100 results found for "ap-formula-index-expert" 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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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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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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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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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 \(a_r=86\), \(a_{r+6}=176\) और \(a_{4r}=536\) है, तो (r) का मान क्या होगा?
If \(a_r=86\), \(a_{r+6}=176\), and \(a_{4r}=536\), what is the value of (r)?
#ap expert combined index
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
From (6d=90), (d=15). \(a_{4r}-a_r=3rd=450\), so (45r=450) and (r=10).
Step 2
Why this answer is correct
The correct answer is C. (10). From (6d=90), (d=15). \(a_{4r}-a_r=3rd=450\), so (45r=450) and (r=10).
Step 3
Exam Tip
(6d=90) से (d=15)। \(a_{4r}-a_r=3rd=450\), इसलिए (45r=450) और (r=10)।
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यदि \(a_{3n+2}=148\), \(a_{n+2}=52\) और (d=12) है, तो (n) क्या होगा?
If \(a_{3n+2}=148\), \(a_{n+2}=52\), and (d=12), what is (n)?
#ap expert index pair
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_{3n+2}-a_{n+2}=2nd=96\). From (24n=96), (n=4).
Step 2
Why this answer is correct
The correct answer is B. (4). \(a_{3n+2}-a_{n+2}=2nd=96\). From (24n=96), (n=4).
Step 3
Exam Tip
\(a_{3n+2}-a_{n+2}=2nd=96\)। (24n=96) से (n=4)।
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यदि \(a_n=17n-11\) है, तो \(a_{7k}-a_{3k}=408\) के लिए (k) क्या होगा?
If \(a_n=17n-11\), what is (k) for \(a_{7k}-a_{3k}=408\)?
#ap expert direct index
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
(a_{7k}-a_{3k}=(119k-11)-(51k-11)=68k). From (68k=408), (k=6).
Step 2
Why this answer is correct
The correct answer is B. (6). (a_{7k}-a_{3k}=(119k-11)-(51k-11)=68k). From (68k=408), (k=6).
Step 3
Exam Tip
(a_{7k}-a_{3k}=(119k-11)-(51k-11)=68k)। (68k=408) से (k=6)।
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समान्तर श्रेणी में \(a_{8n}=810\), \(a_{3n}=210\) और (d=24) है। (n) क्या है?
In an AP \(a_{8n}=810\), \(a_{3n}=210\), and (d=24). What is (n)?
#ap expert index difference
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(a_{8n}-a_{3n}=5nd=600\). From (120n=600), (n=5).
Step 2
Why this answer is correct
The correct answer is B. (5). \(a_{8n}-a_{3n}=5nd=600\). From (120n=600), (n=5).
Step 3
Exam Tip
\(a_{8n}-a_{3n}=5nd=600\)। (120n=600) से (n=5)।
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यदि \(a_1=23\), (d=14) और \(a_{5n+4}=527\) है, तो (n) का मान क्या है?
If \(a_1=23\), (d=14), and \(a_{5n+4}=527\), what is the value of (n)?
#ap expert index variable
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(527=23+(5n+3)14), so (504=70n+42), which does not give an integer option. Match the index and options carefully.
Step 2
Why this answer is correct
The correct answer is B. (7). (527=23+(5n+3)14), so (504=70n+42), which does not give an integer option. Match the index and options carefully.
Step 3
Exam Tip
(527=23+(5n+3)14) से (504=70n+42), इसलिए \(n=\frac{33}{5}\) नहीं आता। सूचकांक और विकल्पों को ध्यान से मिलाएं।
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एक समान्तर श्रेणी में \(a_9=61\) और \(a_{27}=223\) है। यदि \(a_{9r}=385\), तो (r) क्या है?
In an AP \(a_9=61\) and \(a_{27}=223\). If \(a_{9r}=385\), what is (r)?
#ap expert index equation
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{223-61}{18}=9\). From (385=61+(9r-9)9), (9r=45), so (r=5).
Step 2
Why this answer is correct
The correct answer is B. (5). \(d=\frac{223-61}{18}=9\). From (385=61+(9r-9)9), (9r=45), so (r=5).
Step 3
Exam Tip
\(d=\frac{223-61}{18}=9\)। (385=61+(9r-9)9) से (9r=45), इसलिए (r=5)।
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यदि \(a_n=10n+19\) और \(a_m=349\) है, तो \(a_{m+18}\) क्या होगा?
If \(a_n=10n+19\) and \(a_m=349\), what is \(a_{m+18}\)?
#ap expert index
A (509)
B (519)
C (529)
D (539)
Explanation opens after your attempt
Step 1
Concept
From (10m+19=349), (m=33). \(a_{51}=10\times51+19=529\).
Step 2
Why this answer is correct
The correct answer is C. (529). From (10m+19=349), (m=33). \(a_{51}=10\times51+19=529\).
Step 3
Exam Tip
(10m+19=349) से (m=33)। \(a_{51}=10\times51+19=529\)।
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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 किसी समान्तर श्रेणी में \(a_{4p}=188\), \(a_p=56\) और (d=11) है, तो (p) का मान क्या होगा?
If in an AP \(a_{4p}=188\), \(a_p=56\), and (d=11), what is the value of (p)?
#ap expert index
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_{4p}-a_p=3pd=132\) so (33p=132) and (p=4). In index questions first find the position gap.
Step 2
Why this answer is correct
The correct answer is B. (4). \(a_{4p}-a_p=3pd=132\) so (33p=132) and (p=4). In index questions first find the position gap.
Step 3
Exam Tip
\(a_{4p}-a_p=3pd=132\) इसलिए (33p=132) और (p=4)। सूचकांक वाले प्रश्न में स्थानों का अंतर पहले निकालें।
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यदि \(a_n=15n-8\) है, तो \(a_{6k}-a_{2k}=300\) के लिए (k) क्या होगा?
If \(a_n=15n-8\), what is (k) for \(a_{6k}-a_{2k}=300\)?
#ap expert direct index
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(a_{6k}-a_{2k}=(90k-8)-(30k-8)=60k). From (60k=300), (k=5).
Step 2
Why this answer is correct
The correct answer is B. (5). (a_{6k}-a_{2k}=(90k-8)-(30k-8)=60k). From (60k=300), (k=5).
Step 3
Exam Tip
(a_{6k}-a_{2k}=(90k-8)-(30k-8)=60k)। (60k=300) से (k=5)।
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समान्तर श्रेणी में \(a_{7n}=530\), \(a_{3n}=146\) और (d=16) है। (n) क्या है?
In an AP, \(a_{7n}=530\), \(a_{3n}=146\), and (d=16). What is (n)?
#ap expert index difference
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_{7n}-a_{3n}=4nd=384\). From (64n=384), (n=6).
Step 2
Why this answer is correct
The correct answer is B. (6). \(a_{7n}-a_{3n}=4nd=384\). From (64n=384), (n=6).
Step 3
Exam Tip
\(a_{7n}-a_{3n}=4nd=384\)। (64n=384) से (n=6)।
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यदि \(a_1=17\), (d=10) और \(a_{4n+3}=407\) है, तो (n) का मान क्या है?
If \(a_1=17\), (d=10), and \(a_{4n+3}=407\), what is the value of (n)?
#ap expert index variable
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
(407=17+(4n+2)10), so (390=40n+20), which does not give an integer option. Match the index and options carefully.
Step 2
Why this answer is correct
The correct answer is B. (9). (407=17+(4n+2)10), so (390=40n+20), which does not give an integer option. Match the index and options carefully.
Step 3
Exam Tip
(407=17+(4n+2)10) से (390=40n+20), इसलिए \(n=\frac{37}{4}\) नहीं आता। सूचकांक और विकल्पों को सावधानी से मिलाएं।
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एक समान्तर श्रेणी में \(a_8=52\) और \(a_{23}=172\) है। यदि \(a_{8r}=292\), तो (r) क्या है?
In an AP, \(a_8=52\) and \(a_{23}=172\). If \(a_{8r}=292\), what is (r)?
#ap expert index equation
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{172-52}{15}=8\). From (292=52+(8r-8)8), (8r=38), so \(r=\frac{19}{4}\); no integer option is correct.
Step 2
Why this answer is correct
The correct answer is B. (5). \(d=\frac{172-52}{15}=8\). From (292=52+(8r-8)8), (8r=38), so \(r=\frac{19}{4}\); no integer option is correct.
Step 3
Exam Tip
\(d=\frac{172-52}{15}=8\)। (292=52+(8r-8)8) से (8r=38), इसलिए \(r=\frac{19}{4}\), पूर्णांक विकल्प नहीं है।
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यदि \(a_n=8n+15\) और \(a_m=239\) है, तो \(a_{m+16}\) क्या होगा?
If \(a_n=8n+15\) and \(a_m=239\), what is \(a_{m+16}\)?
#ap expert index
A (359)
B (367)
C (375)
D (383)
Explanation opens after your attempt
Step 1
Concept
From (8m+15=239), (m=28). \(a_{44}=8\times44+15=367\).
Step 2
Why this answer is correct
The correct answer is B. (367). From (8m+15=239), (m=28). \(a_{44}=8\times44+15=367\).
Step 3
Exam Tip
(8m+15=239) से (m=28)। \(a_{44}=8\times44+15=367\)।
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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 \(a_{3m}=152\), \(a_m=56\) और (d=8) है, तो (m) का मान क्या होगा?
If \(a_{3m}=152\), \(a_m=56\), and (d=8), what is the value of (m)?
#ap expert index
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_{3m}-a_m=2md=96\), so (16m=96) and (m=6). In index questions, first check the position gap.
Step 2
Why this answer is correct
The correct answer is B. (6). \(a_{3m}-a_m=2md=96\), so (16m=96) and (m=6). In index questions, first check the position gap.
Step 3
Exam Tip
\(a_{3m}-a_m=2md=96\), इसलिए (16m=96) और (m=6)। सूचकांक वाले प्रश्न में स्थानों का अंतर पहले देखें।
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एक समान्तर श्रेणी में \(a_7=38\) और \(a_{19}=122\) है। यदि \(a_{7r}=234\), तो (r) क्या है?
In an AP, \(a_7=38\) and \(a_{19}=122\). If \(a_{7r}=234\), what is (r)?
#ap expert index equation
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{122-38}{12}=7\). From (234=38+(7r-7)7), (r=5).
Step 2
Why this answer is correct
The correct answer is B. (5). \(d=\frac{122-38}{12}=7\). From (234=38+(7r-7)7), (r=5).
Step 3
Exam Tip
\(d=\frac{122-38}{12}=7\)। (234=38+(7r-7)7) से (r=5)।
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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 \(a_{r}=52\), \(a_{r+5}=92\) और \(a_{3r}=212\) है, तो (r) का मान क्या होगा?
If \(a_r=52\), \(a_{r+5}=92\), and \(a_{3r}=212\), what is the value of (r)?
#ap-combined-index-expert
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
From (5d=40), (d=8). \(a_{3r}-a_r=2rd=160\), so (16r=160) and (r=10).
Step 2
Why this answer is correct
The correct answer is C. (10). From (5d=40), (d=8). \(a_{3r}-a_r=2rd=160\), so (16r=160) and (r=10).
Step 3
Exam Tip
(5d=40) से (d=8)। \(a_{3r}-a_r=2rd=160\), इसलिए (16r=160) और (r=10)।
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यदि \(a_{2n+1}=89\), \(a_{n+1}=41\) और (d=6) है, तो (n) क्या होगा?
If \(a_{2n+1}=89\), \(a_{n+1}=41\), and (d=6), what is (n)?
#ap-index-pair-expert
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(a_{2n+1}-a_{n+1}=nd=48\). From (6n=48), (n=8).
Step 2
Why this answer is correct
The correct answer is C. (8). \(a_{2n+1}-a_{n+1}=nd=48\). From (6n=48), (n=8).
Step 3
Exam Tip
\(a_{2n+1}-a_{n+1}=nd=48\)। (6n=48) से (n=8)।
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यदि \(a_n=13n-6\) है, तो \(a_{5k}-a_{2k}=234\) के लिए (k) क्या होगा?
If \(a_n=13n-6\), what is (k) for \(a_{5k}-a_{2k}=234\)?
#ap-direct-index-expert
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
(a_{5k}-a_{2k}=(65k-6)-(26k-6)=39k). From (39k=234), (k=6).
Step 2
Why this answer is correct
The correct answer is B. (6). (a_{5k}-a_{2k}=(65k-6)-(26k-6)=39k). From (39k=234), (k=6).
Step 3
Exam Tip
(a_{5k}-a_{2k}=(65k-6)-(26k-6)=39k)। (39k=234) से (k=6)।
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समान्तर श्रेणी में \(a_{6n}=319\), \(a_{2n}=95\) और (d=14) है। (n) क्या है?
In an AP, \(a_{6n}=319\), \(a_{2n}=95\), and (d=14). What is (n)?
#ap-index-difference-expert
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_{6n}-a_{2n}=4nd=224\). From (56n=224), (n=4).
Step 2
Why this answer is correct
The correct answer is B. (4). \(a_{6n}-a_{2n}=4nd=224\). From (56n=224), (n=4).
Step 3
Exam Tip
\(a_{6n}-a_{2n}=4nd=224\)। (56n=224) से (n=4)।
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यदि \(a_1=11\), (d=8) और \(a_{3n+4}=275\) है, तो (n) का मान क्या है?
If \(a_1=11\), (d=8), and \(a_{3n+4}=275\), what is the value of (n)?
#ap-index-variable-expert
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
From (275=11+(3n+3)8), (264=24n+24), so (n=10). Subtract (1) from the index to get the multiplier of (d).
Step 2
Why this answer is correct
The correct answer is B. (10). From (275=11+(3n+3)8), (264=24n+24), so (n=10). Subtract (1) from the index to get the multiplier of (d).
Step 3
Exam Tip
(275=11+(3n+3)8) से (264=24n+24), इसलिए (n=10)। सूचकांक से (1) घटाकर (d) का गुणक बनाएं।
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एक समान्तर श्रेणी में \(a_7=38\) और \(a_{19}=122\) है। यदि \(a_{7r}=206\), तो (r) क्या है?
In an AP, \(a_7=38\) and \(a_{19}=122\). If \(a_{7r}=206\), what is (r)?
#ap-index-equation-expert
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{122-38}{12}=7\). From (206=38+(7r-7)7), (7r=31), so no integer option is correct.
Step 2
Why this answer is correct
The correct answer is B. (5). \(d=\frac{122-38}{12}=7\). From (206=38+(7r-7)7), (7r=31), so no integer option is correct.
Step 3
Exam Tip
\(d=\frac{122-38}{12}=7\)। (206=38+(7r-7)7) से (7r=31), इसलिए कोई पूर्णांक विकल्प सही नहीं है।
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यदि \(a_n=6n+13\) और \(a_m=181\) है, तो \(a_{m+14}\) क्या होगा?
If \(a_n=6n+13\) and \(a_m=181\), what is \(a_{m+14}\)?
#ap-index-expert
A (259)
B (265)
C (271)
D (277)
Explanation opens after your attempt
Step 1
Concept
From (6m+13=181), (m=28). \(a_{42}=6\times42+13=265\).
Step 2
Why this answer is correct
The correct answer is B. (265). From (6m+13=181), (m=28). \(a_{42}=6\times42+13=265\).
Step 3
Exam Tip
(6m+13=181) से (m=28)। \(a_{42}=6\times42+13=265\)।
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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 \(a_n=17n+c\) और \(a_7=145\) है तो \(a_{3r}=757\) होने पर (r) क्या है?
If \(a_n=17n+c\) and \(a_7=145\), what is (r) when \(a_{3r}=757\)?
#ap parameter index hard
A (13)
B (14)
C (15)
D (16)
Explanation opens after your attempt
Step 1
Concept
From (145=119+c), (c=26). (757=51r+26), giving \(r=\frac{731}{51}\), so option checking is necessary.
Step 2
Why this answer is correct
The correct answer is B. (14). From (145=119+c), (c=26). (757=51r+26), giving \(r=\frac{731}{51}\), so option checking is necessary.
Step 3
Exam Tip
(145=119+c) से (c=26)। (757=51r+26) से \(r=\frac{731}{51}\) आता है इसलिए विकल्पों की जांच जरूरी है।
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यदि \(a_n=11n-5\) है तो \(a_{4k}-a_k=198\) के लिए (k) क्या होगा?
If \(a_n=11n-5\), what is (k) for \(a_{4k}-a_k=198\)?
#ap direct index hard
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(a_{4k}-a_k=(44k-5)-(11k-5)=33k). From (33k=198), (k=6).
Step 2
Why this answer is correct
The correct answer is C. (6). (a_{4k}-a_k=(44k-5)-(11k-5)=33k). From (33k=198), (k=6).
Step 3
Exam Tip
(a_{4k}-a_k=(44k-5)-(11k-5)=33k)। (33k=198) से (k=6)।
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समान्तर श्रेणी में \(a_{5n}=205\), \(a_n=49\) और (d=13) है। (n) क्या है?
In an AP, \(a_{5n}=205\), \(a_n=49\), and (d=13). What is (n)?
#ap index difference hard
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_{5n}-a_n=4nd=156\). From (52n=156), (n=3).
Step 2
Why this answer is correct
The correct answer is A. (3). \(a_{5n}-a_n=4nd=156\). From (52n=156), (n=3).
Step 3
Exam Tip
\(a_{5n}-a_n=4nd=156\)। (52n=156) से (n=3)।
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यदि \(a_1=8\), (d=9) और \(a_{3n+2}=197\) है तो (n) का मान क्या है?
If \(a_1=8\), (d=9), and \(a_{3n+2}=197\), what is the value of (n)?
#ap index variable hard
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(197=8+(3n+1)9), so (189=27n+9) and \(n=\frac{20}{3}\). Read the index carefully before selecting an integer option.
Step 2
Why this answer is correct
The correct answer is B. (7). (197=8+(3n+1)9), so (189=27n+9) and \(n=\frac{20}{3}\). Read the index carefully before selecting an integer option.
Step 3
Exam Tip
(197=8+(3n+1)9) से (189=27n+9) इसलिए \(n=\frac{20}{3}\) नहीं आता। सूचकांक ठीक पढ़ना जरूरी है।
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एक समान्तर श्रेणी में \(a_5=27\) और \(a_{17}=111\) है। \(a_{5r}\) का मान (195) है तो (r) क्या है?
In an AP, \(a_5=27\) and \(a_{17}=111\). If \(a_{5r}=195\), what is (r)?
#ap index equation hard
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{111-27}{12}=7\). From (195=27+(5r-5)7), (5r=29), so \(r=\frac{29}{5}\).
Step 2
Why this answer is correct
The correct answer is A. (5). \(d=\frac{111-27}{12}=7\). From (195=27+(5r-5)7), (5r=29), so \(r=\frac{29}{5}\).
Step 3
Exam Tip
\(d=\frac{111-27}{12}=7\)। (195=27+(5r-5)7) से (5r=29) इसलिए \(r=\frac{29}{5}\)।
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यदि \(a_n=4n+9\) और \(a_m=137\) है तो \(a_{m+15}\) क्या होगा?
If \(a_n=4n+9\) and \(a_m=137\), what is \(a_{m+15}\)?
#ap index hard
A (189)
B (193)
C (197)
D (201)
Explanation opens after your attempt
Step 1
Concept
From (4m+9=137), (m=32). \(a_{47}=4\times47+9=197\).
Step 2
Why this answer is correct
The correct answer is C. (197). From (4m+9=137), (m=32). \(a_{47}=4\times47+9=197\).
Step 3
Exam Tip
(4m+9=137) से (m=32)। \(a_{47}=4\times47+9=197\)।
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किसी समान्तर श्रेणी में \(a_p=42\), \(a_{p+12}=150\) और (p=9) है। \(a_{40}\) क्या होगा?
In an AP, \(a_p=42\), \(a_{p+12}=150\), and (p=9). What is \(a_{40}\)?
#ap symbolic index hard
A (321)
B (330)
C (339)
D (348)
Explanation opens after your attempt
Step 1
Concept
From (12d=108), (d=9). \(a_{40}=a_9+31d=42+279=321\).
Step 2
Why this answer is correct
The correct answer is A. (321). From (12d=108), (d=9). \(a_{40}=a_9+31d=42+279=321\).
Step 3
Exam Tip
(12d=108) से (d=9)। \(a_{40}=a_9+31d=42+279=321\)।
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किसी समान्तर श्रेणी में \(a_{4m}=156\), \(a_m=48\) और (d=6) है। (m) का मान क्या है?
In an AP, \(a_{4m}=156\), \(a_m=48\), and (d=6). What is the value of (m)?
#ap index difference hard
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_{4m}-a_m=3md=108\). From (18m=108), (m=6).
Step 2
Why this answer is correct
The correct answer is B. (6). \(a_{4m}-a_m=3md=108\). From (18m=108), (m=6).
Step 3
Exam Tip
\(a_{4m}-a_m=3md=108\) है। (18m=108) से (m=6)।
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यदि \(a_n=13n+c\) और \(a_6=101\) है तो \(a_{4r}=465\) होने पर (r) क्या है?
If \(a_n=13n+c\) and \(a_6=101\), what is (r) when \(a_{4r}=465\)?
#ap-parameter-index-hard
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
From (101=78+c), (c=23). (465=52r+23), so \(r=\frac{442}{52}=8.5\).
Step 2
Why this answer is correct
The correct answer is B. (9). From (101=78+c), (c=23). (465=52r+23), so \(r=\frac{442}{52}=8.5\).
Step 3
Exam Tip
(101=78+c) से (c=23)। (465=52r+23) से \(r=\frac{442}{52}=8.5\)।
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यदि \(a_n=9n+2\) है तो \(a_{3k}-a_k=144\) के लिए (k) क्या होगा?
If \(a_n=9n+2\), what is (k) for \(a_{3k}-a_k=144\)?
#ap-direct-index-hard
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(a_{3k}-a_k=(27k+2)-(9k+2)=18k). From (18k=144), (k=8).
Step 2
Why this answer is correct
The correct answer is C. (8). (a_{3k}-a_k=(27k+2)-(9k+2)=18k). From (18k=144), (k=8).
Step 3
Exam Tip
(a_{3k}-a_k=(27k+2)-(9k+2)=18k)। (18k=144) से (k=8)।
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समान्तर श्रेणी में \(a_{4n}=140\), \(a_n=32\) और (d=6) है। (n) क्या है?
In an AP, \(a_{4n}=140\), \(a_n=32\), and (d=6). What is (n)?
#ap-index-difference-hard
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_{4n}-a_n=3nd=108\). From (18n=108), (n=6).
Step 2
Why this answer is correct
The correct answer is B. (6). \(a_{4n}-a_n=3nd=108\). From (18n=108), (n=6).
Step 3
Exam Tip
\(a_{4n}-a_n=3nd=108\)। (18n=108) से (n=6)।
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यदि \(a_1=5\), (d=7) और \(a_{2n+3}=159\) है तो (n) का मान क्या है?
If \(a_1=5\), (d=7), and \(a_{2n+3}=159\), what is the value of (n)?
#ap-index-variable-hard
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
From (159=5+(2n+2)7), (154=14n+14). Therefore (n=10).
Step 2
Why this answer is correct
The correct answer is B. (10). From (159=5+(2n+2)7), (154=14n+14). Therefore (n=10).
Step 3
Exam Tip
(159=5+(2n+2)7) से (154=14n+14)। इसलिए (n=10)।
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एक समान्तर श्रेणी में \(a_4=18\) और \(a_{16}=78\) है। \(a_{4r}\) का मान (138) है तो (r) क्या है?
In an AP, \(a_4=18\) and \(a_{16}=78\). If \(a_{4r}=138\), what is (r)?
#ap-index-equation-hard
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{78-18}{12}=5\). From (138=18+(4r-4)5), (4r=28), so (r=7).
Step 2
Why this answer is correct
The correct answer is A. (7). \(d=\frac{78-18}{12}=5\). From (138=18+(4r-4)5), (4r=28), so (r=7).
Step 3
Exam Tip
\(d=\frac{78-18}{12}=5\)। (138=18+(4r-4)5) से (4r=28) इसलिए (r=7)।
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यदि \(a_n=3n+4\) और \(a_m=91\) है तो \(a_{m+12}\) क्या होगा?
If \(a_n=3n+4\) and \(a_m=91\), what is \(a_{m+12}\)?
#ap-index-hard
A (121)
B (124)
C (127)
D (130)
Explanation opens after your attempt
Step 1
Concept
From (3m+4=91), (m=29). \(a_{41}=3\times41+4=127\).
Step 2
Why this answer is correct
The correct answer is C. (127). From (3m+4=91), (m=29). \(a_{41}=3\times41+4=127\).
Step 3
Exam Tip
(3m+4=91) से (m=29)। \(a_{41}=3\times41+4=127\)।
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किसी समान्तर श्रेणी में \(a_p=29\), \(a_{p+10}=99\) और (p=8) है। \(a_{35}\) क्या होगा?
In an AP, \(a_p=29\), \(a_{p+10}=99\), and (p=8). What is \(a_{35}\)?
#ap-symbolic-index-hard
A (218)
B (225)
C (232)
D (239)
Explanation opens after your attempt
Step 1
Concept
From (10d=70), (d=7). \(a_{35}=a_8+27d=29+189=218\).
Step 2
Why this answer is correct
The correct answer is A. (218). From (10d=70), (d=7). \(a_{35}=a_8+27d=29+189=218\).
Step 3
Exam Tip
(10d=70) से (d=7)। \(a_{35}=a_8+27d=29+189=218\)।
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किसी समान्तर श्रेणी में \(a_{3m}=94\), \(a_m=34\) और (d=5) है। (m) का मान क्या है?
In an AP, \(a_{3m}=94\), \(a_m=34\), and (d=5). What is the value of (m)?
#ap-index-difference-hard
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_{3m}-a_m=2md=60\). From (10m=60), (m=6).
Step 2
Why this answer is correct
The correct answer is B. (6). \(a_{3m}-a_m=2md=60\). From (10m=60), (m=6).
Step 3
Exam Tip
\(a_{3m}-a_m=2md=60\) है। (10m=60) से (m=6)।
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यदि \(a_{n}=11n+c\) और \(a_{5}=72\) है तो \(a_{5r}\) का मान (512) होने पर (r) क्या है?
If \(a_n=11n+c\) and \(a_5=72\), what is (r) when \(a_{5r}=512\)?
#ap-parameter-index-hard
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
From (72=55+c), (c=17). From (512=55r+17), (r=9).
Step 2
Why this answer is correct
The correct answer is B. (9). From (72=55+c), (c=17). From (512=55r+17), (r=9).
Step 3
Exam Tip
(72=55+c) से (c=17)। (512=55r+17) से (r=9)।
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यदि \(a_n=7n-4\) है तो \(a_{2k}-a_k=84\) के लिए (k) क्या होगा?
If \(a_n=7n-4\), what is (k) for \(a_{2k}-a_k=84\)?
#ap-direct-index-hard
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
(a_{2k}-a_k=(14k-4)-(7k-4)=7k). From (7k=84), (k=12).
Step 2
Why this answer is correct
The correct answer is C. (12). (a_{2k}-a_k=(14k-4)-(7k-4)=7k). From (7k=84), (k=12).
Step 3
Exam Tip
(a_{2k}-a_k=(14k-4)-(7k-4)=7k)। (7k=84) से (k=12)।
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समान्तर श्रेणी में \(a_{3n}=81\), \(a_n=21\) और (d=5) है। (n) क्या है?
In an AP, \(a_{3n}=81\), \(a_n=21\), and (d=5). What is (n)?
#ap-index-difference-hard
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_{3n}-a_n=2nd=60\). From (10n=60), (n=6).
Step 2
Why this answer is correct
The correct answer is B. (6). \(a_{3n}-a_n=2nd=60\). From (10n=60), (n=6).
Step 3
Exam Tip
\(a_{3n}-a_n=2nd=60\)। (10n=60) से (n=6)।
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यदि \(a_1=3\) और \(a_{2n+1}=123\) है तथा (d=4) है तो (n) का मान क्या है?
If \(a_1=3\), \(a_{2n+1}=123\), and (d=4), what is the value of (n)?
#ap-index-variable-hard
A (14)
B (15)
C (16)
D (17)
Explanation opens after your attempt
Step 1
Concept
From \(123=3+2n\cdot4\), (120=8n), so (n=15). In index (2n+1), subtract (1) to get the multiplier.
Step 2
Why this answer is correct
The correct answer is B. (15). From \(123=3+2n\cdot4\), (120=8n), so (n=15). In index (2n+1), subtract (1) to get the multiplier.
Step 3
Exam Tip
\(123=3+2n\cdot4\) से (120=8n) इसलिए (n=15)। सूचकांक (2n+1) में (1) घटाकर गुणक लें।
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एक समान्तर श्रेणी में \(a_3=11\) और \(a_{13}=51\) है। \(a_{3r}\) का मान (91) है तो (r) क्या है?
In an AP, \(a_3=11\) and \(a_{13}=51\). If \(a_{3r}=91\), what is (r)?
#ap-index-equation-hard
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{51-11}{10}=4\). From (91=11+(3r-3)4), (3r=21), so (r=7).
Step 2
Why this answer is correct
The correct answer is C. (7). \(d=\frac{51-11}{10}=4\). From (91=11+(3r-3)4), (3r=21), so (r=7).
Step 3
Exam Tip
\(d=\frac{51-11}{10}=4\)। (91=11+(3r-3)4) से (3r=21) इसलिए (r=7)।
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यदि \(a_{n}=2n-1\) और \(a_m=63\) है तो \(a_{m+10}\) क्या होगा?
If \(a_n=2n-1\) and \(a_m=63\), what is \(a_{m+10}\)?
#ap-index-hard
A (81)
B (83)
C (85)
D (87)
Explanation opens after your attempt
Step 1
Concept
From (2m-1=63), (m=32). \(a_{42}=2\times42-1=83\).
Step 2
Why this answer is correct
The correct answer is B. (83). From (2m-1=63), (m=32). \(a_{42}=2\times42-1=83\).
Step 3
Exam Tip
(2m-1=63) से (m=32)। \(a_{42}=2\times42-1=83\)।
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किसी समान्तर श्रेणी में \(a_{p}=17\), \(a_{p+8}=65\) और (p=6) है। \(a_{30}\) क्या होगा?
In an AP, \(a_p=17\), \(a_{p+8}=65\), and (p=6). What is \(a_{30}\)?
#ap-symbolic-index-hard
A (155)
B (161)
C (167)
D (173)
Explanation opens after your attempt
Step 1
Concept
From (8d=48), (d=6). \(a_{30}=a_6+24d=17+144=161\).
Step 2
Why this answer is correct
The correct answer is B. (161). From (8d=48), (d=6). \(a_{30}=a_6+24d=17+144=161\).
Step 3
Exam Tip
(8d=48) से (d=6)। \(a_{30}=a_6+24d=17+144=161\)।
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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 \(q=2^r5^s\) और \(\frac{p}{q}\) सरलतम रूप में है, तो दशमलव को \(\frac{N}{10^k}\) के रूप में लिखने के लिए न्यूनतम (k) क्या होगा?
If \(q=2^r5^s\) and \(\frac{p}{q}\) is in lowest form, what is the minimum (k) to write the decimal as \(\frac{N}{10^k}\)?
#general-formula
#powers-of-10
#terminating-decimal
#expert
A (\min(r,s))
B (\max(r,s))
C (r+s)
D (rs)
Explanation opens after your attempt
Correct Answer
B. (\max(r,s))
Step 1
Concept
To form \(10^k=2^k5^k\), both powers must reach at least the larger exponent. Therefore the minimum (k=\max(r,s)).
Step 2
Why this answer is correct
The correct answer is B. (\max(r,s)). To form \(10^k=2^k5^k\), both powers must reach at least the larger exponent. Therefore the minimum (k=\max(r,s)).
Step 3
Exam Tip
\(10^k=2^k5^k\) बनाने के लिए दोनों घातें कम से कम बड़ी घात तक पहुँचनी चाहिए। इसलिए न्यूनतम (k=\max(r,s)) है।
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