n=7n+12\). What is the (41)st term?
#ap
#direct-formula
#nth-term
#class10
A (294)
B (304)
C (309)
D (299)
Explanation opens after your attempt
Step 1
Concept
\(a_{41}=7\times41+12=299\). Put only (n=41) in the formed formula.
Step 2
Why this answer is correct
The correct answer is D. (299). \(a_{41}=7\times41+12=299\). Put only (n=41) in the formed formula.
Step 3
Exam Tip
\(a_{41}=7\times41+12=299\)। बने हुए सूत्र में केवल (n=41) रखें।
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संख्या रेखा पर किसी संख्या (a) और (b) के बीच दूरी का सही सूत्र कौन-सा है?
Which is the correct formula for the distance between two numbers (a) and (b) on the number line?
#distance-formula
#absolute-value
#number-line
A (|a-b|)
B (a+b)
C (ab)
D \(\frac{a}{b}\)
Explanation opens after your attempt
Correct Answer
A. (|a-b|)
Step 1
Concept
The distance on the number line is (|a-b|). Absolute value makes the distance positive.
Step 2
Why this answer is correct
The correct answer is A. (|a-b|). The distance on the number line is (|a-b|). Absolute value makes the distance positive.
Step 3
Exam Tip
संख्या रेखा पर दूरी (|a-b|) होती है। निरपेक्ष मान दूरी को धनात्मक बनाता है।
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\(x^2-22x+79=0\) के मूल द्विघात सूत्र से क्या होंगे?
What are the roots of \(x^2-22x+79=0\) by quadratic formula?
#quadratic
#quadratic-formula
#application
A \(x=11\pm\sqrt{42}\)
B \(x=-11\pm\sqrt{42}\)
C \(x=22\pm\sqrt{42}\)
D \(x=\frac{11\pm\sqrt{42}}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(x=11\pm\sqrt{42}\)
Step 1
Concept
Here (D=(-22)2 -4(1)(79)=168), so \(x=\frac{22\pm2\sqrt{42}}{2}=11\pm\sqrt{42}\). In exams, simplify (D) correctly.
Step 2
Why this answer is correct
The correct answer is A. \(x=11\pm\sqrt{42}\). Here (D=(-22)2 -4(1)(79)=168), so \(x=\frac{22\pm2\sqrt{42}}{2}=11\pm\sqrt{42}\). In exams, simplify (D) correctly.
Step 3
Exam Tip
यहां (D=(-22)2 -4(1)(79)=168), इसलिए \(x=\frac{22\pm2\sqrt{42}}{2}=11\pm\sqrt{42}\) है। परीक्षा में (D) को सही सरल करें।
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\(x^2-14x+13=0\) के मूल द्विघात सूत्र से क्या हैं?
What are the roots of \(x^2-14x+13=0\) by quadratic formula?
#quadratic
#quadratic-formula
#perfect-square-discriminant
A (x=1,13)
B (x=-1,-13)
C \(x=7\pm6\)
D \(x=14\pm\sqrt{13}\)
Explanation opens after your attempt
Correct Answer
A. (x=1,13)
Step 1
Concept
(D=(-14)2 -4(1)(13)=144), so \(x=\frac{14\pm12}{2}\) gives (1) and (13). In exams, if (D) is a perfect square, simplify quickly.
Step 2
Why this answer is correct
The correct answer is A. (x=1,13). (D=(-14)2 -4(1)(13)=144), so \(x=\frac{14\pm12}{2}\) gives (1) and (13). In exams, if (D) is a perfect square, simplify quickly.
Step 3
Exam Tip
(D=(-14)2 -4(1)(13)=144), इसलिए \(x=\frac{14\pm12}{2}\) से (1) और (13) मिलते हैं। परीक्षा में (D) पूर्ण वर्ग हो तो उत्तर जल्दी सरल करें।
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\(x^2-19x+56=0\) के मूल द्विघात सूत्र से क्या होंगे?
What are the roots of \(x^2-19x+56=0\) by quadratic formula?
#quadratic
#quadratic-formula
#application
A \(x=\frac{19\pm\sqrt{137}}{2}\)
B \(x=\frac{-19\pm\sqrt{137}}{2}\)
C \(x=19\pm\sqrt{137}\)
D \(x=\frac{19\pm56}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{19\pm\sqrt{137}}{2}\)
Step 1
Concept
Here (D=(-19)2 -4(1)(56)=137), so \(x=\frac{19\pm\sqrt{137}}{2}\). In exams, finding (D) correctly is important.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{19\pm\sqrt{137}}{2}\). Here (D=(-19)2 -4(1)(56)=137), so \(x=\frac{19\pm\sqrt{137}}{2}\). In exams, finding (D) correctly is important.
Step 3
Exam Tip
यहां (D=(-19)2 -4(1)(56)=137), इसलिए \(x=\frac{19\pm\sqrt{137}}{2}\) है। परीक्षा में (D) को सही निकालना जरूरी है।
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\(x^2-12x+11=0\) के मूल द्विघात सूत्र से क्या हैं?
What are the roots of \(x^2-12x+11=0\) by quadratic formula?
#quadratic
#quadratic-formula
#perfect-square-discriminant
A (x=1,11)
B (x=-1,-11)
C \(x=6\pm5\)
D \(x=12\pm\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
A. (x=1,11)
Step 1
Concept
(D=(-12)2 -4(1)(11)=100), so \(x=\frac{12\pm10}{2}\) gives (1) and (11). In exams, if (D) is a perfect square, simplify quickly.
Step 2
Why this answer is correct
The correct answer is A. (x=1,11). (D=(-12)2 -4(1)(11)=100), so \(x=\frac{12\pm10}{2}\) gives (1) and (11). In exams, if (D) is a perfect square, simplify quickly.
Step 3
Exam Tip
(D=(-12)2 -4(1)(11)=100), इसलिए \(x=\frac{12\pm10}{2}\) से (1) और (11) मिलते हैं। परीक्षा में (D) पूर्ण वर्ग हो तो उत्तर जल्दी सरल करें।
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\(x^2-16x+37=0\) के मूल द्विघात सूत्र से क्या होंगे?
What are the roots of \(x^2-16x+37=0\) by quadratic formula?
#quadratic
#quadratic-formula
#application
A \(x=8\pm3\sqrt{3}\)
B \(x=-8\pm3\sqrt{3}\)
C \(x=16\pm3\sqrt{3}\)
D \(x=8\pm\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(x=8\pm3\sqrt{3}\)
Step 1
Concept
Here (D=(-16)2 -4(1)(37)=108), so \(x=\frac{16\pm6\sqrt{3}}{2}=8\pm3\sqrt{3}\). In exams, simplify (D) correctly.
Step 2
Why this answer is correct
The correct answer is A. \(x=8\pm3\sqrt{3}\). Here (D=(-16)2 -4(1)(37)=108), so \(x=\frac{16\pm6\sqrt{3}}{2}=8\pm3\sqrt{3}\). In exams, simplify (D) correctly.
Step 3
Exam Tip
यहां (D=(-16)2 -4(1)(37)=108), इसलिए \(x=\frac{16\pm6\sqrt{3}}{2}=8\pm3\sqrt{3}\) है। परीक्षा में (D) को सही सरल करें।
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\(x^2-10x+7=0\) के मूल द्विघात सूत्र से क्या हैं?
What are the roots of \(x^2-10x+7=0\) by quadratic formula?
#quadratic
#quadratic-formula
#irrational-roots
A \(x=5\pm3\sqrt{2}\)
B \(x=-5\pm3\sqrt{2}\)
C \(x=10\pm3\sqrt{2}\)
D \(x=5\pm\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(x=5\pm3\sqrt{2}\)
Step 1
Concept
(D=(-10)2 -4(1)(7)=72), so \(x=\frac{10\pm6\sqrt{2}}{2}=5\pm3\sqrt{2}\). In exams, simplify the square root.
Step 2
Why this answer is correct
The correct answer is A. \(x=5\pm3\sqrt{2}\). (D=(-10)2 -4(1)(7)=72), so \(x=\frac{10\pm6\sqrt{2}}{2}=5\pm3\sqrt{2}\). In exams, simplify the square root.
Step 3
Exam Tip
(D=(-10)2 -4(1)(7)=72), इसलिए \(x=\frac{10\pm6\sqrt{2}}{2}=5\pm3\sqrt{2}\) है। परीक्षा में वर्गमूल को सरल करें।
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\(x^2-13x+22=0\) के मूल द्विघात सूत्र से क्या होंगे?
What are the roots of \(x^2-13x+22=0\) by quadratic formula?
#quadratic
#quadratic-formula
#application
A \(x=\frac{13\pm9}{2}\)
B \(x=\frac{-13\pm9}{2}\)
C \(x=13\pm9\)
D \(x=\frac{13\pm\sqrt{22}}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{13\pm9}{2}\)
Step 1
Concept
Here (D=(-13)2 -4(1)(22)=81), so \(x=\frac{13\pm9}{2}\). In exams, if (D) is a perfect square, the answer simplifies quickly.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{13\pm9}{2}\). Here (D=(-13)2 -4(1)(22)=81), so \(x=\frac{13\pm9}{2}\). In exams, if (D) is a perfect square, the answer simplifies quickly.
Step 3
Exam Tip
यहां (D=(-13)2 -4(1)(22)=81), इसलिए \(x=\frac{13\pm9}{2}\) है। परीक्षा में (D) पूर्ण वर्ग हो तो उत्तर जल्दी सरल होता है।
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\(x^2-8x+3=0\) के मूल द्विघात सूत्र से क्या हैं?
What are the roots of \(x^2-8x+3=0\) by quadratic formula?
#quadratic
#quadratic-formula
#irrational-roots
A \(x=4\pm\sqrt{13}\)
B \(x=-4\pm\sqrt{13}\)
C \(x=8\pm\sqrt{13}\)
D \(x=4\pm13\)
Explanation opens after your attempt
Correct Answer
A. \(x=4\pm\sqrt{13}\)
Step 1
Concept
(D=(-8)2 -4(1)(3)=52), so \(x=\frac{8\pm2\sqrt{13}}{2}=4\pm\sqrt{13}\). In exams, simplify the square root.
Step 2
Why this answer is correct
The correct answer is A. \(x=4\pm\sqrt{13}\). (D=(-8)2 -4(1)(3)=52), so \(x=\frac{8\pm2\sqrt{13}}{2}=4\pm\sqrt{13}\). In exams, simplify the square root.
Step 3
Exam Tip
(D=(-8)2 -4(1)(3)=52), इसलिए \(x=\frac{8\pm2\sqrt{13}}{2}=4\pm\sqrt{13}\) है। परीक्षा में वर्गमूल को सरल करें।
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\(x^2-10x+11=0\) के मूल द्विघात सूत्र से क्या होंगे?
What are the roots of \(x^2-10x+11=0\) by quadratic formula?
#quadratic
#quadratic-formula
#irrational-roots
A \(x=5\pm\sqrt{14}\)
B \(x=-5\pm\sqrt{14}\)
C \(x=10\pm\sqrt{14}\)
D \(x=5\pm14\)
Explanation opens after your attempt
Correct Answer
A. \(x=5\pm\sqrt{14}\)
Step 1
Concept
Here (D=(-10)2 -4(1)(11)=56), so \(x=\frac{10\pm2\sqrt{14}}{2}=5\pm\sqrt{14}\). In exams, simplify (D) correctly.
Step 2
Why this answer is correct
The correct answer is A. \(x=5\pm\sqrt{14}\). Here (D=(-10)2 -4(1)(11)=56), so \(x=\frac{10\pm2\sqrt{14}}{2}=5\pm\sqrt{14}\). In exams, simplify (D) correctly.
Step 3
Exam Tip
यहां (D=(-10)2 -4(1)(11)=56), इसलिए \(x=\frac{10\pm2\sqrt{14}}{2}=5\pm\sqrt{14}\) है। परीक्षा में (D) को सही सरल करें।
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\(x^2-6x+2=0\) के मूल द्विघात सूत्र से क्या हैं?
What are the roots of \(x^2-6x+2=0\) by quadratic formula?
#quadratic
#quadratic-formula
#irrational-roots
A \(x=3\pm\sqrt{7}\)
B \(x=-3\pm\sqrt{7}\)
C \(x=6\pm\sqrt{7}\)
D \(x=3\pm7\)
Explanation opens after your attempt
Correct Answer
A. \(x=3\pm\sqrt{7}\)
Step 1
Concept
(D=(-6)2 -4(1)(2)=28), so \(x=\frac{6\pm2\sqrt{7}}{2}=3\pm\sqrt{7}\). In exams, simplify the square root.
Step 2
Why this answer is correct
The correct answer is A. \(x=3\pm\sqrt{7}\). (D=(-6)2 -4(1)(2)=28), so \(x=\frac{6\pm2\sqrt{7}}{2}=3\pm\sqrt{7}\). In exams, simplify the square root.
Step 3
Exam Tip
(D=(-6)2 -4(1)(2)=28), इसलिए \(x=\frac{6\pm2\sqrt{7}}{2}=3\pm\sqrt{7}\) है। परीक्षा में वर्गमूल को सरल करें।
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\(x^2-7x+4=0\) के मूल द्विघात सूत्र से क्या होंगे?
What are the roots of \(x^2-7x+4=0\) by quadratic formula?
#quadratic
#quadratic-formula
#irrational-roots
A \(x=\frac{7\pm\sqrt{33}}{2}\)
B \(x=\frac{-7\pm\sqrt{33}}{2}\)
C \(x=7\pm\sqrt{33}\)
D \(x=\frac{7\pm\sqrt{45}}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{7\pm\sqrt{33}}{2}\)
Step 1
Concept
Here (D=(-7)2 -4(1)(4)=33), so \(x=\frac{7\pm\sqrt{33}}{2}\). In exams, finding (D) correctly is important.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{7\pm\sqrt{33}}{2}\). Here (D=(-7)2 -4(1)(4)=33), so \(x=\frac{7\pm\sqrt{33}}{2}\). In exams, finding (D) correctly is important.
Step 3
Exam Tip
यहां (D=(-7)2 -4(1)(4)=33), इसलिए \(x=\frac{7\pm\sqrt{33}}{2}\) है। परीक्षा में (D) को सही निकालना जरूरी है।
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\(x^2-4x+1=0\) के मूल द्विघात सूत्र से क्या हैं?
What are the roots of \(x^2-4x+1=0\) by quadratic formula?
#quadratic
#quadratic-formula
#irrational-roots
A \(x=2\pm\sqrt{3}\)
B \(x=-2\pm\sqrt{3}\)
C \(x=4\pm\sqrt{3}\)
D \(x=2\pm3\)
Explanation opens after your attempt
Correct Answer
A. \(x=2\pm\sqrt{3}\)
Step 1
Concept
(D=(-4)2 -4(1)(1)=12), so \(x=\frac{4\pm2\sqrt{3}}{2}=2\pm\sqrt{3}\). In exams, simplify the square root.
Step 2
Why this answer is correct
The correct answer is A. \(x=2\pm\sqrt{3}\). (D=(-4)2 -4(1)(1)=12), so \(x=\frac{4\pm2\sqrt{3}}{2}=2\pm\sqrt{3}\). In exams, simplify the square root.
Step 3
Exam Tip
(D=(-4)2 -4(1)(1)=12), इसलिए \(x=\frac{4\pm2\sqrt{3}}{2}=2\pm\sqrt{3}\) है। परीक्षा में वर्गमूल को सरल करें।
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\(x^2+3x-3=0\) के मूल द्विघात सूत्र से क्या हैं?
What are the roots of \(x^2+3x-3=0\) by the quadratic formula?
#quadratic
#quadratic-formula
#irrational-roots
A \(x=\frac{-3\pm\sqrt{21}}{2}\)
B \(x=\frac{3\pm\sqrt{21}}{2}\)
C \(x=-3\pm\sqrt{21}\)
D \(x=\frac{-3\pm\sqrt{9}}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{-3\pm\sqrt{21}}{2}\)
Step 1
Concept
Here (D=32 -4(1)(-3)=21), so \(x=\frac{-3\pm\sqrt{21}}{2}\). In exams, keep the sign of (c=-3) correct.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{-3\pm\sqrt{21}}{2}\). Here (D=32 -4(1)(-3)=21), so \(x=\frac{-3\pm\sqrt{21}}{2}\). In exams, keep the sign of (c=-3) correct.
Step 3
Exam Tip
यहां (D=32 -4(1)(-3)=21), इसलिए \(x=\frac{-3\pm\sqrt{21}}{2}\) है। परीक्षा में (c=-3) का संकेत सही रखें।
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द्विघात सूत्र में (a=1,b=-14,c=45) रखने पर मूल क्या होंगे?
What roots are obtained by putting (a=1,b=-14,c=45) in the quadratic formula?
#quadratic
#quadratic-formula
#substitution
A (x=5,9)
B (x=-5,-9)
C (x=3,15)
D (x=7,8)
Explanation opens after your attempt
Correct Answer
A. (x=5,9)
Step 1
Concept
(D=(-14)2 -4(1)(45)=16), so \(x=\frac{14\pm4}{2}\) gives (5) and (9). In exams, keep the sign of (b) correct in the formula.
Step 2
Why this answer is correct
The correct answer is A. (x=5,9). (D=(-14)2 -4(1)(45)=16), so \(x=\frac{14\pm4}{2}\) gives (5) and (9). In exams, keep the sign of (b) correct in the formula.
Step 3
Exam Tip
(D=(-14)2 -4(1)(45)=16), इसलिए \(x=\frac{14\pm4}{2}\) से (5) और (9) मिलते हैं। परीक्षा में सूत्र में (b) का चिन्ह सही रखें।
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द्विघात सूत्र से \(x^2-10x+24=0\) के मूल क्या मिलेंगे?
Using the quadratic formula, what roots are obtained for \(x^2-10x+24=0\)?
#quadratic
#quadratic-formula
#roots
A (x=4,6)
B (x=-4,-6)
C (x=2,12)
D (x=5,24)
Explanation opens after your attempt
Correct Answer
A. (x=4,6)
Step 1
Concept
Here (D=(-10)2 -4(1)(24)=4), so \(x=\frac{10\pm2}{2}\). In exams, keep the sign of (-b) correct.
Step 2
Why this answer is correct
The correct answer is A. (x=4,6). Here (D=(-10)2 -4(1)(24)=4), so \(x=\frac{10\pm2}{2}\). In exams, keep the sign of (-b) correct.
Step 3
Exam Tip
यहां (D=(-10)2 -4(1)(24)=4), इसलिए \(x=\frac{10\pm2}{2}\) मिलता है। परीक्षा में (-b) का चिन्ह सही रखें।
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\(x^2+2x-2=0\) के मूल द्विघात सूत्र से क्या हैं?
What are the roots of \(x^2+2x-2=0\) by the quadratic formula?
#quadratic
#quadratic-formula
#irrational-roots
A \(x=-1\pm\sqrt{3}\)
B \(x=1\pm\sqrt{3}\)
C \(x=-2\pm\sqrt{3}\)
D \(x=\frac{-1\pm\sqrt{3}}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(x=-1\pm\sqrt{3}\)
Step 1
Concept
Here (D=22 -4(1)(-2)=12), so \(x=\frac{-2\pm\sqrt{12}}{2}=-1\pm\sqrt{3}\). In exams, simplify \(\sqrt{12}=2\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(x=-1\pm\sqrt{3}\). Here (D=22 -4(1)(-2)=12), so \(x=\frac{-2\pm\sqrt{12}}{2}=-1\pm\sqrt{3}\). In exams, simplify \(\sqrt{12}=2\sqrt{3}\).
Step 3
Exam Tip
यहां (D=22 -4(1)(-2)=12), इसलिए \(x=\frac{-2\pm\sqrt{12}}{2}=-1\pm\sqrt{3}\) है। परीक्षा में \(\sqrt{12}=2\sqrt{3}\) सरल करें।
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द्विघात सूत्र में (a=1,b=-10,c=21) रखने पर मूल क्या होंगे?
What roots are obtained by putting (a=1,b=-10,c=21) in the quadratic formula?
#quadratic
#quadratic-formula
#substitution
A (x=3,7)
B (x=-3,-7)
C (x=1,21)
D (x=5,6)
Explanation opens after your attempt
Correct Answer
A. (x=3,7)
Step 1
Concept
(D=(-10)2 -4(1)(21)=16), so \(x=\frac{10\pm4}{2}\) gives (3) and (7). In exams, keep the sign of (b) correct in the formula.
Step 2
Why this answer is correct
The correct answer is A. (x=3,7). (D=(-10)2 -4(1)(21)=16), so \(x=\frac{10\pm4}{2}\) gives (3) and (7). In exams, keep the sign of (b) correct in the formula.
Step 3
Exam Tip
(D=(-10)2 -4(1)(21)=16), इसलिए \(x=\frac{10\pm4}{2}\) से (3) और (7) मिलते हैं। परीक्षा में सूत्र में (b) का चिन्ह सही रखें।
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द्विघात सूत्र से \(x^2-8x+12=0\) के मूल क्या मिलेंगे?
Using the quadratic formula, what roots are obtained for \(x^2-8x+12=0\)?
#quadratic
#quadratic-formula
#roots
A (x=2,6)
B (x=-2,-6)
C (x=4,12)
D (x=3,5)
Explanation opens after your attempt
Correct Answer
A. (x=2,6)
Step 1
Concept
Here (D=(-8)2 -4(1)(12)=16), so \(x=\frac{8\pm4}{2}\). In exams, keep the sign of (-b) correct.
Step 2
Why this answer is correct
The correct answer is A. (x=2,6). Here (D=(-8)2 -4(1)(12)=16), so \(x=\frac{8\pm4}{2}\). In exams, keep the sign of (-b) correct.
Step 3
Exam Tip
यहां (D=(-8)2 -4(1)(12)=16), इसलिए \(x=\frac{8\pm4}{2}\) मिलता है। परीक्षा में (-b) का चिन्ह सही रखें।
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\(x^2+x-1=0\) के मूल द्विघात सूत्र से क्या हैं?
What are the roots of \(x^2+x-1=0\) by the quadratic formula?
#quadratic
#quadratic-formula
#irrational-roots
A \(x=\frac{-1\pm\sqrt{5}}{2}\)
B \(x=\frac{1\pm\sqrt{5}}{2}\)
C \(x=-1\pm\sqrt{5}\)
D \(x=\frac{-1\pm\sqrt{3}}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{-1\pm\sqrt{5}}{2}\)
Step 1
Concept
Here (D=1-4(1)(-1)=5), so \(x=\frac{-1\pm\sqrt{5}}{2}\). In exams, keep the sign of (c=-1) correct.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{-1\pm\sqrt{5}}{2}\). Here (D=1-4(1)(-1)=5), so \(x=\frac{-1\pm\sqrt{5}}{2}\). In exams, keep the sign of (c=-1) correct.
Step 3
Exam Tip
यहां (D=1-4(1)(-1)=5), इसलिए \(x=\frac{-1\pm\sqrt{5}}{2}\) है। परीक्षा में (c=-1) का संकेत सही रखें।
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किस समीकरण में गुणनखंड विधि की जगह द्विघात सूत्र अधिक सुविधाजनक है?
For which equation is the quadratic formula more convenient than factorisation?
#quadratic
#method-selection
#quadratic-formula
A \(x^2+x-1=0\)
B \(x^2+5x+6=0\)
C \(x^2-9=0\)
D \(x^2-4x+4=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+x-1=0\)
Step 1
Concept
\(x^2+x-1=0\) has no simple integer factors, so the formula method is easier. In exams, the quadratic formula is safe in such cases.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+x-1=0\). \(x^2+x-1=0\) has no simple integer factors, so the formula method is easier. In exams, the quadratic formula is safe in such cases.
Step 3
Exam Tip
\(x^2+x-1=0\) के सरल पूर्णांक गुणनखंड नहीं मिलते, इसलिए सूत्र विधि आसान है। परीक्षा में ऐसे मामलों में द्विघात सूत्र सुरक्षित रहता है।
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द्विघात सूत्र में (a=1,b=-6,c=8) रखने पर मूल क्या होंगे?
What roots are obtained by putting (a=1,b=-6,c=8) in the quadratic formula?
#quadratic
#quadratic-formula
#substitution
A (x=2,4)
B (x=-2,-4)
C (x=1,8)
D (x=6,8)
Explanation opens after your attempt
Correct Answer
A. (x=2,4)
Step 1
Concept
(D=(-6)2 -4(1)(8)=4), so \(x=\frac{6\pm2}{2}\) gives (2) and (4). In exams, keep the sign of (-b) correct.
Step 2
Why this answer is correct
The correct answer is A. (x=2,4). (D=(-6)2 -4(1)(8)=4), so \(x=\frac{6\pm2}{2}\) gives (2) and (4). In exams, keep the sign of (-b) correct.
Step 3
Exam Tip
(D=(-6)2 -4(1)(8)=4), इसलिए \(x=\frac{6\pm2}{2}\) से (2) और (4) मिलते हैं। परीक्षा में (-b) का चिन्ह सही रखें।
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द्विघात सूत्र से \(x^2-4x-5=0\) के मूल क्या मिलेंगे?
Using the quadratic formula, what roots are obtained for \(x^2-4x-5=0\)?
#quadratic
#quadratic-formula
#roots
A (x=5,-1)
B (x=-5,1)
C (x=4,-5)
D (x=2,-3)
Explanation opens after your attempt
Correct Answer
A. (x=5,-1)
Step 1
Concept
Here (D=(-4)2 -4(1)(-5)=36), so \(x=\frac{4\pm6}{2}\). In exams, do not forget the negative sign of (c) while using the formula.
Step 2
Why this answer is correct
The correct answer is A. (x=5,-1). Here (D=(-4)2 -4(1)(-5)=36), so \(x=\frac{4\pm6}{2}\). In exams, do not forget the negative sign of (c) while using the formula.
Step 3
Exam Tip
यहां (D=(-4)2 -4(1)(-5)=36), इसलिए \(x=\frac{4\pm6}{2}\) मिलता है। परीक्षा में सूत्र लगाते समय (c) का ऋण चिन्ह न भूलें।
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द्विघात सूत्र में वर्गमूल के अंदर का सही भाग कौनसा होता है?
What is the correct part inside the square root in the quadratic formula?
#quadratic
#formula
#discriminant
A \(b^2-4ac\)
B \(b^2+4ac\)
C \(a^2-4bc\)
D \(c^2-4ab\)
Explanation opens after your attempt
Correct Answer
A. \(b^2-4ac\)
Step 1
Concept
In the quadratic formula, the part inside the square root is \(b^2-4ac\). In exams, it is also called the discriminant (D).
Step 2
Why this answer is correct
The correct answer is A. \(b^2-4ac\). In the quadratic formula, the part inside the square root is \(b^2-4ac\). In exams, it is also called the discriminant (D).
Step 3
Exam Tip
द्विघात सूत्र में वर्गमूल के अंदर \(b^2-4ac\) होता है। परीक्षा में इसे विविक्तकर (D) भी कहते हैं।
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द्विघात सूत्र लगाने के लिए \(5x^2+2x-7=0\) में (a), (b), (c) क्या हैं?
For applying the quadratic formula to \(5x^2+2x-7=0\), what are (a), (b), and (c)?
#quadratic
#coefficients
#formula
A (a=5,b=2,c=-7)
B (a=2,b=5,c=-7)
C (a=5,b=-2,c=7)
D (a=-7,b=2,c=5)
Explanation opens after your attempt
Correct Answer
A. (a=5,b=2,c=-7)
Step 1
Concept
From standard form \(ax^2+bx+c=0\), (a=5), (b=2), and (c=-7). In exams, always check the sign of (c).
Step 2
Why this answer is correct
The correct answer is A. (a=5,b=2,c=-7). From standard form \(ax^2+bx+c=0\), (a=5), (b=2), and (c=-7). In exams, always check the sign of (c).
Step 3
Exam Tip
मानक रूप \(ax^2+bx+c=0\) से (a=5), (b=2), (c=-7) हैं। परीक्षा में (c) का संकेत जरूर देखें।
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द्विघात सूत्र में हर का सही रूप कौनसा होता है?
What is the correct denominator in the quadratic formula?
#quadratic
#formula
#denominator
A (2a)
B (a)
C (2b)
D (4a)
Explanation opens after your attempt
Step 1
Concept
In \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\), the denominator is (2a). In exams, forgetting (2a) is a common mistake.
Step 2
Why this answer is correct
The correct answer is A. (2a). In \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\), the denominator is (2a). In exams, forgetting (2a) is a common mistake.
Step 3
Exam Tip
द्विघात सूत्र \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) में हर (2a) होता है। परीक्षा में (2a) भूलना सामान्य गलती है।
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द्विघात सूत्र लगाने के लिए \(4x^2-3x-1=0\) में (a), (b), (c) क्या हैं?
For applying the quadratic formula to \(4x^2-3x-1=0\), what are (a), (b), and (c)?
#quadratic
#coefficients
#formula
A (a=4,b=-3,c=-1)
B (a=4,b=3,c=-1)
C (a=-3,b=4,c=-1)
D (a=4,b=-1,c=-3)
Explanation opens after your attempt
Correct Answer
A. (a=4,b=-3,c=-1)
Step 1
Concept
From standard form \(ax^2+bx+c=0\), (a=4), (b=-3), and (c=-1). In exams, write the signs of (b) and (c) carefully.
Step 2
Why this answer is correct
The correct answer is A. (a=4,b=-3,c=-1). From standard form \(ax^2+bx+c=0\), (a=4), (b=-3), and (c=-1). In exams, write the signs of (b) and (c) carefully.
Step 3
Exam Tip
मानक रूप \(ax^2+bx+c=0\) से (a=4), (b=-3), (c=-1) हैं। परीक्षा में (b) और (c) के चिन्ह जरूर लिखें।
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द्विघात सूत्र में \(b^2-4ac\) को क्या कहते हैं?
What is \(b^2-4ac\) called in the quadratic formula?
#quadratic
#discriminant
#formula
A विविक्तकर / Discriminant
B गुणनखंड / Factor
C घातांक / Exponent
D चर / Variable
Explanation opens after your attempt
Correct Answer
A. विविक्तकर / Discriminant
Step 1
Concept
\(b^2-4ac\) is called the discriminant and it tells the nature of roots. In exams, it is also written as (D).
Step 2
Why this answer is correct
The correct answer is A. विविक्तकर / Discriminant. \(b^2-4ac\) is called the discriminant and it tells the nature of roots. In exams, it is also written as (D).
Step 3
Exam Tip
\(b^2-4ac\) को विविक्तकर कहते हैं और यह मूलों की प्रकृति बताता है। परीक्षा में इसे (D) से भी लिखा जाता है।
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द्विघात सूत्र लगाने से पहले \(3x^2+5x-2=0\) में (a), (b), (c) क्या हैं?
Before applying the quadratic formula to \(3x^2+5x-2=0\), what are (a), (b), and (c)?
#quadratic
#formula
#coefficients
A (a=3,b=5,c=-2)
B (a=5,b=3,c=-2)
C (a=3,b=-5,c=2)
D (a=-2,b=5,c=3)
Explanation opens after your attempt
Correct Answer
A. (a=3,b=5,c=-2)
Step 1
Concept
From standard form \(ax^2+bx+c=0\), (a=3), (b=5), and (c=-2). In exams, always check the sign of (c).
Step 2
Why this answer is correct
The correct answer is A. (a=3,b=5,c=-2). From standard form \(ax^2+bx+c=0\), (a=3), (b=5), and (c=-2). In exams, always check the sign of (c).
Step 3
Exam Tip
मानक रूप \(ax^2+bx+c=0\) से (a=3), (b=5), (c=-2) हैं। परीक्षा में (c) का संकेत जरूर देखें।
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इस उपविषय के लिए सबसे अच्छा विश्लेषण सूत्र कौन सा है?
What is the best analytical formula for this subtopic?
#exam-strategy
#analysis-formula
#differing-strands
A क्षेत्र समूह मुद्दा नेतृत्व और स्वराज अर्थ को साथ पढ़ना / Studying region group issue leadership and meaning of swaraj together
B केवल एक तारीख और एक नाम याद करना / Remembering only one date and one name
C सभी समूहों को एक ही मांग से जोड़ना / Linking all groups with one demand
D स्थानीय अनुभवों को छोड़ देना / Leaving out local experiences
Explanation opens after your attempt
Correct Answer
A. क्षेत्र समूह मुद्दा नेतृत्व और स्वराज अर्थ को साथ पढ़ना / Studying region group issue leadership and meaning of swaraj together
Step 1
Concept
This subtopic includes regions like Awadh Gudem and Assam.
Step 2
Why this answer is correct
Each region has a different group and issue.
Step 3
Exam Tip
For hard questions make a chain of region group issue leadership and meaning. चरण 1: इस उपविषय में अवध गुडेम और असम जैसे क्षेत्र हैं। चरण 2: हर क्षेत्र में समूह और मुद्दा अलग है। चरण 3: कठिन प्रश्नों के लिए क्षेत्र समूह मुद्दा नेतृत्व और अर्थ की कड़ी बनाएं।
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प्लास्टर ऑफ पेरिस का सूत्र कौन सा है?
Which is the formula of plaster of Paris?
#plaster-of-paris
#formula
#calcium-sulphate
#expert
A CaSO4 ·1 / 2H2O
B CaSO4 ·2H2O
C Na2 CO3 ·10H2O
D NaHCO3
Explanation opens after your attempt
Correct Answer
A. CaSO4 ·1 / 2H2O
Step 1
Concept
Plaster of Paris is the hemihydrate form of calcium sulphate.
Step 2
Why this answer is correct
It has half a water molecule per formula unit.
Step 3
Exam Tip
Therefore its formula is CaSO4 ·1/2H2O. चरण 1: प्लास्टर ऑफ पेरिस कैल्सियम सल्फेट का अर्ध जलयुक्त रूप है। चरण 2: इसमें आधा जल अणु प्रति सूत्र इकाई माना जाता है। चरण 3: इसलिए इसका सूत्र कैल्सियम सल्फेट अर्ध जल है।
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धोने के सोडे का सूत्र क्या है?
What is the formula of washing soda?
#washing-soda
#formula
#hydrated-salt
#expert
A Na2 CO3 ·10H2O
B NaHCO3
C CaSO4 ·1 / 2H2O
D CaSO4 ·2H2O
Explanation opens after your attempt
Correct Answer
A. Na2 CO3 ·10H2O
Step 1
Concept
Washing soda is hydrated sodium carbonate.
Step 2
Why this answer is correct
It contains ten water molecules of crystallisation.
Step 3
Exam Tip
Therefore its formula is Na2 CO3 ·10H2O. चरण 1: धोने का सोडा सोडियम कार्बोनेट का जलयुक्त रूप है। चरण 2: इसमें क्रिस्टलीकरण जल के दस अणु होते हैं। चरण 3: इसलिए इसका सूत्र सोडियम कार्बोनेट दश जल है।
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समीकरण \(ax^2+bx+c=0\) में विविक्तकर का सही सूत्र कौन सा है?
What is the correct formula of the discriminant in \(ax^2+bx+c=0\)?
#quadratic equations
#nature of roots
#discriminant
A \(D=b^2-4ac\)
B \(D=a^2-4bc\)
C \(D=c^2-4ab\)
D (D=b-4ac)
Explanation opens after your attempt
Correct Answer
A. \(D=b^2-4ac\)
Step 1
Concept
The discriminant is always \(D=b^2-4ac\). In exams identify (a), (b), and (c) before using the formula.
Step 2
Why this answer is correct
The correct answer is A. \(D=b^2-4ac\). The discriminant is always \(D=b^2-4ac\). In exams identify (a), (b), and (c) before using the formula.
Step 3
Exam Tip
विविक्तकर हमेशा \(D=b^2-4ac\) होता है। परीक्षा में सूत्र लिखने से पहले (a), (b), (c) पहचानें।
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द्विघात सूत्र से \(5x^2-10x-3=0\) के लिए (D) का मान क्या है?
Using the quadratic formula setup, what is the value of (D) for \(5x^2-10x-3=0\)?
#quadratic
#discriminant
#calculation
A (160)
B (100)
C (60)
D (40)
Explanation opens after your attempt
Step 1
Concept
Here (D=(-10)2 -4(5)(-3)=160). In exams, a negative (c) makes the second term add.
Step 2
Why this answer is correct
The correct answer is A. (160). Here (D=(-10)2 -4(5)(-3)=160). In exams, a negative (c) makes the second term add.
Step 3
Exam Tip
यहां (D=(-10)2 -4(5)(-3)=160) है। परीक्षा में ऋणात्मक (c) के कारण दूसरा पद जुड़ता है।
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द्विघात सूत्र से \(3x^2-6x-2=0\) के लिए (D) का मान क्या है?
Using the quadratic formula setup, what is the value of (D) for \(3x^2-6x-2=0\)?
#quadratic
#discriminant
#calculation
A (60)
B (36)
C (12)
D (24)
Explanation opens after your attempt
Step 1
Concept
Here (D=(-6)2 -4(3)(-2)=60). In exams, a negative (c) makes the second term add.
Step 2
Why this answer is correct
The correct answer is A. (60). Here (D=(-6)2 -4(3)(-2)=60). In exams, a negative (c) makes the second term add.
Step 3
Exam Tip
यहां (D=(-6)2 -4(3)(-2)=60) है। परीक्षा में ऋणात्मक (c) के कारण दूसरा पद जुड़ता है।
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द्विघात सूत्र से \(2x^2-4x-3=0\) के लिए (D) का मान क्या है?
Using the quadratic formula setup, what is the value of (D) for \(2x^2-4x-3=0\)?
#quadratic
#discriminant
#calculation
A (40)
B (16)
C (24)
D (8)
Explanation opens after your attempt
Step 1
Concept
Here (D=(-4)2 -4(2)(-3)=40). In exams, a negative (c) makes the term add.
Step 2
Why this answer is correct
The correct answer is A. (40). Here (D=(-4)2 -4(2)(-3)=40). In exams, a negative (c) makes the term add.
Step 3
Exam Tip
यहां (D=(-4)2 -4(2)(-3)=40) है। परीक्षा में ऋणात्मक (c) के कारण जोड़ बनता है।
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सूत्र या गुणनखंडन से \(x^2-3x+2=0\) के मूल कौन से हैं?
Using formula or factorisation what are the roots of \(x^2-3x+2=0\)?
#roots
#factorisation
#formula_check
A (1) और (2) / (1) and (2)
B (-1) और (-2) / (-1) and (-2)
C (0) और (3) / (0) and (3)
D (2) और (3) / (2) and (3)
Explanation opens after your attempt
Correct Answer
A. (1) और (2) / (1) and (2)
Step 1
Concept
(x-2 -3x+2=(x-1)(x-2)) so the roots are (1) and (2). For small numbers factorisation is faster.
Step 2
Why this answer is correct
The correct answer is A. (1) और (2) / (1) and (2). (x-2 -3x+2=(x-1)(x-2)) so the roots are (1) and (2). For small numbers factorisation is faster.
Step 3
Exam Tip
(x-2 -3x+2=(x-1)(x-2)) इसलिए मूल (1) और (2) हैं। छोटे अंकों में गुणनखंडन तेज रहता है।
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\(\sqrt{2}\), \(\sqrt{3}\), और \(\sqrt{5}\) की अपरिमेयता के लिए सबसे अच्छा परीक्षा-सूत्र कौन-सा है?
What is the best exam formula for proving irrationality of \(\sqrt{2}\), \(\sqrt{3}\), and \(\sqrt{5}\)?
#real-numbers
#irrationality
#exam-tip
#proof-structure
A दशमलव लिखो और उत्तर दे दो / Write the decimal and answer
B सरलतम परिमेय रूप लो, वर्ग करो, अभाज्य विभाज्यता लगाओ, सहअभाज्यता से विरोधाभास लिखो / Take lowest rational form, square, apply prime divisibility, write contradiction with coprimality
C हर बार हर को शून्य रखो / Make the denominator zero every time
D हर वर्गमूल को पूर्णांक मानो / Treat every square root as an integer
Explanation opens after your attempt
Correct Answer
B. सरलतम परिमेय रूप लो, वर्ग करो, अभाज्य विभाज्यता लगाओ, सहअभाज्यता से विरोधाभास लिखो / Take lowest rational form, square, apply prime divisibility, write contradiction with coprimality
Step 1
Concept
First assume \(\sqrt{r}=\frac{p}{q}\) in lowest form.
Step 2
Why this answer is correct
Square and use the related prime (r) to show \(r\mid p\) and \(r\mid q\).
Step 3
Exam Tip
Finally write the contradiction with coprimality. चरण 1: पहले \(\sqrt{r}=\frac{p}{q}\) सरलतम रूप में मानें। चरण 2: वर्ग करके संबंधित अभाज्य (r) की विभाज्यता से \(r\mid p\) और \(r\mid q\) दिखाएँ। चरण 3: अंत में सहअभाज्यता से विरोधाभास लिखें।
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इस पूरे उपविषय को याद रखने के लिए सबसे उपयोगी सूत्र कौन सा है?
What is the most useful formula for remembering this whole subtopic?
#exam-strategy
#differing-strands
#swaraj
A क्षेत्र समूह मुद्दा और स्वराज अर्थ को साथ याद करें / Remember region group issue and meaning of swaraj together
B केवल एक नाम और एक तारीख याद करें / Remember only one name and one date
C सभी समूहों की मांग को समान मानें / Treat the demands of all groups as the same
D स्थानीय अनुभवों को पूरी तरह छोड़ दें / Completely leave out local experiences
Explanation opens after your attempt
Correct Answer
A. क्षेत्र समूह मुद्दा और स्वराज अर्थ को साथ याद करें / Remember region group issue and meaning of swaraj together
Step 1
Concept
This subtopic has different regions like Awadh Gudem and Assam.
Step 2
Why this answer is correct
Each region has a different group issue and meaning of swaraj.
Step 3
Exam Tip
For exams study through four links region group issue and meaning. चरण 1: इस उपविषय में अवध गुडेम और असम जैसे अलग क्षेत्र हैं। चरण 2: हर क्षेत्र में समूह मुद्दा और स्वराज अर्थ अलग है। चरण 3: परीक्षा के लिए क्षेत्र समूह मुद्दा और अर्थ की चार कड़ियां बनाकर पढ़ें।
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वाशिंग सोडा का सूत्र सोडियम कार्बोनेट दशजल को दर्शाता है। दशजल शब्द किस बात को बताता है?
The formula of washing soda shows sodium carbonate decahydrate. What does the word decahydrate indicate?
#washing-soda
#decahydrate
#water-of-crystallisation
#class10
A क्रिस्टल में जल के दस अणु / Ten water molecules in the crystal
B क्रिस्टल में दस धातुएँ / Ten metals in the crystal
C क्रिस्टल में दस अम्ल / Ten acids in the crystal
D क्रिस्टल में कोई जल नहीं / No water in the crystal
Explanation opens after your attempt
Correct Answer
A. क्रिस्टल में जल के दस अणु / Ten water molecules in the crystal
Step 1
Concept
Decahydrate means ten molecules of water.
Step 2
Why this answer is correct
Washing soda contains sodium carbonate with water of crystallisation.
Step 3
Exam Tip
Such numbers in hydrated salts are important for exams. पहला बिंदु: दशजल का अर्थ जल के दस अणुओं से है। दूसरा बिंदु: वाशिंग सोडा में सोडियम कार्बोनेट के साथ क्रिस्टलीय जल होता है। तीसरा बिंदु: जलयुक्त लवणों के नाम में ऐसी संख्याएँ महत्त्वपूर्ण होती हैं।
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समीकरण संतुलित करते समय यदि कोई छात्र जल के सूत्र में छोटा अंक बदल देता है तो गलती क्या है?
If a student changes the subscript in the formula of water while balancing an equation what is the mistake?
#science
#class10
#hard
#balancing
#subscripts
A पदार्थ की रचना बदल जाती है / Composition of substance changes
B गुणांक सही हो जाता है / Coefficient becomes correct
C द्रव्यमान अपने आप बढ़ जाता है / Mass automatically increases
D अवक्षेप बन जाता है / Precipitate forms
Explanation opens after your attempt
Correct Answer
A. पदार्थ की रचना बदल जाती है / Composition of substance changes
Step 1
Concept
A subscript is part of a chemical formula.
Step 2
Why this answer is correct
Changing it changes the identity of the substance.
Step 3
Exam Tip
Balancing should be done only by changing coefficients. चरण 1: छोटा अंक रासायनिक सूत्र का भाग होता है। चरण 2: इसे बदलने से पदार्थ की पहचान बदल जाती है। चरण 3: संतुलन केवल गुणांक बदलकर करना चाहिए।
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कार्बनिक यौगिकों में समान आणविक सूत्र पर अलग संरचना होने की घटना को क्या कहते हैं?
What is the phenomenon in which organic compounds have the same molecular formula but different structures called?
#science
#class10
#isomerism
#organic-compounds
A समावयवता / Isomerism
B शृंखलन / Catenation
C दहन / Combustion
D वाष्पीकरण / Evaporation
Explanation opens after your attempt
Correct Answer
A. समावयवता / Isomerism
Step 1
Concept
Some organic compounds may have the same formula.
Step 2
Why this answer is correct
Different structures can give different properties.
Step 3
Exam Tip
This phenomenon is called isomerism. चरण 1: कुछ कार्बनिक यौगिकों का सूत्र समान हो सकता है। चरण 2: उनकी संरचना अलग होने से गुण बदल सकते हैं। चरण 3: इस घटना को समावयवता कहते हैं।
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यदि \(S_n=4n^2-n\) किसी समान्तर श्रेणी का योग है तो प्रथम (12) पदों का योग कितना होगा?
If \(S_n=4n^2-n\) is the sum of an arithmetic progression, what is the sum of the first (12) terms?
#ap
#given-sum-formula
#expert
A (552)
B (564)
C (576)
D (588)
Explanation opens after your attempt
Step 1
Concept
Substituting (n=12) in the given formula gives \(S_{12}=564\). Exam tip: directly substitute (n) in the given \(S_n\).
Step 2
Why this answer is correct
The correct answer is B. (564). Substituting (n=12) in the given formula gives \(S_{12}=564\). Exam tip: directly substitute (n) in the given \(S_n\).
Step 3
Exam Tip
दिए गए सूत्र में (n=12) रखने पर \(S_{12}=564\) मिलता है। परीक्षा में दिए गए \(S_n\) में सीधे (n) रखें।
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यदि किसी समान्तर श्रेणी के पहले (18) पदों का योग (999) और प्रथम पद (13) है तो अंतिम पद क्या होगा?
If the sum of the first (18) terms of an arithmetic progression is (999) and the first term is (13), what is the last term?
#ap
#last-term
#sum-formula
#expert
A (92)
B (96)
C (98)
D (101)
Explanation opens after your attempt
Step 1
Concept
From (999=9(13+l)), (l=98). Exam tip: (S_n=\frac{n}{2}(a+l)) is the shortest method here.
Step 2
Why this answer is correct
The correct answer is C. (98). From (999=9(13+l)), (l=98). Exam tip: (S_n=\frac{n}{2}(a+l)) is the shortest method here.
Step 3
Exam Tip
(999=9(13+l)) से (l=98) मिलता है। परीक्षा में (S_n=\frac{n}{2}(a+l)) सबसे छोटा तरीका है।
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यदि (a=9), (d=5) और (n=25), तो \(S_{25}\) का मान ज्ञात कीजिए।
If (a=9), (d=5), and (n=25), find the value of \(S_{25}\).
#direct formula
#ap sum
#class 10
A (1700)
B (1750)
C (1675)
D (1725)
Explanation opens after your attempt
Step 1
Concept
\(S_{25}=\frac{25}{2}[18+120]=1725\). Add (2a) and ((n-1)d) separately inside the bracket.
Step 2
Why this answer is correct
The correct answer is D. (1725). \(S_{25}=\frac{25}{2}[18+120]=1725\). Add (2a) and ((n-1)d) separately inside the bracket.
Step 3
Exam Tip
\(S_{25}=\frac{25}{2}[18+120]=1725\) है। कोष्ठक के अंदर (2a) और ((n-1)d) अलग-अलग जोड़ें।
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किसी समांतर श्रेढ़ी में पहला पद (14), अंतिम पद (104) और पदों की संख्या (19) है। योग कितना होगा?
In an AP, the first term is (14), the last term is (104), and the number of terms is (19). What is the sum?
#first last sum
#ap formula
#class 10
A (1101)
B (1111)
C (1121)
D (1131)
Explanation opens after your attempt
Step 1
Concept
(S_{19}=\frac{19}{2}(14+104)=1121). When first and last terms are given, finding (d) is not necessary.
Step 2
Why this answer is correct
The correct answer is C. (1121). (S_{19}=\frac{19}{2}(14+104)=1121). When first and last terms are given, finding (d) is not necessary.
Step 3
Exam Tip
(S_{19}=\frac{19}{2}(14+104)=1121)। पहला और अंतिम पद दिए हों तो (d) निकालना जरूरी नहीं है।
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पहले (32) प्राकृतिक संख्याओं का योग ज्ञात कीजिए।
Find the sum of the first (32) natural numbers.
#natural numbers
#sum formula
#class 10
A (520)
B (528)
C (536)
D (544)
Explanation opens after your attempt
Step 1
Concept
\(\frac{32\times33}{2}=528\). For natural numbers, (\frac{n(n+1)}{2}) is the fastest formula.
Step 2
Why this answer is correct
The correct answer is B. (528). \(\frac{32\times33}{2}=528\). For natural numbers, (\frac{n(n+1)}{2}) is the fastest formula.
Step 3
Exam Tip
\(\frac{32\times33}{2}=528\)। प्राकृतिक संख्याओं के लिए (\frac{n(n+1)}{2}) सबसे तेज सूत्र है।
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समांतर श्रेढ़ी \(7,12,17,\ldots,82\) का योग ज्ञात कीजिए।
Find the sum of the AP \(7,12,17,\ldots,82\).
#finite ap
#last term
#sum formula
A (700)
B (712)
C (720)
D (724)
Explanation opens after your attempt
Step 1
Concept
From (82=7+(n-1)5), (n=16), and then the sum is (712). Finding (n) from the last term is the first step.
Step 2
Why this answer is correct
The correct answer is B. (712). From (82=7+(n-1)5), (n=16), and then the sum is (712). Finding (n) from the last term is the first step.
Step 3
Exam Tip
(82=7+(n-1)5) से (n=16), फिर योग (712) है। अंतिम पद से (n) निकालना पहला कदम है।
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यदि समांतर श्रेढ़ी का (a=20), (d=-1) और (n=25), तो \(S_{25}\) कितना होगा?
If an AP has (a=20), (d=-1), and (n=25), what is \(S_{25}\)?
#negative d
#sum formula
#ap
A (195)
B (200)
C (205)
D (210)
Explanation opens after your attempt
Step 1
Concept
The formula gives \(S_{25}=\frac{25}{2}[40-24]=200\). In a decreasing AP, the last term may be smaller.
Step 2
Why this answer is correct
The correct answer is B. (200). The formula gives \(S_{25}=\frac{25}{2}[40-24]=200\). In a decreasing AP, the last term may be smaller.
Step 3
Exam Tip
सूत्र से \(S_{25}=\frac{25}{2}[40-24]=200\) मिलता है। घटती श्रेढ़ी में अंतिम पद छोटा हो सकता है।
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किसी समांतर श्रेढ़ी में \(S_n=2n^2+5n\) है। पहले (8) पदों का योग क्या होगा?
In an AP, \(S_n=2n^2+5n\). What is the sum of the first (8) terms?
#sum formula
#given sn
#substitution
A (168)
B (160)
C (172)
D (176)
Explanation opens after your attempt
Step 1
Concept
(S_8=2(8)2 +5(8)=168). Put (n=8) directly in the given \(S_n\).
Step 2
Why this answer is correct
The correct answer is A. (168). (S_8=2(8)2 +5(8)=168). Put (n=8) directly in the given \(S_n\).
Step 3
Exam Tip
(S_8=2(8)2 +5(8)=168)। दिए गए \(S_n\) में सीधे (n=8) रखें।
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यदि किसी समांतर श्रेढ़ी में (a=12), (d=-2) और (n=15), तो \(S_{15}\) का मान ज्ञात कीजिए।
If an AP has (a=12), (d=-2), and (n=15), find the value of \(S_{15}\).
#arithmetic progression
#negative difference
#sum formula
A (30)
B (-30)
C (45)
D (-45)
Explanation opens after your attempt
Step 1
Concept
This is a decreasing AP, and the formula gives \(S_{15}=-30\). Do not forget the sign of the negative common difference.
Step 2
Why this answer is correct
The correct answer is B. (-30). This is a decreasing AP, and the formula gives \(S_{15}=-30\). Do not forget the sign of the negative common difference.
Step 3
Exam Tip
यह घटती हुई श्रेढ़ी है और सूत्र से \(S_{15}=-30\) मिलता है। ऋणात्मक सार्व अंतर का संकेत न भूलें।
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यदि किसी समांतर श्रेणी का (n)वाँ पद \(a_n=3n+10\) है, तो पहले (16) पदों का योग क्या है?
If the (n)th term of an arithmetic progression is \(a_n=3n+10\), what is the sum of the first (16) terms?
#nth_term
#ap_sum
#formula
A (538)
B (548)
C (558)
D (568)
Explanation opens after your attempt
Step 1
Concept
The first term is (13) and the sixteenth term is (58), so \(S_{16}=568\). Use \(a_n\) to find (a) and (l), then apply the sum formula.
Step 2
Why this answer is correct
The correct answer is D. (568). The first term is (13) and the sixteenth term is (58), so \(S_{16}=568\). Use \(a_n\) to find (a) and (l), then apply the sum formula.
Step 3
Exam Tip
पहला पद (13) और सोलहवाँ पद (58) है, इसलिए \(S_{16}=568\)। \(a_n\) से (a) और (l) निकालकर योग लगाएँ।
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किसी समांतर श्रेणी में पहले और अंतिम पद का योग (144) है और कुल पद (18) हैं। श्रेणी का योग कितना होगा?
In an arithmetic progression, the sum of the first and last terms is (144), and there are (18) terms. What will be the sum of the progression?
#first_last_sum
#ap_sum
#formula
A (1276)
B (1286)
C (1296)
D (1306)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}(a+l)), \(S_{18}=\frac{18}{2}\times144=1296\). If (a+l) is directly given, use it immediately.
Step 2
Why this answer is correct
The correct answer is C. (1296). Using (S_n=\frac{n}{2}(a+l)), \(S_{18}=\frac{18}{2}\times144=1296\). If (a+l) is directly given, use it immediately.
Step 3
Exam Tip
(S_n=\frac{n}{2}(a+l)) से \(S_{18}=\frac{18}{2}\times144=1296\)। (a+l) सीधे दिया हो तो उसे तुरंत उपयोग करें।
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यदि किसी समांतर श्रेणी का पहला पद (18), अंतिम पद (126) और कुल पद (19) हैं, तो योग कितना होगा?
If the first term of an arithmetic progression is (18), the last term is (126), and there are (19) terms, what is the sum?
#first_last
#ap_sum
#formula
A (1348)
B (1368)
C (1388)
D (1408)
Explanation opens after your attempt
Step 1
Concept
(S_{19}=\frac{19}{2}(18+126)=1368). If the first and last terms are given, use the shorter formula.
Step 2
Why this answer is correct
The correct answer is B. (1368). (S_{19}=\frac{19}{2}(18+126)=1368). If the first and last terms are given, use the shorter formula.
Step 3
Exam Tip
(S_{19}=\frac{19}{2}(18+126)=1368)। पहला और अंतिम पद दिए हों तो छोटा सूत्र लगाएँ।
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यदि किसी समांतर श्रेणी में (a=12), (d=5), और (n=18) है, तो पहले (18) पदों का योग कितना होगा?
If an arithmetic progression has (a=12), (d=5), and (n=18), what is the sum of the first (18) terms?
#ap_sum
#formula
#common_difference
A (951)
B (961)
C (971)
D (981)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}[2a+(n-1)d]), we get \(S_{18}=981\). Calculate ((n-1)d) carefully.
Step 2
Why this answer is correct
The correct answer is D. (981). Using (S_n=\frac{n}{2}[2a+(n-1)d]), we get \(S_{18}=981\). Calculate ((n-1)d) carefully.
Step 3
Exam Tip
सूत्र (S_n=\frac{n}{2}[2a+(n-1)d]) से \(S_{18}=981\) मिलता है। ((n-1)d) को ध्यान से निकालें।
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यदि किसी समांतर श्रेणी में (a=3), (d=7), और (n=20) है, तो पहले (20) पदों का योग कितना होगा?
If an arithmetic progression has (a=3), (d=7), and (n=20), what is the sum of the first (20) terms?
#ap_sum
#formula
#common_difference
A (1360)
B (1370)
C (1380)
D (1390)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}[2a+(n-1)d]), we get \(S_{20}=1390\). Calculate ((n-1)d) carefully.
Step 2
Why this answer is correct
The correct answer is D. (1390). Using (S_n=\frac{n}{2}[2a+(n-1)d]), we get \(S_{20}=1390\). Calculate ((n-1)d) carefully.
Step 3
Exam Tip
सूत्र (S_n=\frac{n}{2}[2a+(n-1)d]) से \(S_{20}=1390\) मिलता है। ((n-1)d) की गणना ध्यान से करें।
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पहले (35) प्राकृतिक संख्याओं का योग क्या होगा?
What will be the sum of the first (35) natural numbers?
#natural_numbers
#ap_sum
#formula
A (610)
B (620)
C (630)
D (640)
Explanation opens after your attempt
Step 1
Concept
\(\frac{35\times36}{2}=630\), so the sum is (630). Divide (n(n+1)) by (2).
Step 2
Why this answer is correct
The correct answer is C. (630). \(\frac{35\times36}{2}=630\), so the sum is (630). Divide (n(n+1)) by (2).
Step 3
Exam Tip
\(\frac{35\times36}{2}=630\), इसलिए योग (630) है। (n(n+1)) को (2) से भाग दें।
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पहले (21) सम प्राकृतिक संख्याओं का योग क्या है?
What is the sum of the first (21) even natural numbers?
#even_numbers
#ap_sum
#formula
A (452)
B (462)
C (472)
D (482)
Explanation opens after your attempt
Step 1
Concept
The sum of the first (21) even numbers is \(21\times22=462\). Use (n(n+1)) for even numbers.
Step 2
Why this answer is correct
The correct answer is B. (462). The sum of the first (21) even numbers is \(21\times22=462\). Use (n(n+1)) for even numbers.
Step 3
Exam Tip
पहले (21) सम संख्याओं का योग \(21\times22=462\) है। सम संख्याओं के लिए (n(n+1)) प्रयोग करें।
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यदि किसी समांतर श्रेणी में (a=12), (d=8), और (n=10) है, तो \(S_{10}\) का मान क्या होगा?
If an arithmetic progression has (a=12), (d=8), and (n=10), what will be the value of \(S_{10}\)?
#ap_sum
#formula
#value
A (470)
B (480)
C (490)
D (500)
Explanation opens after your attempt
Step 1
Concept
\(S_{10}=\frac{10}{2}[24+72]=480\). Do the calculation inside the bracket first.
Step 2
Why this answer is correct
The correct answer is B. (480). \(S_{10}=\frac{10}{2}[24+72]=480\). Do the calculation inside the bracket first.
Step 3
Exam Tip
\(S_{10}=\frac{10}{2}[24+72]=480\)। कोष्ठक के अंदर की गणना पहले करें।
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यदि समांतर श्रेणी का पहला पद (11), अंतिम पद (71) और पदों की संख्या (16) है, तो योग कितना होगा?
If the first term of an arithmetic progression is (11), the last term is (71), and the number of terms is (16), what is the sum?
#first_last
#ap_sum
#formula
A (636)
B (646)
C (656)
D (666)
Explanation opens after your attempt
Step 1
Concept
(S_{16}=\frac{16}{2}(11+71)=656). If the first and last terms are given, use the shorter formula.
Step 2
Why this answer is correct
The correct answer is C. (656). (S_{16}=\frac{16}{2}(11+71)=656). If the first and last terms are given, use the shorter formula.
Step 3
Exam Tip
(S_{16}=\frac{16}{2}(11+71)=656)। पहला और अंतिम पद मिले हों तो छोटा सूत्र लगाएँ।
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समांतर श्रेणी \(18,22,26,\ldots\) के पहले (15) पदों का योग ज्ञात करें।
Find the sum of the first (15) terms of the arithmetic progression \(18,22,26,\ldots\).
#ap_sum
#fifteen_terms
#formula
A (680)
B (690)
C (700)
D (710)
Explanation opens after your attempt
Step 1
Concept
The fifteenth term is (74), so (S_{15}=\frac{15}{2}(18+74)=690). The sum can also be found using the average of the first and last terms.
Step 2
Why this answer is correct
The correct answer is B. (690). The fifteenth term is (74), so (S_{15}=\frac{15}{2}(18+74)=690). The sum can also be found using the average of the first and last terms.
Step 3
Exam Tip
पंद्रहवाँ पद (74) है, इसलिए (S_{15}=\frac{15}{2}(18+74)=690)। पहले और अंतिम पद का औसत लेकर भी योग मिल जाता है।
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यदि किसी समांतर श्रेणी का पहला पद (8), अंतिम पद (62) और कुल पद (10) हैं, तो योग क्या होगा?
If the first term of an arithmetic progression is (8), the last term is (62), and there are (10) terms, what is the sum?
#first_last
#ap_sum
#formula
A (330)
B (340)
C (350)
D (360)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}(a+l)), \(S_{10}=350\). If the last term is given, finding (d) is not needed.
Step 2
Why this answer is correct
The correct answer is C. (350). Using (S_n=\frac{n}{2}(a+l)), \(S_{10}=350\). If the last term is given, finding (d) is not needed.
Step 3
Exam Tip
(S_n=\frac{n}{2}(a+l)) से \(S_{10}=350\)। अंतिम पद दिया हो तो (d) निकालने की जरूरत नहीं होती।
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यदि किसी समांतर श्रेणी में पहला पद (4), अंतर (5) और पदों की संख्या (13) है, तो पहले (13) पदों का योग कितना होगा?
If an arithmetic progression has first term (4), common difference (5), and (13) terms, what is the sum of the first (13) terms?
#ap
#sum
#formula
A (422)
B (432)
C (442)
D (452)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}[2a+(n-1)d]), we get \(S_{13}=442\). Write ((n-1)d) carefully in the formula.
Step 2
Why this answer is correct
The correct answer is C. (442). Using (S_n=\frac{n}{2}[2a+(n-1)d]), we get \(S_{13}=442\). Write ((n-1)d) carefully in the formula.
Step 3
Exam Tip
सूत्र (S_n=\frac{n}{2}[2a+(n-1)d]) से \(S_{13}=442\) मिलता है। सूत्र में ((n-1)d) ध्यान से लिखें।
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समांतर श्रेढ़ी \(18,24,30,\ldots\) के पहले (7) पदों का योग कितना है?
What is the sum of the first (7) terms of the arithmetic progression \(18,24,30,\ldots\)?
#ap_sum
#seven_terms
#formula
A (250)
B (252)
C (254)
D (256)
Explanation opens after your attempt
Step 1
Concept
The seventh term is (54), so (S_7=\frac{7}{2}(18+54)=252). Find the last term and use the average method.
Step 2
Why this answer is correct
The correct answer is B. (252). The seventh term is (54), so (S_7=\frac{7}{2}(18+54)=252). Find the last term and use the average method.
Step 3
Exam Tip
सातवाँ पद (54) है, इसलिए (S_7=\frac{7}{2}(18+54)=252)। अंतिम पद निकालकर औसत विधि अपनाएँ।
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यदि किसी समांतर श्रेढ़ी में (a=13), (l=49) और (n=10) है, तो \(S_n\) कितना होगा?
If an arithmetic progression has (a=13), (l=49), and (n=10), what is \(S_n\)?
#ap_sum
#last_term
#formula
A (300)
B (310)
C (320)
D (330)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}(a+l)), \(S_{10}=310\). If (l) is given, use this shorter formula.
Step 2
Why this answer is correct
The correct answer is B. (310). Using (S_n=\frac{n}{2}(a+l)), \(S_{10}=310\). If (l) is given, use this shorter formula.
Step 3
Exam Tip
(S_n=\frac{n}{2}(a+l)) से \(S_{10}=310\)। (l) दिया हो तो यही छोटा सूत्र लें।
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किसी समांतर श्रेढ़ी में (a=11), (d=2), (n=20) है। पहले (20) पदों का योग क्या होगा?
In an arithmetic progression, (a=11), (d=2), and (n=20). What will be the sum of the first (20) terms?
#ap_sum
#formula
#twenty_terms
A (590)
B (600)
C (610)
D (620)
Explanation opens after your attempt
Step 1
Concept
\(S_{20}=\frac{20}{2}[22+38]=600\). Find (2a) and ((n-1)d) separately.
Step 2
Why this answer is correct
The correct answer is B. (600). \(S_{20}=\frac{20}{2}[22+38]=600\). Find (2a) and ((n-1)d) separately.
Step 3
Exam Tip
\(S_{20}=\frac{20}{2}[22+38]=600\)। (2a) और ((n-1)d) अलग-अलग निकालें।
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यदि किसी समांतर श्रेढ़ी में पहला पद (2), अंतिम पद (50) और पदों की संख्या (13) है, तो योग कितना है?
If an arithmetic progression has first term (2), last term (50), and (13) terms, what is the sum?
#ap_sum
#first_last
#formula
A (328)
B (338)
C (348)
D (358)
Explanation opens after your attempt
Step 1
Concept
(S_{13}=\frac{13}{2}(2+50)=338). Add the first and last terms and multiply by half the number of terms.
Step 2
Why this answer is correct
The correct answer is B. (338). (S_{13}=\frac{13}{2}(2+50)=338). Add the first and last terms and multiply by half the number of terms.
Step 3
Exam Tip
(S_{13}=\frac{13}{2}(2+50)=338)। पहला और अंतिम पद जोड़कर आधे पदों से गुणा करें।
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किसी समांतर श्रेढ़ी के पहले (7) पदों का योग (140) है और पहला पद (5) है। यदि अंतिम पद पूछा जाए तो योग सूत्र से (l) क्या होगा?
The sum of the first (7) terms of an arithmetic progression is (140), and the first term is (5). Using the sum formula, what is the last term (l)?
#ap_sum
#reverse_formula
#last_term
A (30)
B (35)
C (40)
D (45)
Explanation opens after your attempt
Step 1
Concept
From (140=\frac{7}{2}(5+l)), (l=35). Learn to use the sum formula in reverse too.
Step 2
Why this answer is correct
The correct answer is B. (35). From (140=\frac{7}{2}(5+l)), (l=35). Learn to use the sum formula in reverse too.
Step 3
Exam Tip
(140=\frac{7}{2}(5+l)) से (l=35)। योग सूत्र को उल्टा लगाना भी सीखें।
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यदि (a=4), (d=6) और (n=9) है, तो समांतर श्रेढ़ी के पहले (9) पदों का योग ज्ञात करें।
If (a=4), (d=6), and (n=9), find the sum of the first (9) terms of the arithmetic progression.
#ap
#sum
#formula
A (248)
B (250)
C (252)
D (256)
Explanation opens after your attempt
Step 1
Concept
Substituting values gives \(S_9=\frac{9}{2}[8+48]=252\). Simplify inside the bracket first.
Step 2
Why this answer is correct
The correct answer is C. (252). Substituting values gives \(S_9=\frac{9}{2}[8+48]=252\). Simplify inside the bracket first.
Step 3
Exam Tip
सूत्र में मान रखने पर \(S_9=\frac{9}{2}[8+48]=252\)। कोष्ठक के अंदर पहले सरल करें।
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यदि पहले (n) पदों का योग (S_n=\frac{n}{2}(3n+1)) है तो \(S_{10}\) क्या होगा?
If the sum of the first (n) terms is (S_n=\frac{n}{2}(3n+1)), what is \(S_{10}\)?
#ap-sum-direct-formula
A (145)
B (155)
C (165)
D (175)
Explanation opens after your attempt
Step 1
Concept
Put (n=10) in the formula. (S_{10}=\frac{10}{2}(31)=155).
Step 2
Why this answer is correct
The correct answer is B. (155). Put (n=10) in the formula. (S_{10}=\frac{10}{2}(31)=155).
Step 3
Exam Tip
सूत्र में (n=10) रखें। (S_{10}=\frac{10}{2}(31)=155)।
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यदि (a=6), (d=2), (n=20) है तो \(S_n\) क्या होगा?
If (a=6), (d=2), (n=20), what is \(S_n\)?
#ap-sum-formula
A (480)
B (500)
C (520)
D (560)
Explanation opens after your attempt
Step 1
Concept
Use (S_n=\frac{n}{2}[2a+(n-1)d]). \(S_{20}=10[12+38]=500\).
Step 2
Why this answer is correct
The correct answer is B. (500). Use (S_n=\frac{n}{2}[2a+(n-1)d]). \(S_{20}=10[12+38]=500\).
Step 3
Exam Tip
(S_n=\frac{n}{2}[2a+(n-1)d]) लगाएं। \(S_{20}=10[12+38]=500\)।
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समान्तर श्रेणी \(18,35,52,\ldots\) में \(a_n\) को (n) के रूप में लिखकर \(a_{5k}\) ज्ञात कीजिए जब (k=8)।
Write \(a_n\) in terms of (n) for the AP \(18,35,52,\ldots\), and find \(a_{5k}\) when (k=8).
#ap expert formula index
A (681)
B (687)
C (691)
D (697)
Explanation opens after your attempt
Step 1
Concept
Here (a_n=18+17(n-1)=17n+1). \(a_{40}=17\times40+1=681\).
Step 2
Why this answer is correct
The correct answer is A. (681). Here (a_n=18+17(n-1)=17n+1). \(a_{40}=17\times40+1=681\).
Step 3
Exam Tip
यहां (a_n=18+17(n-1)=17n+1)। \(a_{40}=17\times40+1=681\)।
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समान्तर श्रेणी \(12,25,38,\ldots\) में \(a_n\) को (n) के रूप में लिखकर \(a_{4k}\) ज्ञात कीजिए जब (k=9)।
Write \(a_n\) in terms of (n) for the AP \(12,25,38,\ldots\), and find \(a_{4k}\) when (k=9).
#ap-formula-index-expert
A (467)
B (471)
C (479)
D (485)
Explanation opens after your attempt
Step 1
Concept
Here (a_n=12+13(n-1)=13n-1). \(a_{36}=13\times36-1=467\).
Step 2
Why this answer is correct
The correct answer is A. (467). Here (a_n=12+13(n-1)=13n-1). \(a_{36}=13\times36-1=467\).
Step 3
Exam Tip
यहां (a_n=12+13(n-1)=13n-1)। \(a_{36}=13\times36-1=467\)।
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यदि \(a_n=3n+p\) और \(a_{12}=50\) है तो \(a_{27}\) क्या होगा?
If \(a_n=3n+p\) and \(a_{12}=50\), what is \(a_{27}\)?
#ap-direct-formula-hard
A (92)
B (95)
C (98)
D (101)
Explanation opens after your attempt
Step 1
Concept
From (50=36+p), (p=14) and \(a_{27}=81+14=95\). First find the constant, then substitute the required term number.
Step 2
Why this answer is correct
The correct answer is B. (95). From (50=36+p), (p=14) and \(a_{27}=81+14=95\). First find the constant, then substitute the required term number.
Step 3
Exam Tip
(50=36+p) से (p=14) और \(a_{27}=81+14=95\)। पहले स्थिरांक निकालें फिर मांगा पद रखें।
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यदि \(a_n=10-3n\) है तो कौन-सा पद (-44) होगा?
If \(a_n=10-3n\), which term will be (-44)?
#ap direct-formula term-number class10
A (16)वां / (16)th
B (17)वां / (17)th
C (18)वां / (18)th
D (19)वां / (19)th
Explanation opens after your attempt
Correct Answer
C. (18)वां / (18)th
Step 1
Concept
From (-44=10-3n), (3n=54) so (n=18). Solve the direct formula equation directly.
Step 2
Why this answer is correct
The correct answer is C. (18)वां / (18)th. From (-44=10-3n), (3n=54) so (n=18). Solve the direct formula equation directly.
Step 3
Exam Tip
(-44=10-3n) से (3n=54) इसलिए (n=18)। प्रत्यक्ष सूत्र में समीकरण को सीधे हल करें।
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यदि \(a_n=13n-6\) है तो \(a_{18}-a_{11}\) का मान क्या होगा?
If \(a_n=13n-6\), what is the value of \(a_{18}-a_{11}\)?
#ap direct-formula difference-of-terms
A (78)
B (84)
C (91)
D (97)
Explanation opens after your attempt
Step 1
Concept
The position gap is (18-11=7) and (d=13) so the difference is \(7\times13=91\). You do not need to find both terms separately.
Step 2
Why this answer is correct
The correct answer is C. (91). The position gap is (18-11=7) and (d=13) so the difference is \(7\times13=91\). You do not need to find both terms separately.
Step 3
Exam Tip
स्थान अंतर (18-11=7) और (d=13) है इसलिए अंतर \(7\times13=91\)। दोनों पद अलग से निकालना जरूरी नहीं।
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यदि \(a_n=4n+11\) है तो पहला पद और सार्व अंतर क्या होंगे?
If \(a_n=4n+11\), what are the first term and common difference?
#ap direct-formula first-term class10
A (a=15,d=4)
B (a=11,d=4)
C (a=4,d=11)
D (a=15,d=11)
Explanation opens after your attempt
Correct Answer
A. (a=15,d=4)
Step 1
Concept
Putting (n=1), \(a_1=15\) and the coefficient of (n) is (d=4). The direct formula gives both values quickly.
Step 2
Why this answer is correct
The correct answer is A. (a=15,d=4). Putting (n=1), \(a_1=15\) and the coefficient of (n) is (d=4). The direct formula gives both values quickly.
Step 3
Exam Tip
(n=1) रखने पर \(a_1=15\) और (n) का गुणांक (4) ही (d) है। प्रत्यक्ष सूत्र से दोनों मान तुरंत मिलते हैं।
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यदि \(a_n=95-5n\) है तो (26)वां पद क्या होगा?
If \(a_n=95-5n\), what will be the (26)th term?
#ap direct-formula decreasing class10
A (-35)
B (-30)
C (-25)
D (-20)
Explanation opens after your attempt
Step 1
Concept
\(a_{26}=95-5\times26=-35\). In a decreasing formula check the sign after subtraction.
Step 2
Why this answer is correct
The correct answer is A. (-35). \(a_{26}=95-5\times26=-35\). In a decreasing formula check the sign after subtraction.
Step 3
Exam Tip
\(a_{26}=95-5\times26=-35\)। घटते सूत्र में घटाव के बाद चिन्ह जांचें।
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यदि \(a_n=6n+7\) है तो \(a_{34}\) क्या होगा?
If \(a_n=6n+7\), what is \(a_{34}\)?
#ap direct-formula nth-term class10
A (207)
B (211)
C (215)
D (219)
Explanation opens after your attempt
Step 1
Concept
Putting (n=34), \(a_{34}=6\times34+7=211\). Substitute only the correct value of (n) in the direct formula.
Step 2
Why this answer is correct
The correct answer is B. (211). Putting (n=34), \(a_{34}=6\times34+7=211\). Substitute only the correct value of (n) in the direct formula.
Step 3
Exam Tip
(n=34) रखने पर \(a_{34}=6\times34+7=211\)। प्रत्यक्ष सूत्र में केवल सही (n) रखें।
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यदि \(a_n=7-2n\) है तो कौन-सा पद (-35) होगा?
If \(a_n=7-2n\), which term will be (-35)?
#ap
#direct-formula
#term-number
#class10
A (21)वां / (21)th
B (19)वां / (19)th
C (20)वां / (20)th
D (22)वां / (22)th
Explanation opens after your attempt
Correct Answer
A. (21)वां / (21)th
Step 1
Concept
From (-35=7-2n), (2n=42) so (n=21). Solve the direct formula equation directly.
Step 2
Why this answer is correct
The correct answer is A. (21)वां / (21)th. From (-35=7-2n), (2n=42) so (n=21). Solve the direct formula equation directly.
Step 3
Exam Tip
(-35=7-2n) से (2n=42) इसलिए (n=21)। प्रत्यक्ष सूत्र में समीकरण सीधा हल करें।
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यदि \(a_n=11n-4\) है तो \(a_{15}-a_9\) का मान क्या होगा?
If \(a_n=11n-4\), what is the value of \(a_{15}-a_9\)?
#ap
#direct-formula
#difference-of-terms
A (55)
B (66)
C (60)
D (72)
Explanation opens after your attempt
Step 1
Concept
The position gap is (15-9=6) and (d=11), so the difference is \(6\times11=66\). You do not need to find both terms separately.
Step 2
Why this answer is correct
The correct answer is B. (66). The position gap is (15-9=6) and (d=11), so the difference is \(6\times11=66\). You do not need to find both terms separately.
Step 3
Exam Tip
स्थान अंतर (15-9=6) है और (d=11) है इसलिए अंतर \(6\times11=66\)। ऐसे प्रश्न में दोनों पद अलग से निकालना जरूरी नहीं।
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यदि \(a_n=3n-2\) है तो पहला पद और सार्व अंतर क्या होंगे?
If \(a_n=3n-2\), what are the first term and common difference?
#ap
#direct-formula
#first-term
#class10
A (a=3,d=1)
B (a=2,d=3)
C (a=1,d=2)
D (a=1,d=3)
Explanation opens after your attempt
Correct Answer
D. (a=1,d=3)
Step 1
Concept
Putting (n=1), \(a_1=1\) and the coefficient of (n) is (d=3). The direct formula gives both values quickly.
Step 2
Why this answer is correct
The correct answer is D. (a=1,d=3). Putting (n=1), \(a_1=1\) and the coefficient of (n) is (d=3). The direct formula gives both values quickly.
Step 3
Exam Tip
(n=1) रखने पर \(a_1=1\) और (n) का गुणांक (3) ही (d) है। प्रत्यक्ष सूत्र से दोनों मान तुरंत मिलते हैं।
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यदि \(a_n=82-4n\) है तो समान्तर श्रेणी का (23)वां पद क्या होगा?
If \(a_n=82-4n\), what will be the (23)rd term of the AP?
#ap
#direct-formula
#decreasing
#class10
A (-10)
B (-8)
C (-12)
D (-14)
Explanation opens after your attempt
Step 1
Concept
\(a_{23}=82-4\times23=-10\). Do subtraction carefully in a decreasing direct formula.
Step 2
Why this answer is correct
The correct answer is A. (-10). \(a_{23}=82-4\times23=-10\). Do subtraction carefully in a decreasing direct formula.
Step 3
Exam Tip
\(a_{23}=82-4\times23=-10\)। घटते प्रत्यक्ष सूत्र में घटाव को ध्यान से करें।
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यदि \(a_n=5n+8\) है तो \(a_{26}\) का मान क्या है?
If \(a_n=5n+8\), what is the value of \(a_{26}\)?
#ap
#direct-formula
#nth-term
#class10
A (132)
B (136)
C (138)
D (142)
Explanation opens after your attempt
Step 1
Concept
Putting (n=26), \(a_{26}=5\times26+8=138\). Substitute the correct term number in the direct formula.
Step 2
Why this answer is correct
The correct answer is C. (138). Putting (n=26), \(a_{26}=5\times26+8=138\). Substitute the correct term number in the direct formula.
Step 3
Exam Tip
(n=26) रखने पर \(a_{26}=5\times26+8=138\)। प्रत्यक्ष सूत्र में सही पद संख्या रखें।
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समान्तर श्रेणी \(11,17,23,\ldots\) का (n)वां पद \(a_n=6n+5\) है। इसका (32)वां पद क्या होगा?
The (n)th term of the AP \(11,17,23,\ldots\) is \(a_n=6n+5\). What is its (32)nd term?
#ap
#direct-formula
#nth-term
#class10
A (191)
B (197)
C (203)
D (209)
Explanation opens after your attempt
Step 1
Concept
\(a_{32}=6\times32+5=197\). Substitute the correct value of (n) in the formed formula.
Step 2
Why this answer is correct
The correct answer is B. (197). \(a_{32}=6\times32+5=197\). Substitute the correct value of (n) in the formed formula.
Step 3
Exam Tip
\(a_{32}=6\times32+5=197\)। बनाए गए सूत्र में (n) का सही मान रखें।
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यदि \(a_n=50-4n\) है, तो AP का कौन-सा पद (-10) होगा?
If \(a_n=50-4n\), which term of the AP will be (-10)?
#ap
#direct-formula
#term-number
#class10
A (13)वां / (13)th
B (14)वां / (14)th
C (15)वां / (15)th
D (16)वां / (16)th
Explanation opens after your attempt
Correct Answer
C. (15)वां / (15)th
Step 1
Concept
From (-10=50-4n), (4n=60), so (n=15). Solve the direct formula equation directly.
Step 2
Why this answer is correct
The correct answer is C. (15)वां / (15)th. From (-10=50-4n), (4n=60), so (n=15). Solve the direct formula equation directly.
Step 3
Exam Tip
(-10=50-4n) से (4n=60), अतः (n=15)। प्रत्यक्ष सूत्र में समीकरण को सीधे हल करें।
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यदि समान्तर श्रेणी का (n)वां पद \(a_n=9n+2\) है, तो \(a_{11}-a_5\) का मान क्या होगा?
If the (n)th term of an AP is \(a_n=9n+2\), what is the value of \(a_{11}-a_5\)?
#ap
#direct-formula
#difference-of-terms
#class10
A (45)
B (54)
C (63)
D (72)
Explanation opens after your attempt
Step 1
Concept
(a_{11}-a_5=(101)-(47)=54), or \(6d=6\times9=54\). Use the difference of positions for term differences.
Step 2
Why this answer is correct
The correct answer is B. (54). (a_{11}-a_5=(101)-(47)=54), or \(6d=6\times9=54\). Use the difference of positions for term differences.
Step 3
Exam Tip
(a_{11}-a_5=(101)-(47)=54), या \(6d=6\times9=54\)। पदों के अंतर में स्थानों का अंतर उपयोग करें।
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यदि \(a_n=2n+5\) है, तो समान्तर श्रेणी का पहला पद और सार्व अंतर क्या होंगे?
If \(a_n=2n+5\), what are the first term and common difference of the AP?
#ap
#direct-formula
#first-term
#class10
A (a=7,d=2)
B (a=5,d=2)
C (a=2,d=5)
D (a=7,d=5)
Explanation opens after your attempt
Correct Answer
A. (a=7,d=2)
Step 1
Concept
Putting (n=1), \(a_1=7\), and consecutive terms differ by (2). In a direct formula, (d) is the coefficient of (n).
Step 2
Why this answer is correct
The correct answer is A. (a=7,d=2). Putting (n=1), \(a_1=7\), and consecutive terms differ by (2). In a direct formula, (d) is the coefficient of (n).
Step 3
Exam Tip
(n=1) रखने पर \(a_1=7\) और लगातार पदों का अंतर (2) है। प्रत्यक्ष सूत्र में (d) (n) के गुणांक से मिलता है।
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यदि \(a_n=7-3n\) है, तो समान्तर श्रेणी का (22)वां पद क्या होगा?
If \(a_n=7-3n\), what is the (22)nd term of the AP?
#ap
#direct-formula
#nth-term
#class10
A (-59)
B (-57)
C (-61)
D (-63)
Explanation opens after your attempt
Step 1
Concept
\(a_{22}=7-3\times22=-59\). Pay special attention to the negative sign in a decreasing direct formula.
Step 2
Why this answer is correct
The correct answer is A. (-59). \(a_{22}=7-3\times22=-59\). Pay special attention to the negative sign in a decreasing direct formula.
Step 3
Exam Tip
\(a_{22}=7-3\times22=-59\)। घटते प्रत्यक्ष सूत्र में ऋण चिह्न पर विशेष ध्यान दें।
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यदि \(a_n=4n-1\) से किसी समान्तर श्रेणी का (n)वां पद दिया है, तो \(a_{30}\) क्या होगा?
If the (n)th term of an AP is given by \(a_n=4n-1\), what is \(a_{30}\)?
#ap
#formula-based
#nth-term
#class10
A (117)
B (119)
C (121)
D (123)
Explanation opens after your attempt
Step 1
Concept
Putting (n=30), \(a_{30}=4\times30-1=119\). In a direct formula, substitute the correct (n).
Step 2
Why this answer is correct
The correct answer is B. (119). Putting (n=30), \(a_{30}=4\times30-1=119\). In a direct formula, substitute the correct (n).
Step 3
Exam Tip
(n=30) रखने पर \(a_{30}=4\times30-1=119\)। प्रत्यक्ष सूत्र में केवल सही (n) रखें।
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समांतर श्रेढ़ी \(45,39,33,27,\ldots\) का (10)वाँ पद ज्ञात करें।
Find the (10)th term of the AP \(45,39,33,27,\ldots\).
#ap decreasing
#nth term
#formula
A (-3)
B (-9)
C (3)
D (0)
Explanation opens after your attempt
Step 1
Concept
Here (d=-6), so (a_{10}=45+9(-6)=-9). Subtract (9) differences, not (10).
Step 2
Why this answer is correct
The correct answer is B. (-9). Here (d=-6), so (a_{10}=45+9(-6)=-9). Subtract (9) differences, not (10).
Step 3
Exam Tip
यहाँ (d=-6) है, इसलिए (a_{10}=45+9(-6)=-9)। (9) अंतर घटाने हैं, (10) नहीं।
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एक समांतर श्रेढ़ी में (a=3) और (d=10) है। (13)वाँ पद क्या होगा?
In an AP, (a=3) and (d=10). What will be the (13)th term?
#ap formula
#nth term
#school exam
A (120)
B (130)
C (123)
D (133)
Explanation opens after your attempt
Step 1
Concept
\(a_{13}=3+12\times10=123\). It is easy to find (12d) first and then add (a).
Step 2
Why this answer is correct
The correct answer is C. (123). \(a_{13}=3+12\times10=123\). It is easy to find (12d) first and then add (a).
Step 3
Exam Tip
\(a_{13}=3+12\times10=123\)। पहले (12d) निकालकर (a) जोड़ना आसान है।
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यदि समांतर श्रेढ़ी में (a=14) और (d=6) है, तो (19)वाँ पद ज्ञात करें।
If an AP has (a=14) and (d=6), find the (19)th term.
#arithmetic progression
#nth term
#formula
A (116)
B (128)
C (122)
D (120)
Explanation opens after your attempt
Step 1
Concept
\(a_{19}=14+18\times6=122\). Multiply by (n-1) and then add the first term.
Step 2
Why this answer is correct
The correct answer is C. (122). \(a_{19}=14+18\times6=122\). Multiply by (n-1) and then add the first term.
Step 3
Exam Tip
\(a_{19}=14+18\times6=122\)। (n-1) को गुणा करके फिर प्रथम पद जोड़ें।
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समांतर श्रेढ़ी \(2,9,16,23,\ldots\) का (22)वाँ पद क्या है?
What is the (22)nd term of the AP \(2,9,16,23,\ldots\)?
#ap formula
#nth term
#easy level
A (142)
B (149)
C (156)
D (147)
Explanation opens after your attempt
Step 1
Concept
Here (a=2), (d=7), so \(a_{22}=2+21\times7=149\). The (22)nd term adds (21) common differences.
Step 2
Why this answer is correct
The correct answer is B. (149). Here (a=2), (d=7), so \(a_{22}=2+21\times7=149\). The (22)nd term adds (21) common differences.
Step 3
Exam Tip
यहाँ (a=2), (d=7) है, इसलिए \(a_{22}=2+21\times7=149\)। (22)वें पद में (21) समान अंतर जुड़ते हैं।
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एक समांतर श्रेढ़ी का प्रथम पद (25) और सार्व अंतर (4) है। (21)वाँ पद क्या होगा?
The first term of an AP is (25) and the common difference is (4). What will be the (21)st term?
#ap formula
#nth term
#class 10
A (101)
B (105)
C (109)
D (96)
Explanation opens after your attempt
Step 1
Concept
\(a_{21}=25+20\times4=105\). Do not forget to subtract (1) from the term number.
Step 2
Why this answer is correct
The correct answer is B. (105). \(a_{21}=25+20\times4=105\). Do not forget to subtract (1) from the term number.
Step 3
Exam Tip
\(a_{21}=25+20\times4=105\)। पद संख्या से (1) घटाना न भूलें।
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यदि समांतर श्रेढ़ी \(10,13,16,19,\ldots\) दी हो, तो (30)वाँ पद क्या है?
If the AP \(10,13,16,19,\ldots\) is given, what is the (30)th term?
#arithmetic progression
#nth term
#formula use
A (94)
B (100)
C (87)
D (97)
Explanation opens after your attempt
Step 1
Concept
Here (a=10), (d=3), so \(a_{30}=10+29\times3=97\). The (30)th term contains (29) differences.
Step 2
Why this answer is correct
The correct answer is D. (97). Here (a=10), (d=3), so \(a_{30}=10+29\times3=97\). The (30)th term contains (29) differences.
Step 3
Exam Tip
यहाँ (a=10), (d=3) है, इसलिए \(a_{30}=10+29\times3=97\)। (30)वें पद में (29) अंतर होते हैं।
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