70 results found for "b calculation" in Class 10.
यदि \(28,21,14,7,\ldots\) में (d) ज्ञात करना हो तो सही गणना कौन सी है?
If (d) is to be found in \(28,21,14,7,\ldots\), which calculation is correct?
#ap
#correct calculation
#negative d
#medium
A (28-21=7)
B (28+21=49)
C (21-28=-7)
D \(28\times21=588\)
Explanation opens after your attempt
Correct Answer
C. (21-28=-7)
Step 1
Concept
The common difference is next term minus previous term, so (21-28=-7). In a decreasing sequence the order of subtraction is very important.
Step 2
Why this answer is correct
The correct answer is C. (21-28=-7). The common difference is next term minus previous term, so (21-28=-7). In a decreasing sequence the order of subtraction is very important.
Step 3
Exam Tip
सार्व अंतर अगला पद घटा पिछला पद है इसलिए (21-28=-7)। घटते अनुक्रम में घटाव का क्रम बहुत जरूरी है।
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यदि \(15,10,5,0,\ldots\) में (d) ज्ञात करना हो तो सही गणना कौन सी है?
If (d) is to be found in \(15,10,5,0,\ldots\), which calculation is correct?
#ap
#correct calculation
#negative d
#medium
A (15-10=5)
B (15+10=25)
C (10-15=-5)
D \(15\times10=150\)
Explanation opens after your attempt
Correct Answer
C. (10-15=-5)
Step 1
Concept
The common difference is next term minus previous term, so (10-15=-5). In a decreasing sequence the order of subtraction is very important.
Step 2
Why this answer is correct
The correct answer is C. (10-15=-5). The common difference is next term minus previous term, so (10-15=-5). In a decreasing sequence the order of subtraction is very important.
Step 3
Exam Tip
सार्व अंतर बाद वाला पद घटा पहले वाला पद है इसलिए (10-15=-5)। घटते अनुक्रम में घटाव का क्रम बहुत जरूरी है।
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खिलाफत और असहयोग आंदोलनों के मेल में गांधीजी की सबसे बड़ी राजनीतिक गणना क्या थी?
What was Gandhi's main political calculation in linking Khilafat and Non-Cooperation movements?
#indian freedom movement
#khilafat
#non cooperation
A कांग्रेस को केवल चुनावी दल बनाना / To make Congress only an electoral party
B हिंदू मुस्लिम जनाधार को साझा औपनिवेशिक विरोध में जोड़ना / To unite Hindu-Muslim mass base in common anti-colonial opposition
C ब्रिटिश शासन को स्थायी बनाना / To make British rule permanent
D रियासतों को स्वतंत्र छोड़ना / To leave princely states independent
Explanation opens after your attempt
Correct Answer
B. हिंदू मुस्लिम जनाधार को साझा औपनिवेशिक विरोध में जोड़ना / To unite Hindu-Muslim mass base in common anti-colonial opposition
Step 1
Concept
Gandhi tried to build wider mass unity. Exam tip: remember both alliance and mass base.
Step 2
Why this answer is correct
The correct answer is B. हिंदू मुस्लिम जनाधार को साझा औपनिवेशिक विरोध में जोड़ना / To unite Hindu-Muslim mass base in common anti-colonial opposition. Gandhi tried to build wider mass unity. Exam tip: remember both alliance and mass base.
Step 3
Exam Tip
गांधीजी ने व्यापक जन एकता बनाने की कोशिश की। परीक्षा में गठबंधन और जनाधार दोनों याद रखें।
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माया सभ्यता की कौन सी उपलब्धि खगोल और समय गणना से सबसे अधिक जुड़ी है?
Which achievement of the Maya civilization is most strongly linked with astronomy and time calculation?
#world history
#ancient civilizations
#maya
#calendar
A जिगुरात / Ziggurats
B पिरामिड समाधियां / Pyramid tombs
C उन्नत पंचांग प्रणाली / Advanced calendar system
D लौह रथ / Iron chariots
Explanation opens after your attempt
Correct Answer
C. उन्नत पंचांग प्रणाली / Advanced calendar system
Step 1
Concept
The Maya are famous for astronomy and calendars. For exams connect the Maya with Mesoamerica.
Step 2
Why this answer is correct
The correct answer is C. उन्नत पंचांग प्रणाली / Advanced calendar system. The Maya are famous for astronomy and calendars. For exams connect the Maya with Mesoamerica.
Step 3
Exam Tip
माया सभ्यता खगोल ज्ञान और कैलेंडर के लिए प्रसिद्ध है। परीक्षा में माया को मेसोअमेरिका से जोड़ें।
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लखनऊ समझौते में कांग्रेस द्वारा पृथक निर्वाचक मंडल स्वीकार करना किस राजनीतिक गणना को दिखाता है?
Congress accepting separate electorates in the Lucknow Pact shows which political calculation?
#modern indian history
#lucknow pact
#separate electorates
A स्वदेशी शिक्षा समाप्त करना / Ending Swadeshi education
B कंपनी शासन लौटाना / Restoring Company rule
C मुस्लिम लीग के साथ संयुक्त औपनिवेशिक विरोध बनाना / Creating a united anti-colonial front with Muslim League
D भारत को तुरंत गणतंत्र बनाना / Making India a republic immediately
Explanation opens after your attempt
Correct Answer
C. मुस्लिम लीग के साथ संयुक्त औपनिवेशिक विरोध बनाना / Creating a united anti-colonial front with Muslim League
Step 1
Concept
Congress made this compromise for wider political unity. Exam tip: remember both achievement and limitation of the Pact.
Step 2
Why this answer is correct
The correct answer is C. मुस्लिम लीग के साथ संयुक्त औपनिवेशिक विरोध बनाना / Creating a united anti-colonial front with Muslim League. Congress made this compromise for wider political unity. Exam tip: remember both achievement and limitation of the Pact.
Step 3
Exam Tip
कांग्रेस ने व्यापक राजनीतिक एकता के लिए यह समझौता किया। परीक्षा में समझौते की उपलब्धि और सीमा दोनों याद रखें।
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समीकरणों (4x+3y=34) और (2x-y=4) के लिए (x) का मान क्या है?
For (4x+3y=34) and (2x-y=4), what is the value of (x)?
#linear equations
#substitution
#careful calculation
#medium
#class 10
A (x=3)
B (x=4)
C (x=5)
D (x=6)
Explanation opens after your attempt
Step 1
Concept
From the second equation use (y=2x-4). Correct substitution gives (4x+6x-12=34), so \(x=\frac{23}{5}\).
Step 2
Why this answer is correct
The correct answer is C. (x=5). From the second equation use (y=2x-4). Correct substitution gives (4x+6x-12=34), so \(x=\frac{23}{5}\).
Step 3
Exam Tip
दूसरे समीकरण से (y=2x-4) रखें। पहले में रखने पर (10x-12=34) नहीं, सही गणना (4x+6x-12=34) से \(x=\frac{23}{5}\) आती है।
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(2x+3y=18) में (y=4) रखने पर (x) क्या होगा?
In (2x+3y=18), if (y=4), what is (x)?
#linear equations
#substitution
#calculation
#easy
#class 10
A (x=3)
B (x=4)
C (x=5)
D (x=6)
Explanation opens after your attempt
Step 1
Concept
(2x+12=18), so (2x=6) and (x=3). Multiply first and then separate the constant term.
Step 2
Why this answer is correct
The correct answer is A. (x=3). (2x+12=18), so (2x=6) and (x=3). Multiply first and then separate the constant term.
Step 3
Exam Tip
(2x+12=18), इसलिए (2x=6) और (x=3)। पहले गुणा करके स्थिर पद अलग करें।
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प्रतिस्थापन विधि से (3x+y=10) में (x=2) रखने पर (y) क्या होगा?
Using substitution in (3x+y=10), if (x=2), what is (y)?
#linear equations
#substitution
#simple calculation
#easy
#class 10
A (y=4)
B (y=3)
C (y=2)
D (y=5)
Explanation opens after your attempt
Step 1
Concept
(3(2)+y=10), so (6+y=10) and (y=4). Multiply first and then subtract.
Step 2
Why this answer is correct
The correct answer is A. (y=4). (3(2)+y=10), so (6+y=10) and (y=4). Multiply first and then subtract.
Step 3
Exam Tip
(3(2)+y=10), इसलिए (6+y=10) और (y=4)। गुणा पहले और घटाव बाद में करें।
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\(4^0+5^2\) का मान क्या है?
What is the value of \(4^0+5^2\)?
#polynomials
#zero exponent
#calculation
A (25)
B (26)
C (29)
D (30)
Explanation opens after your attempt
Step 1
Concept
Here \(4^0=1\) and \(5^2=25\). Therefore (1+25=26).
Step 2
Why this answer is correct
The correct answer is B. (26). Here \(4^0=1\) and \(5^2=25\). Therefore (1+25=26).
Step 3
Exam Tip
यहाँ \(4^0=1\) और \(5^2=25\) है। इसलिए (1+25=26) है।
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\(9^0+3^2\) का मान क्या है?
What is the value of \(9^0+3^2\)?
#polynomials
#zero exponent
#calculation
A (9)
B (10)
C (18)
D (82)
Explanation opens after your attempt
Step 1
Concept
Here \(9^0=1\) and \(3^2=9\). Therefore (1+9=10).
Step 2
Why this answer is correct
The correct answer is B. (10). Here \(9^0=1\) and \(3^2=9\). Therefore (1+9=10).
Step 3
Exam Tip
यहाँ \(9^0=1\) और \(3^2=9\) है। इसलिए (1+9=10) है।
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\(3x^2-11x+2=0\) का विविक्तकर (D) क्या है?
What is the discriminant (D) of \(3x^2-11x+2=0\)?
#quadratic
#discriminant
#calculation
A (97)
B (121)
C (73)
D (105)
Explanation opens after your attempt
Step 1
Concept
Here (D=(-11)2 -4(3)(2)=97). In exams, identify (a,b,c) correctly while finding (D).
Step 2
Why this answer is correct
The correct answer is A. (97). Here (D=(-11)2 -4(3)(2)=97). In exams, identify (a,b,c) correctly while finding (D).
Step 3
Exam Tip
यहां (D=(-11)2 -4(3)(2)=97) है। परीक्षा में (a,b,c) सही पहचानकर (D) निकालें।
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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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\(2x^2-7x+1=0\) का विविक्तकर (D) क्या है?
What is the discriminant (D) of \(2x^2-7x+1=0\)?
#quadratic
#discriminant
#calculation
A (41)
B (49)
C (33)
D (57)
Explanation opens after your attempt
Step 1
Concept
Here (D=(-7)2 -4(2)(1)=41). In exams, identify (a,b,c) correctly while finding (D).
Step 2
Why this answer is correct
The correct answer is A. (41). Here (D=(-7)2 -4(2)(1)=41). In exams, identify (a,b,c) correctly while finding (D).
Step 3
Exam Tip
यहां (D=(-7)2 -4(2)(1)=41) है। परीक्षा में (D) निकालते समय (a,b,c) सही पहचानें।
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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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\(4x^2-8x-1=0\) का विविक्तकर (D) क्या है?
What is the discriminant (D) of \(4x^2-8x-1=0\)?
#quadratic
#discriminant
#calculation
A (80)
B (64)
C (48)
D (16)
Explanation opens after your attempt
Step 1
Concept
Here (D=(-8)2 -4(4)(-1)=80). In exams, a negative (c) increases (D).
Step 2
Why this answer is correct
The correct answer is A. (80). Here (D=(-8)2 -4(4)(-1)=80). In exams, a negative (c) increases (D).
Step 3
Exam Tip
यहां (D=(-8)2 -4(4)(-1)=80) है। परीक्षा में ऋणात्मक (c) से (D) बढ़ जाता 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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\(x^2+2x+1=0\) का विविक्तकर (D) क्या होगा?
What will be the discriminant (D) of \(x^2+2x+1=0\)?
#quadratic
#discriminant
#calculation
A (0)
B (1)
C (2)
D (4)
Explanation opens after your attempt
Step 1
Concept
Here (D=22 -4(1)(1)=0). In exams, (D=0) gives equal roots.
Step 2
Why this answer is correct
The correct answer is A. (0). Here (D=22 -4(1)(1)=0). In exams, (D=0) gives equal roots.
Step 3
Exam Tip
यहां (D=22 -4(1)(1)=0) है। परीक्षा में (D=0) से समान मूल मिलते हैं।
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\(x^2-2x+1=0\) का विविक्तकर (D) क्या होगा?
What will be the discriminant (D) of \(x^2-2x+1=0\)?
#quadratic
#discriminant
#calculation
A (0)
B (1)
C (2)
D (4)
Explanation opens after your attempt
Step 1
Concept
Here (D=(-2)2 -4(1)(1)=0). In exams, square (b) with its sign.
Step 2
Why this answer is correct
The correct answer is A. (0). Here (D=(-2)2 -4(1)(1)=0). In exams, square (b) with its sign.
Step 3
Exam Tip
यहां (D=(-2)2 -4(1)(1)=0) है। परीक्षा में (b) का चिन्ह लगाकर वर्ग करें।
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\(x^2-4x+4=0\) का विविक्तकर (D) क्या है?
What is the discriminant (D) of \(x^2-4x+4=0\)?
#quadratic
#discriminant
#calculation
A (0)
B (4)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
Here (a=1), (b=-4), (c=4), so (D=(-4)2 -4(1)(4)=0). In exams, use (b) with its sign.
Step 2
Why this answer is correct
The correct answer is A. (0). Here (a=1), (b=-4), (c=4), so (D=(-4)2 -4(1)(4)=0). In exams, use (b) with its sign.
Step 3
Exam Tip
यहां (a=1), (b=-4), (c=4), इसलिए (D=(-4)2 -4(1)(4)=0)। परीक्षा में संकेत सहित (b) रखें।
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यदि \(\alpha\) और \(\beta\) समीकरण \(6x^2+5x-4=0\) के मूल हैं तो \(\alpha\beta\) क्या है?
If \(\alpha\) and \(\beta\) are roots of \(6x^2+5x-4=0\), what is \(\alpha\beta\)?
#roots
#product_of_roots
#calculation
A -\(\frac{2}{3}\)
B \(\frac{2}{3}\)
C -\(\frac{5}{6}\)
D \(\frac{5}{6}\)
Explanation opens after your attempt
Correct Answer
A. -\(\frac{2}{3}\)
Step 1
Concept
The product of roots is \(\frac{c}{a}=\frac{-4}{6}=-\frac{2}{3}\). Do not forget the sign of (c).
Step 2
Why this answer is correct
The correct answer is A. -\(\frac{2}{3}\). The product of roots is \(\frac{c}{a}=\frac{-4}{6}=-\frac{2}{3}\). Do not forget the sign of (c).
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{c}{a}=\frac{-4}{6}=-\frac{2}{3}\) होता है। (c) का चिन्ह न भूलें।
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यदि \(\alpha\) और \(\beta\) समीकरण \(4x^2-20x+7=0\) के मूल हैं तो \(\alpha+\beta\) क्या है?
If \(\alpha\) and \(\beta\) are roots of \(4x^2-20x+7=0\), what is \(\alpha+\beta\)?
#roots
#sum_of_roots
#calculation
A (5)
B (-5)
C \(\frac{7}{4}\)
D -\(\frac{7}{4}\)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is \(-\frac{b}{a}=-\frac{-20}{4}=5\). Keep the sign of (b) correct in the formula.
Step 2
Why this answer is correct
The correct answer is A. (5). The sum of roots is \(-\frac{b}{a}=-\frac{-20}{4}=5\). Keep the sign of (b) correct in the formula.
Step 3
Exam Tip
मूलों का योग \(-\frac{b}{a}=-\frac{-20}{4}=5\) है। सूत्र में (b) का चिन्ह सही रखें।
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यदि \(\alpha\) और \(\beta\) समीकरण \(5x^2+3x-2=0\) के मूल हैं तो \(\alpha\beta\) क्या है?
If \(\alpha\) and \(\beta\) are roots of \(5x^2+3x-2=0\), what is \(\alpha\beta\)?
#roots
#product_of_roots
#calculation
A -\(\frac{2}{5}\)
B \(\frac{2}{5}\)
C (3)
D (-3)
Explanation opens after your attempt
Correct Answer
A. -\(\frac{2}{5}\)
Step 1
Concept
The product of roots is \(\frac{c}{a}=\frac{-2}{5}\). Do not forget the sign of (c).
Step 2
Why this answer is correct
The correct answer is A. -\(\frac{2}{5}\). The product of roots is \(\frac{c}{a}=\frac{-2}{5}\). Do not forget the sign of (c).
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{c}{a}=\frac{-2}{5}\) होता है। (c) का चिन्ह न भूलें।
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यदि \(\alpha\) और \(\beta\) समीकरण \(3x^2-12x+5=0\) के मूल हैं तो \(\alpha+\beta\) क्या है?
If \(\alpha\) and \(\beta\) are roots of \(3x^2-12x+5=0\), what is \(\alpha+\beta\)?
#roots
#sum_of_roots
#calculation
A (4)
B (-4)
C \(\frac{5}{3}\)
D -\(\frac{5}{3}\)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is \(-\frac{b}{a}=-\frac{-12}{3}=4\). Keep the sign of (b) correct in the formula.
Step 2
Why this answer is correct
The correct answer is A. (4). The sum of roots is \(-\frac{b}{a}=-\frac{-12}{3}=4\). Keep the sign of (b) correct in the formula.
Step 3
Exam Tip
मूलों का योग \(-\frac{b}{a}=-\frac{-12}{3}=4\) है। सूत्र में (b) का चिन्ह सही रखें।
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यदि \(\alpha\) और \(\beta\) समीकरण \(4x^2+4x-3=0\) के मूल हैं तो \(\alpha\beta\) क्या है?
If \(\alpha\) and \(\beta\) are roots of \(4x^2+4x-3=0\), what is \(\alpha\beta\)?
#roots
#product_of_roots
#calculation
A -\(\frac{3}{4}\)
B \(\frac{3}{4}\)
C (1)
D (-1)
Explanation opens after your attempt
Correct Answer
A. -\(\frac{3}{4}\)
Step 1
Concept
The product of roots is \(\frac{c}{a}=\frac{-3}{4}\). Do not forget the sign of (c).
Step 2
Why this answer is correct
The correct answer is A. -\(\frac{3}{4}\). The product of roots is \(\frac{c}{a}=\frac{-3}{4}\). Do not forget the sign of (c).
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{c}{a}=\frac{-3}{4}\) होता है। (c) का चिन्ह न भूलें।
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यदि \(\alpha\) और \(\beta\) समीकरण \(2x^2-6x+1=0\) के मूल हैं तो \(\alpha+\beta\) क्या है?
If \(\alpha\) and \(\beta\) are roots of \(2x^2-6x+1=0\), what is \(\alpha+\beta\)?
#roots
#sum_of_roots
#calculation
A (3)
B (-3)
C \(\frac{1}{2}\)
D -\(\frac{1}{2}\)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is \(-\frac{b}{a}=-\frac{-6}{2}=3\). Keep the sign of (b) correct in the formula.
Step 2
Why this answer is correct
The correct answer is A. (3). The sum of roots is \(-\frac{b}{a}=-\frac{-6}{2}=3\). Keep the sign of (b) correct in the formula.
Step 3
Exam Tip
मूलों का योग \(-\frac{b}{a}=-\frac{-6}{2}=3\) है। सूत्र में (b) का चिन्ह सही रखें।
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समीकरण \(x^2+4x+4=0\) का डिस्क्रिमिनेंट (D) क्या है?
What is the discriminant (D) of \(x^2+4x+4=0\)?
#roots
#discriminant
#calculation
A (16)
B (0)
C (-16)
D (8)
Explanation opens after your attempt
Step 1
Concept
Here \(D=b^2-4ac=16-16=0\). Therefore the two roots will be equal.
Step 2
Why this answer is correct
The correct answer is B. (0). Here \(D=b^2-4ac=16-16=0\). Therefore the two roots will be equal.
Step 3
Exam Tip
यहां \(D=b^2-4ac=16-16=0\) है। इसलिए दोनों मूल बराबर होंगे।
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समीकरण \(x^2-4x+4=0\) के डिस्क्रिमिनेंट (D) का मान क्या है?
What is the value of discriminant (D) for \(x^2-4x+4=0\)?
#roots
#discriminant
#calculation
A (4)
B (0)
C (-4)
D (8)
Explanation opens after your attempt
Step 1
Concept
Here \(D=b^2-4ac=16-16=0\). Therefore its roots will be equal.
Step 2
Why this answer is correct
The correct answer is B. (0). Here \(D=b^2-4ac=16-16=0\). Therefore its roots will be equal.
Step 3
Exam Tip
यहां \(D=b^2-4ac=16-16=0\) है। इसलिए इसके मूल बराबर होंगे।
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किस विकल्प में \(\sqrt{50}+3\sqrt{8}-\sqrt{18}\) का सही सरल रूप है?
Which option gives the correct simplified form of \(\sqrt{50}+3\sqrt{8}-\sqrt{18}\)?
#surd-simplification
#like-radicals
#calculation
A \(8\sqrt{2}\)
B \(14\sqrt{2}\)
C \(5\sqrt{2}\)
D \(\sqrt{40}\)
Explanation opens after your attempt
Correct Answer
A. \(8\sqrt{2}\)
Step 1
Concept
\(\sqrt{50}=5\sqrt{2}\), \(3\sqrt{8}=6\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\). Hence the value is \(8\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(8\sqrt{2}\). \(\sqrt{50}=5\sqrt{2}\), \(3\sqrt{8}=6\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\). Hence the value is \(8\sqrt{2}\).
Step 3
Exam Tip
\(\sqrt{50}=5\sqrt{2}\), \(3\sqrt{8}=6\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\) है। इसलिए मान \(8\sqrt{2}\) है।
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यदि \(x=2+\sqrt{7}\), तो \(x+\frac{1}{x}\) का सही मान क्या है?
If \(x=2+\sqrt{7}\), what is the correct value of \(x+\frac{1}{x}\)?
#reciprocal
#surds
#advanced-calculation
A \(\frac{4+4\sqrt{7}}{3}\)
B \(2\sqrt{7}\)
C (4)
D \(\frac{2+\sqrt{7}}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{4+4\sqrt{7}}{3}\)
Step 1
Concept
\(\frac{1}{2+\sqrt{7}}=\frac{\sqrt{7}-2}{3}\) so the total is \(\frac{4+4\sqrt{7}}{3}\). In exams rationalize the reciprocal first.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{4+4\sqrt{7}}{3}\). \(\frac{1}{2+\sqrt{7}}=\frac{\sqrt{7}-2}{3}\) so the total is \(\frac{4+4\sqrt{7}}{3}\). In exams rationalize the reciprocal first.
Step 3
Exam Tip
\(\frac{1}{2+\sqrt{7}}=\frac{\sqrt{7}-2}{3}\) है इसलिए कुल \(\frac{4+4\sqrt{7}}{3}\) मिलता है। परीक्षा में व्युत्क्रम को पहले परिमेयकृत करें।
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यदि \(x=2+\sqrt{7}\), तो \(x+\frac{1}{x}\) का मान क्या है?
If \(x=2+\sqrt{7}\), what is the value of \(x+\frac{1}{x}\)?
#rationalization
#careful-calculation
#error-check
A \(2\sqrt{7}\)
B (4)
C \(\sqrt{7}\)
D \(2+\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{7}\)
Step 1
Concept
\(\frac{1}{2+\sqrt{7}}\) equals \(\frac{2-\sqrt{7}}{-3}=\frac{\sqrt{7}-2}{3}\). So \(x+\frac{1}{x}=2+\sqrt{7}+\frac{\sqrt{7}-2}{3}=\frac{4+4\sqrt{7}}{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{7}\). \(\frac{1}{2+\sqrt{7}}\) equals \(\frac{2-\sqrt{7}}{-3}=\frac{\sqrt{7}-2}{3}\). So \(x+\frac{1}{x}=2+\sqrt{7}+\frac{\sqrt{7}-2}{3}=\frac{4+4\sqrt{7}}{3}\).
Step 3
Exam Tip
\(\frac{1}{2+\sqrt{7}}=\frac{\sqrt{7}-2}{3}\) नहीं बल्कि हर (4-7=-3) से मान \(\frac{2-\sqrt{7}}{3}\) है इसलिए सीधा विकल्प नहीं बनेगा। सही सरलीकरण जांचे बिना उत्तर न चुनें।
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कौन सा विकल्प \(\sqrt{0.49}+\frac{1}{\sqrt{25}}\) का मान है?
Which option is the value of \(\sqrt{0.49}+\frac{1}{\sqrt{25}}\)?
#decimal-square-root
#rational-number
#calculation
A (0.9)
B (0.75)
C (1.2)
D (0.2)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{0.49}=0.7\) and \(\frac{1}{\sqrt{25}}=\frac{1}{5}=0.2\). The sum is (0.9).
Step 2
Why this answer is correct
The correct answer is A. (0.9). \(\sqrt{0.49}=0.7\) and \(\frac{1}{\sqrt{25}}=\frac{1}{5}=0.2\). The sum is (0.9).
Step 3
Exam Tip
\(\sqrt{0.49}=0.7\) और \(\frac{1}{\sqrt{25}}=\frac{1}{5}=0.2\) है। योग (0.9) है।
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कौन सा विकल्प \(\sqrt{0.36}+\sqrt{0.49}\) का मान है?
Which option is the value of \(\sqrt{0.36}+\sqrt{0.49}\)?
#decimal-square-root
#rational-number
#calculation
A (1.3)
B (0.13)
C (1.1)
D (0.85)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{0.36}=0.6\) and \(\sqrt{0.49}=0.7\). The sum is (1.3), which is rational.
Step 2
Why this answer is correct
The correct answer is A. (1.3). \(\sqrt{0.36}=0.6\) and \(\sqrt{0.49}=0.7\). The sum is (1.3), which is rational.
Step 3
Exam Tip
\(\sqrt{0.36}=0.6\) और \(\sqrt{0.49}=0.7\) है। योग (1.3) है जो परिमेय है।
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कौन सा विकल्प (\(\sqrt{3}+\sqrt{12}\)2 ) का मान है?
Which option is the value of (\(\sqrt{3}+\sqrt{12}\)2 )?
#surds
#square
#calculation
A (27)
B (15)
C \(9\sqrt{3}\)
D \(3+\sqrt{12}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\), so the bracket becomes \(3\sqrt{3}\). Its square is (27).
Step 2
Why this answer is correct
The correct answer is A. (27). \(\sqrt{12}=2\sqrt{3}\), so the bracket becomes \(3\sqrt{3}\). Its square is (27).
Step 3
Exam Tip
\(\sqrt{12}=2\sqrt{3}\) इसलिए कोष्ठक \(3\sqrt{3}\) बनता है। उसका वर्ग (27) है।
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कौन सा विकल्प \(\sqrt{0.64}+\sqrt{0.09}\) का मान है?
Which option is the value of \(\sqrt{0.64}+\sqrt{0.09}\)?
#decimal-square-root
#rational-number
#calculation
A (1.1)
B (0.11)
C (0.89)
D (1.7)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{0.64}=0.8\) and \(\sqrt{0.09}=0.3\). The sum is (1.1).
Step 2
Why this answer is correct
The correct answer is A. (1.1). \(\sqrt{0.64}=0.8\) and \(\sqrt{0.09}=0.3\). The sum is (1.1).
Step 3
Exam Tip
\(\sqrt{0.64}=0.8\) और \(\sqrt{0.09}=0.3\) है। योग (1.1) है।
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कौन सा विकल्प \(\sqrt{0.81}\) का मान है?
Which option is the value of \(\sqrt{0.81}\)?
#decimal-square-root
#rational-number
#calculation
A (0.9)
B (0.09)
C (9)
D (0.081)
Explanation opens after your attempt
Step 1
Concept
Since \(0.9\times0.9=0.81\), \(\sqrt{0.81}=0.9\). It is a terminating decimal.
Step 2
Why this answer is correct
The correct answer is A. (0.9). Since \(0.9\times0.9=0.81\), \(\sqrt{0.81}=0.9\). It is a terminating decimal.
Step 3
Exam Tip
\(0.9\times0.9=0.81\) इसलिए \(\sqrt{0.81}=0.9\)। यह सांत दशमलव है।
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कौन सा विकल्प \(\sqrt{0.25}+\sqrt{0.04}\) का मान है?
Which option is the value of \(\sqrt{0.25}+\sqrt{0.04}\)?
#decimal-square-root
#rational-numbers
#calculation
A (0.7)
B (0.3)
C (0.54)
D (0.29)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{0.25}=0.5\) and \(\sqrt{0.04}=0.2\). The sum is (0.7), which is rational.
Step 2
Why this answer is correct
The correct answer is A. (0.7). \(\sqrt{0.25}=0.5\) and \(\sqrt{0.04}=0.2\). The sum is (0.7), which is rational.
Step 3
Exam Tip
\(\sqrt{0.25}=0.5\) और \(\sqrt{0.04}=0.2\) है। योग (0.7) है जो परिमेय है।
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कौन सा विकल्प \(\sqrt{0.16}\) का मान है?
Which option is the value of \(\sqrt{0.16}\)?
#decimal-square-root
#rational-number
#calculation
A (0.4)
B (0.04)
C (4)
D (1.6)
Explanation opens after your attempt
Step 1
Concept
Since \(0.4\times0.4=0.16\), \(\sqrt{0.16}=0.4\). This is a rational number.
Step 2
Why this answer is correct
The correct answer is A. (0.4). Since \(0.4\times0.4=0.16\), \(\sqrt{0.16}=0.4\). This is a rational number.
Step 3
Exam Tip
\(0.4\times0.4=0.16\) इसलिए \(\sqrt{0.16}=0.4\)। यह परिमेय संख्या है।
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कौन सा विकल्प \(\sqrt{\frac{49}{64}}\) का मान है?
Which option is the value of \(\sqrt{\frac{49}{64}}\)?
#fraction-square-root
#rational-numbers
#calculation
A \(\frac{7}{8}\)
B \(\frac{49}{8}\)
C \(\frac{7}{64}\)
D \(\frac{14}{16}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{7}{8}\)
Step 1
Concept
\(\sqrt{\frac{49}{64}}=\frac{\sqrt{49}}{\sqrt{64}}=\frac{7}{8}\). This is a rational number.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{7}{8}\). \(\sqrt{\frac{49}{64}}=\frac{\sqrt{49}}{\sqrt{64}}=\frac{7}{8}\). This is a rational number.
Step 3
Exam Tip
\(\sqrt{\frac{49}{64}}=\frac{\sqrt{49}}{\sqrt{64}}=\frac{7}{8}\) है। यह परिमेय संख्या है।
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यदि \(x=\sqrt{19}\) है तो \(x^2\) क्या होगा?
If \(x=\sqrt{19}\), what is \(x^2\)?
#square-root
#square
#calculation
A (19)
B \(\sqrt{19}\)
C (38)
D (361)
Explanation opens after your attempt
Step 1
Concept
(\(\sqrt{19}\)2 =19). Squaring removes the square root.
Step 2
Why this answer is correct
The correct answer is A. (19). (\(\sqrt{19}\)2 =19). Squaring removes the square root.
Step 3
Exam Tip
(\(\sqrt{19}\)2 =19) होता है। वर्ग करने पर वर्गमूल हट जाती है।
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\(\sqrt{0.09}\) का मान क्या है?
What is the value of \(\sqrt{0.09}\)?
#decimal-square-root
#rational-numbers
#calculation
A (0.3)
B (0.03)
C (3)
D (0.9)
Explanation opens after your attempt
Step 1
Concept
Since \(0.3\times0.3=0.09\), \(\sqrt{0.09}=0.3\). It is a terminating decimal.
Step 2
Why this answer is correct
The correct answer is A. (0.3). Since \(0.3\times0.3=0.09\), \(\sqrt{0.09}=0.3\). It is a terminating decimal.
Step 3
Exam Tip
\(0.3\times0.3=0.09\) इसलिए \(\sqrt{0.09}=0.3\)। यह सांत दशमलव है।
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यदि \(x=\sqrt{13}\) है तो \(x^2\) का मान क्या है?
If \(x=\sqrt{13}\), what is the value of \(x^2\)?
#square-root
#square
#calculation
A (13)
B \(\sqrt{13}\)
C (169)
D (26)
Explanation opens after your attempt
Step 1
Concept
(\(\sqrt{13}\)2 =13). Squaring and taking the square root cancel each other.
Step 2
Why this answer is correct
The correct answer is A. (13). (\(\sqrt{13}\)2 =13). Squaring and taking the square root cancel each other.
Step 3
Exam Tip
(\(\sqrt{13}\)2 =13) होता है। वर्ग और वर्गमूल एक-दूसरे को समाप्त कर देते हैं।
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कौन सा विकल्प \(\frac{3}{32}\) के सही दशमलव रूप को दिखाता है?
Which option shows the correct decimal form of \(\frac{3}{32}\)?
#fraction-to-decimal
#powers-of-two
#calculation
A (0.09375)
B (0.9375)
C (0.009375)
D (0.375)
Explanation opens after your attempt
Correct Answer
A. (0.09375)
Step 1
Concept
\(32=2^5\), so the decimal ends after (5) places.
Step 2
Why this answer is correct
\(32\times3125=100000\), so \(\frac{3}{32}=\frac{9375}{100000}=0.09375\).
Step 3
Exam Tip
Exam tip: Count the total decimal places carefully while placing the decimal point. चरण 1: \(32=2^5\) है, इसलिए दशमलव (5) स्थानों पर समाप्त होगा। चरण 2: \(32\times3125=100000\), अतः \(\frac{3}{32}=\frac{9375}{100000}=0.09375\)। चरण 3: परीक्षा सुझाव: दशमलव बिंदु लगाते समय कुल स्थानों की गिनती करें।
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\(\frac{91}{625}\) का दशमलव रूप क्या है?
What is the decimal form of \(\frac{91}{625}\)?
#fraction-to-decimal
#terminating-decimal
#calculation
A (0.1456)
B (0.01456)
C (1.456)
D (0.1564)
Explanation opens after your attempt
Correct Answer
A. (0.1456)
Step 1
Concept
\(625\times16=10000\).
Step 2
Why this answer is correct
\(\frac{91}{625}=\frac{1456}{10000}=0.1456\).
Step 3
Exam Tip
Exam tip: When the denominator is (625), multiply by (16) to make (10000). चरण 1: \(625\times16=10000\) है। चरण 2: \(\frac{91}{625}=\frac{1456}{10000}=0.1456\) होता है। चरण 3: परीक्षा सुझाव: हर (625) हो तो उसे (10000) बनाने के लिए (16) से गुणा करना याद रखें।
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कौन सा दशमलव \(\frac{7}{16}\) के बराबर है?
Which decimal is equal to \(\frac{7}{16}\)?
#fraction-to-decimal
#terminating
#calculation
A (0.4375)
B (0.375)
C (0.625)
D (0.875)
Explanation opens after your attempt
Correct Answer
A. (0.4375)
Step 1
Concept
\(16\times625=10000\).
Step 2
Why this answer is correct
\(\frac{7}{16}=\frac{4375}{10000}=0.4375\).
Step 3
Exam Tip
Exam tip: For denominators like (16), (32), and (64), making a power of (10) is useful. चरण 1: \(16\times625=10000\) है। चरण 2: \(\frac{7}{16}=\frac{4375}{10000}=0.4375\) है। चरण 3: परीक्षा सुझाव: (16), (32), (64) जैसे हरों के लिए (10) की घात बनाना उपयोगी रहता है।
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\(\frac{3}{80}\) का दशमलव प्रसार कितने दशमलव स्थानों पर समाप्त होगा?
After how many decimal places will \(\frac{3}{80}\) terminate?
#decimal-places
#terminating-decimal
#calculation
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(80=2^4\times5\).
Step 2
Why this answer is correct
The larger exponent is (4), so the decimal has (4) places.
Step 3
Exam Tip
Exam tip: You can also check by writing \(\frac{3}{80}=0.0375\). चरण 1: \(80=2^4\times5\) है। चरण 2: बड़ी घात (4) है, इसलिए दशमलव (4) स्थानों तक जाएगा। चरण 3: परीक्षा सुझाव: \(\frac{3}{80}=0.0375\) लिखकर भी जाँच सकते हैं।
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\(\frac{7}{125}\) का दशमलव रूप क्या है?
What is the decimal form of \(\frac{7}{125}\)?
#fraction-to-decimal
#terminating-decimal
#calculation
A (0.56)
B (0.056)
C (0.0056)
D (0.075)
Explanation opens after your attempt
Correct Answer
B. (0.056)
Step 1
Concept
\(125\times8=1000\).
Step 2
Why this answer is correct
\(\frac{7}{125}=\frac{56}{1000}=0.056\).
Step 3
Exam Tip
Exam tip: When making the denominator (1000), keep three decimal places carefully. चरण 1: \(125\times8=1000\) है। चरण 2: \(\frac{7}{125}=\frac{56}{1000}=0.056\) है। चरण 3: परीक्षा सुझाव: हर को (1000) बनाने पर तीन दशमलव स्थान ध्यान से रखें।
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\(2^4 \times 3\) से बनी संख्या कौन सी है?
Which number is formed by \(2^4 \times 3\)?
#real-numbers
#prime-factorisation
#calculation
A 24
B 36
C 48
D 64
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\).
Step 2
Why this answer is correct
\(16 \times 3=48\), so the number is (48).
Step 3
Exam Tip
Evaluating the power first makes calculation easier. चरण 1: \(2^4\) का मान (16) है। चरण 2: \(16 \times 3=48\), इसलिए बनी संख्या (48) है। चरण 3: पहले घात का मान निकालना गणना को आसान बनाता है।
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किस संख्या का अभाज्य गुणनखंड रूप \(2^2\times3\times7^2\) है?
Which number has the prime factorisation \(2^2\times3\times7^2\)?
#real numbers
#prime factorisation
#value calculation
#exam practice
A (588)
B (294)
C (1176)
D (441)
Explanation opens after your attempt
Step 1
Concept
Multiply the prime factors according to their powers.
Step 2
Why this answer is correct
\(2^2=4\) and \(7^2=49\), so \(4\times3\times49=588\).
Step 3
Exam Tip
First evaluate powers, then multiply carefully. चरण 1: अभाज्य गुणनखंडों को उनकी घात के अनुसार गुणा करें। चरण 2: \(2^2=4\), \(7^2=49\), इसलिए \(4\times3\times49=588\)। चरण 3: पहले घातों का मान निकालें, फिर धीरे-धीरे गुणा करें।
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(1000) को (33) से भाग देने पर भागफल क्या होगा?
What is the quotient when (1000) is divided by (33)?
#real-numbers
#quotient
#division-calculation
A (29)
B (30)
C (31)
D (33)
Explanation opens after your attempt
Step 1
Concept
\(33 \times 30=990\) and \(33 \times 31=1023\).
Step 2
Why this answer is correct
Since (1023) is greater, the quotient is (30).
Step 3
Exam Tip
The quotient is the greatest integer whose product with the divisor does not exceed the dividend. चरण 1: \(33 \times 30=990\) और \(33 \times 31=1023\) है। चरण 2: (1023) बड़ा है, इसलिए भागफल (30) होगा। चरण 3: भागफल वह सबसे बड़ा पूर्णांक है जिससे गुणनफल भाज्य से अधिक न हो।
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(437) को (35) से भाग देने पर शेषफल क्या होगा?
What is the remainder when (437) is divided by (35)?
#real-numbers
#remainder
#division-calculation
A (12)
B (17)
C (22)
D (35)
Explanation opens after your attempt
Step 1
Concept
\(35 \times 12=420\).
Step 2
Why this answer is correct
(437-420=17), so the remainder is (17).
Step 3
Exam Tip
After getting the answer, check that (17<35). चरण 1: \(35 \times 12=420\) है। चरण 2: (437-420=17), इसलिए शेषफल (17) है। चरण 3: उत्तर के बाद यह जरूर जाँचें कि (17<35) है।
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(310) को (27) से भाग देने पर शेषफल क्या होगा?
What is the remainder when (310) is divided by (27)?
#real-numbers
#remainder
#division-calculation
A (10)
B (11)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
\(27 \times 11=297\).
Step 2
Why this answer is correct
(310-297=13), so the remainder is (13).
Step 3
Exam Tip
The final remainder must be less than the divisor (27). चरण 1: \(27 \times 11=297\) है। चरण 2: (310-297=13), इसलिए शेषफल (13) है। चरण 3: अंतिम शेषफल भाजक (27) से छोटा होना चाहिए।
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(221) को (18) से भाग देने पर शेषफल क्या होगा?
What is the remainder when (221) is divided by (18)?
#real-numbers
#remainder-calculation
#division-practice
A (3)
B (5)
C (7)
D (11)
Explanation opens after your attempt
Step 1
Concept
\(18 \times 12=216\).
Step 2
Why this answer is correct
(221-216=5), so the remainder is (5).
Step 3
Exam Tip
Confirm that the remainder (5<18). चरण 1: \(18 \times 12=216\) है। चरण 2: (221-216=5), इसलिए शेषफल (5) है। चरण 3: शेषफल की पुष्टि करें कि (5<18) है।
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(144) को (13) से भाग देने पर शेषफल क्या होगा?
What is the remainder when (144) is divided by (13)?
#real-numbers
#remainder
#calculation
A (0)
B (1)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
\(13 \times 11=143\).
Step 2
Why this answer is correct
(144-143=1), so the remainder is (1).
Step 3
Exam Tip
Finding the nearest smaller multiple saves time. चरण 1: \(13 \times 11=143\) है। चरण 2: (144-143=1), इसलिए शेषफल (1) है। चरण 3: निकटतम छोटा गुणज खोजना समय बचाता है।
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उसी स्थिति में (a=250), (b=37) के लिए शेषफल (r) क्या होगा?
In the same situation, for (a=250) and (b=37), what is the remainder (r)?
#real-numbers
#remainder
#calculation
A (18)
B (28)
C (37)
D (43)
Explanation opens after your attempt
Step 1
Concept
From the previous calculation, (q=6).
Step 2
Why this answer is correct
\(r=250-37 \times 6=250-222=28\).
Step 3
Exam Tip
After getting the answer, check that (28<37). चरण 1: पिछले हिसाब से (q=6) है। चरण 2: \(r=250-37 \times 6=250-222=28\)। चरण 3: उत्तर के बाद जाँचें कि (28<37) है।
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यदि (a=148) और (b=20), तो शेषफल (r) क्या होगा?
If (a=148) and (b=20), what is the remainder (r)?
#real-numbers
#remainder-calculation
#mcq
A (8)
B (12)
C (20)
D (28)
Explanation opens after your attempt
Step 1
Concept
\(20 \times 7=140\).
Step 2
Why this answer is correct
(148-140=8), so (r=8).
Step 3
Exam Tip
If an option gives a remainder equal to or greater than (20), reject it immediately. चरण 1: \(20 \times 7=140\)। चरण 2: (148-140=8), इसलिए (r=8)। चरण 3: यदि विकल्पों में (20) या उससे बड़ा शेषफल हो, तो उसे तुरंत गलत मानें।
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यदि (99) को (14) से भाग दिया जाए तो भागफल क्या होगा?
What is the quotient when (99) is divided by (14)?
#quotient calculation
#division by 14
#euclid
A (7)
B (8)
C (6)
D (14)
Explanation opens after your attempt
Step 1
Concept
\(14 \times 7=98\) and \(14 \times 8=112\).
Step 2
Why this answer is correct
(112) is greater than (99), so the quotient is (7).
Step 3
Exam Tip
For the quotient, choose a multiple less than or equal to the dividend. चरण 1: \(14 \times 7=98\) और \(14 \times 8=112\) है। चरण 2: (112), (99) से बड़ा है, इसलिए भागफल (7) होगा। चरण 3: भागफल के लिए भाज्य से छोटा या बराबर गुणज चुनें।
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यदि (99) को (14) से भाग दिया जाए तो शेषफल क्या होगा?
What is the remainder when (99) is divided by (14)?
#remainder calculation
#division by 14
#real numbers
A (1)
B (14)
C (7)
D (0)
Explanation opens after your attempt
Step 1
Concept
\(14 \times 7=98\).
Step 2
Why this answer is correct
(99-98=1), so the remainder is (1).
Step 3
Exam Tip
The nearest smaller multiple helps find the remainder quickly. चरण 1: \(14 \times 7=98\) है। चरण 2: (99-98=1), इसलिए शेषफल (1) है। चरण 3: निकटतम छोटे गुणज से शेषफल जल्दी मिलता है।
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यदि (a=120) और (b=17) हो तो (r) का सही मान क्या होगा?
If (a=120) and (b=17), what is the correct value of (r)?
#remainder calculation
#division by 17
#euclidean lemma
A (1)
B (7)
C (17)
D (0)
Explanation opens after your attempt
Step 1
Concept
\(17 \times 7=119\).
Step 2
Why this answer is correct
(120-119=1), so the remainder is (1).
Step 3
Exam Tip
Since (1<17), this remainder is valid. चरण 1: \(17 \times 7=119\) है। चरण 2: (120-119=1), इसलिए शेषफल (1) होगा। चरण 3: (1<17), इसलिए यह शेषफल मान्य है।
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यदि (a=120) और (b=17) हो तो (q) का सही मान क्या होगा?
If (a=120) and (b=17), what is the correct value of (q)?
#quotient calculation
#division lemma
#class 10
A (7)
B (6)
C (8)
D (17)
Explanation opens after your attempt
Step 1
Concept
\(17 \times 7=119\) and \(17 \times 8=136\).
Step 2
Why this answer is correct
(136) is greater than (120), so the quotient is (7).
Step 3
Exam Tip
Choose the quotient so that the product does not exceed the dividend. चरण 1: \(17 \times 7=119\) और \(17 \times 8=136\) है। चरण 2: (136), (120) से बड़ा है, इसलिए भागफल (7) होगा। चरण 3: भागफल वह लें जिससे गुणनफल भाज्य से अधिक न हो।
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यदि (a=95) और (b=12) हो तो (a=bq+r) में (r) का मान क्या होगा?
If (a=95) and (b=12), what is the value of (r) in (a=bq+r)?
#remainder calculation
#euclidean division
#class 10
A (11)
B (12)
C (7)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(12 \times 7=84\) and \(12 \times 8=96\).
Step 2
Why this answer is correct
The nearest smaller multiple of (12) is (84), so (95-84=11).
Step 3
Exam Tip
Since (11<12), remainder (11) is valid. चरण 1: \(12 \times 7=84\) और \(12 \times 8=96\) है। चरण 2: (95) से छोटा निकटतम गुणज (84) है, इसलिए (95-84=11)। चरण 3: (11<12), इसलिए शेषफल (11) मान्य है।
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यदि (58) को (6) से भाग दें तो भागफल क्या होगा?
What is the quotient when (58) is divided by (6)?
#quotient calculation
#division by 6
#euclid
A (9)
B (8)
C (10)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(6 \times 9=54\) and \(6 \times 10=60\).
Step 2
Why this answer is correct
(60) is greater than (58), so the quotient is (9).
Step 3
Exam Tip
Choose the quotient so that the product does not exceed the dividend. चरण 1: \(6 \times 9=54\) और \(6 \times 10=60\) है। चरण 2: (60), (58) से बड़ा है, इसलिए भागफल (9) होगा। चरण 3: भागफल वही लें जिससे गुणज भाज्य से बड़ा न हो।
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यदि (58) को (6) से भाग दें तो सही शेषफल क्या होगा?
What is the correct remainder when (58) is divided by (6)?
#remainder calculation
#division by 6
#easy
A (4)
B (6)
C (2)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(6 \times 9=54\).
Step 2
Why this answer is correct
(58-54=4), so the remainder is (4).
Step 3
Exam Tip
Since (4<6), the answer is valid. चरण 1: \(6 \times 9=54\) है। चरण 2: (58-54=4), इसलिए शेषफल (4) है। चरण 3: (4<6), इसलिए उत्तर मान्य है।
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यदि (100) को (9) से भाग दिया जाए तो शेषफल क्या होगा?
What is the remainder when (100) is divided by (9)?
#remainder calculation
#division by 9
#exam practice
A (1)
B (9)
C (10)
D (0)
Explanation opens after your attempt
Step 1
Concept
\(9 \times 11=99\).
Step 2
Why this answer is correct
(100-99=1), so the remainder is (1).
Step 3
Exam Tip
Using the nearest smaller multiple helps in quick calculation. चरण 1: \(9 \times 11=99\) है। चरण 2: (100-99=1), इसलिए शेषफल (1) होगा। चरण 3: निकटतम छोटे गुणज का उपयोग तेज गणना में मदद करता है।
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एक विलयन का पीएच एक है और दूसरे का पीएच चार है। पहले विलयन में हाइड्रोजन आयन की मात्रा दूसरे से कितनी अधिक होगी?
One solution has pH 1 and another has pH 4. How much greater is the hydrogen ion concentration in the first solution?
#pH calculation
#hydrogen ions
#acidity
A दस गुना / Ten times
B सौ गुना / Hundred times
C हजार गुना / Thousand times
D तीन गुना / Three times
Explanation opens after your attempt
Correct Answer
C. हजार गुना / Thousand times
Step 1
Concept
One pH unit difference means a tenfold difference in hydrogen ion concentration.
Step 2
Why this answer is correct
pH 1 and pH 4 differ by three units.
Step 3
Exam Tip
Therefore the first solution is one thousand times more acidic. चरण 1: पीएच में एक इकाई का अंतर हाइड्रोजन आयन में दस गुना अंतर दिखाता है। चरण 2: पीएच एक और चार में तीन इकाई का अंतर है। चरण 3: इसलिए पहला विलयन हजार गुना अधिक अम्लीय है।
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किसी अम्लीय विलयन का पीएच दो है। यदि उसे दस हजार गुना कम अम्लीय किया जाए तो नया पीएच लगभग कितना होगा?
An acidic solution has pH 2. If it is made ten thousand times less acidic, what will be the approximate new pH?
#pH calculation
#acidity
#hydrogen ions
A चार / Four
B छह / Six
C आठ / Eight
D बारह / Twelve
Explanation opens after your attempt
Step 1
Concept
A one-unit increase in pH means ten times fewer hydrogen ions.
Step 2
Why this answer is correct
Ten thousand times less acidic means pH rises by four units.
Step 3
Exam Tip
Adding four to two gives about pH 6. चरण 1: पीएच में एक इकाई वृद्धि हाइड्रोजन आयन की दस गुना कमी बताती है। चरण 2: दस हजार गुना कमी के लिए पीएच चार इकाई बढ़ेगा। चरण 3: दो में चार जोड़ने पर नया पीएच लगभग छह होगा।
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किसी विलयन का पीएच तीन है। यदि हाइड्रोजन आयन सांद्रता सौ गुना कम हो जाए तो नया पीएच लगभग कितना होगा?
A solution has pH 3. If the hydrogen ion concentration becomes one hundred times lower, what will be the approximate new pH?
#pH calculation
#hydrogen ions
#acidity
A एक / One
B पाँच / Five
C छह / Six
D तेरह / Thirteen
Explanation opens after your attempt
Correct Answer
B. पाँच / Five
Step 1
Concept
A one-unit increase in pH means ten times fewer hydrogen ions.
Step 2
Why this answer is correct
A hundred times decrease means pH rises by two units.
Step 3
Exam Tip
Adding two to three gives about pH 5. चरण 1: पीएच में एक इकाई वृद्धि हाइड्रोजन आयन की दस गुना कमी दिखाती है। चरण 2: सौ गुना कमी के लिए पीएच दो इकाई बढ़ेगा। चरण 3: तीन में दो जोड़ने पर नया पीएच लगभग पाँच होगा।
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किसी अम्लीय विलयन का पीएच चार है। यदि उसे हजार गुना कम अम्लीय किया जाए तो नया पीएच लगभग कितना होगा?
An acidic solution has pH 4. If it is made one thousand times less acidic, what will be the approximate new pH?
#pH calculation
#acidity
#hydrogen ions
A एक / One
B चार / Four
C सात / Seven
D बारह / Twelve
Explanation opens after your attempt
Correct Answer
C. सात / Seven
Step 1
Concept
An increase of one pH unit means ten times fewer hydrogen ions.
Step 2
Why this answer is correct
A thousand times decrease means pH rises by three units.
Step 3
Exam Tip
Adding three to four gives about pH 7. चरण 1: पीएच में एक इकाई वृद्धि हाइड्रोजन आयन की दस गुना कमी बताती है। चरण 2: हजार गुना कमी के लिए पीएच तीन इकाई बढ़ेगा। चरण 3: चार में तीन जोड़ने पर नया पीएच लगभग सात होगा।
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दो विलयनों के पीएच क्रमशः दो और छह हैं। पहले विलयन में हाइड्रोजन आयन की मात्रा दूसरे की तुलना में कितनी अधिक होगी?
Two solutions have pH values 2 and 6 respectively. How much greater is the hydrogen ion concentration in the first solution than in the second?
#pH calculation
#hydrogen ions
#hard
A दस हजार गुना / Ten thousand times
B चार गुना / Four times
C सौ गुना / Hundred times
D दो गुना / Two times
Explanation opens after your attempt
Correct Answer
A. दस हजार गुना / Ten thousand times
Step 1
Concept
A difference of one pH unit means a tenfold difference in hydrogen ion concentration.
Step 2
Why this answer is correct
The difference between pH 2 and pH 6 is four units.
Step 3
Exam Tip
So the first solution has ten thousand times more hydrogen ions. चरण 1: पीएच में एक इकाई का अंतर हाइड्रोजन आयन में दस गुना अंतर दिखाता है। चरण 2: दो और छह में चार इकाई का अंतर है। चरण 3: इसलिए पहले विलयन में हाइड्रोजन आयन दस हजार गुना अधिक होंगे।
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यदि किसी विलयन का पीएच मान तीन है और उसे सौ गुना कम अम्लीय करना है तो नया पीएच लगभग कितना होगा?
If a solution has pH 3 and it is made one hundred times less acidic, what will be the approximate new pH?
#pH calculation
#acidity
#logarithmic scale
A एक / One
B दो / Two
C पाँच / Five
D तेरह / Thirteen
Explanation opens after your attempt
Correct Answer
C. पाँच / Five
Step 1
Concept
An increase of one pH unit means ten times lower hydrogen ion concentration.
Step 2
Why this answer is correct
One hundred times less acidic means pH increases by two units.
Step 3
Exam Tip
Thus pH 3 becomes about pH 5. चरण 1: पीएच में एक इकाई वृद्धि हाइड्रोजन आयन में दस गुना कमी दिखाती है। चरण 2: सौ गुना कम अम्लीय होने के लिए पीएच दो इकाई बढ़ेगा। चरण 3: तीन में दो जोड़ने पर नया पीएच लगभग पाँच होगा।
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जल के वैद्युत वियोजन में यदि ऑक्सीजन आठ मिलीलीटर है तो हाइड्रोजन का अपेक्षित आयतन कितना होगा?
In electrolysis of water if oxygen is eight millilitres what will be the expected volume of hydrogen?
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A चार मिलीलीटर / Four millilitres
B आठ मिलीलीटर / Eight millilitres
C सोलह मिलीलीटर / Sixteen millilitres
D बत्तीस मिलीलीटर / Thirty two millilitres
Explanation opens after your attempt
Correct Answer
C. सोलह मिलीलीटर / Sixteen millilitres
Step 1
Concept
The volume ratio of hydrogen to oxygen is two to one.
Step 2
Why this answer is correct
Oxygen is eight millilitres.
Step 3
Exam Tip
Therefore hydrogen will be sixteen millilitres. चरण 1: हाइड्रोजन और ऑक्सीजन का आयतन अनुपात दो अनुपात एक है। चरण 2: ऑक्सीजन आठ मिलीलीटर है। चरण 3: इसलिए हाइड्रोजन सोलह मिलीलीटर होगी।
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