13 results found for "400 km" in Class 10.
(400) का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of (400)?
#real-numbers
#prime-factorisation
#400
A \(2^2 \times 5^2\)
B \(2^4 \times 5^2\)
C \(2^3 \times 5^2\)
D \(4^2 \times 5^2\)
Explanation opens after your attempt
Correct Answer
B. \(2^4 \times 5^2\)
Step 1
Concept
Write \(400=4 \times 100\).
Step 2
Why this answer is correct
\(4=2^2\) and \(100=2^2 \times 5^2\), so \(400=2^4 \times 5^2\).
Step 3
Exam Tip
(4) is not prime, so final factorisation must use only prime bases. चरण 1: \(400=4 \times 100\) लिखें। चरण 2: \(4=2^2\) और \(100=2^2 \times 5^2\), इसलिए \(400=2^4 \times 5^2\)। चरण 3: (4) अभाज्य नहीं है, इसलिए अंतिम रूप में केवल अभाज्य आधार लिखें।
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संख्या 400 का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of 400?
#prime-factorisation
#number-400
#easy
A \(2^4\times5^2\)
B \(20\times20\)
C \(4\times100\)
D \(2^2\times10^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times5^2\)
Step 1
Concept
Write \(400=16\times25\).
Step 2
Why this answer is correct
\(16=2^4\) and \(25=5^2\), so \(400=2^4\times5^2\).
Step 3
Exam Tip
Composite forms like 20 or 10 are not final answers. चरण 1: \(400=16\times25\) लिखें। चरण 2: \(16=2^4\) और \(25=5^2\), इसलिए \(400=2^4\times5^2\)। चरण 3: 20 या 10 जैसे संयुक्त रूप अंतिम उत्तर नहीं होते।
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एक गाड़ी की सर्विस लागत पहले वर्ष (1500) रुपये है और हर अगले वर्ष (400) रुपये बढ़ती है। (5)वें वर्ष लागत कितनी होगी?
The service cost of a vehicle is (1500) rupees in the first year and increases by (400) rupees each next year. What is the cost in the (5)th year?
#ap
#word-problem
#cost
A (2700) रुपये / (2700) rupees
B (2900) रुपये / (2900) rupees
C (3100) रुपये / (3100) rupees
D (3300) रुपये / (3300) rupees
Explanation opens after your attempt
Correct Answer
C. (3100) रुपये / (3100) rupees
Step 1
Concept
The cost forms an AP. (a_5=1500+4(400)=3100).
Step 2
Why this answer is correct
The correct answer is C. (3100) रुपये / (3100) rupees. The cost forms an AP. (a_5=1500+4(400)=3100).
Step 3
Exam Tip
लागत समान्तर श्रेणी है। (a_5=1500+4(400)=3100)।
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(200) और (400) के बीच (12) से विभाज्य संख्याओं का योग ज्ञात कीजिए।
Find the sum of the numbers divisible by (12) between (200) and (400).
#divisibility
#range
#ap_sum
A (5000)
B (5100)
C (5200)
D (5300)
Explanation opens after your attempt
Step 1
Concept
The numbers are \(204,216,\ldots,396\), and there are (17) terms, so the sum is (5100). Choose the first and last terms carefully in boundary questions.
Step 2
Why this answer is correct
The correct answer is B. (5100). The numbers are \(204,216,\ldots,396\), and there are (17) terms, so the sum is (5100). Choose the first and last terms carefully in boundary questions.
Step 3
Exam Tip
संख्याएँ \(204,216,\ldots,396\) हैं और (17) पद हैं, इसलिए योग (5100) है। सीमा में पहला और अंतिम पद सावधानी से चुनें।
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समान्तर श्रेणी \(24,33,42,\ldots\) में कितने पद (400) से कम हैं?
In the AP \(24,33,42,\ldots\), how many terms are less than (400)?
#ap-count-terms-hard
A (40)
B (41)
C (42)
D (43)
Explanation opens after your attempt
Step 1
Concept
From (24+9(n-1)<400), (9(n-1)<376). The greatest (n=42).
Step 2
Why this answer is correct
The correct answer is C. (42). From (24+9(n-1)<400), (9(n-1)<376). The greatest (n=42).
Step 3
Exam Tip
(24+9(n-1)<400) से (9(n-1)<376)। सबसे बड़ा (n=42) है।
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(400) से बड़े (12) के गुणजों की AP \(408,420,432,\ldots\) है। इसका (18)वां पद क्या होगा?
The AP of multiples of (12) greater than (400) is \(408,420,432,\ldots\). What is its (18)th term?
#ap multiples nth-term class10
A (612)
B (624)
C (636)
D (648)
Explanation opens after your attempt
Step 1
Concept
Here (a=408) and (d=12) so \(a_{18}=408+17\times12=612\). Choose the first correct multiple after the limit.
Step 2
Why this answer is correct
The correct answer is A. (612). Here (a=408) and (d=12) so \(a_{18}=408+17\times12=612\). Choose the first correct multiple after the limit.
Step 3
Exam Tip
यहां (a=408) और (d=12) है इसलिए \(a_{18}=408+17\times12=612\)। सीमा के बाद पहला सही गुणज चुनें।
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एक संख्या के वर्ग में उस संख्या का (9) गुना जोड़ने पर (400) मिलता है। धनात्मक संख्या क्या है?
When (9) times a number is added to its square, the result is (400). What is the positive number?
#quadratic equations
#number problem
#square
A (16)
B (18)
C (20)
D (25)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2+9x=400\). From \(x^2+9x-400=0\), the positive root is (x=16).
Step 2
Why this answer is correct
The correct answer is A. (16). The equation is \(x^2+9x=400\). From \(x^2+9x-400=0\), the positive root is (x=16).
Step 3
Exam Tip
समीकरण \(x^2+9x=400\) है। \(x^2+9x-400=0\) से धनात्मक हल (x=16) है।
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एक वर्गाकार आँगन का क्षेत्रफल (400) वर्ग मीटर है। उसका परिमाप क्या है?
A square courtyard has area (400) square m. What is its perimeter?
#quadratic equations
#square
#perimeter
A (40) मीटर / (40) m
B (60) मीटर / (60) m
C (80) मीटर / (80) m
D (100) मीटर / (100) m
Explanation opens after your attempt
Correct Answer
C. (80) मीटर / (80) m
Step 1
Concept
\(x^2=400\) gives side (20) m and perimeter (4x=80) m. Area and perimeter formulas are different.
Step 2
Why this answer is correct
The correct answer is C. (80) मीटर / (80) m. \(x^2=400\) gives side (20) m and perimeter (4x=80) m. Area and perimeter formulas are different.
Step 3
Exam Tip
\(x^2=400\) से भुजा (20) मीटर और परिमाप (4x=80) मीटर है। क्षेत्रफल और परिमाप के सूत्र अलग होते हैं।
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एक आयताकार खेत की लंबाई चौड़ाई से (9) मीटर अधिक है और क्षेत्रफल (400) वर्ग मीटर है। चौड़ाई क्या है?
A rectangular field has length (9) m more than its breadth and area (400) square m. What is its breadth?
#quadratic equations
#rectangle
#field
A (16) मीटर / (16) m
B (20) मीटर / (20) m
C (25) मीटर / (25) m
D (30) मीटर / (30) m
Explanation opens after your attempt
Correct Answer
A. (16) मीटर / (16) m
Step 1
Concept
Taking breadth as (x), (x(x+9)=400), giving (x=16). Do not accept the wrong negative value as a dimension.
Step 2
Why this answer is correct
The correct answer is A. (16) मीटर / (16) m. Taking breadth as (x), (x(x+9)=400), giving (x=16). Do not accept the wrong negative value as a dimension.
Step 3
Exam Tip
चौड़ाई (x) लेने पर (x(x+9)=400), जिससे (x=16) मिलता है। गलत ऋणात्मक मान को आयाम में स्वीकार न करें।
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\(\frac{43}{400}\) का दशमलव प्रसार कितने स्थानों पर समाप्त होगा?
After how many places will the decimal expansion of \(\frac{43}{400}\) terminate?
#decimal places
#terminating decimals
#prime factorisation
A (2) स्थान / (2) places
B (3) स्थान / (3) places
C (4) स्थान / (4) places
D असमाप्त रहेगा / It will not terminate
Explanation opens after your attempt
Correct Answer
B. (3) स्थान / (3) places
Step 1
Concept
\(400=2^4\times5^2\).
Step 2
Why this answer is correct
The larger exponent is (4), and \(\frac{43}{400}=0.1075\) has four places.
Step 3
Exam Tip
Therefore it terminates after (4) places. चरण 1: \(400=2^4\times5^2\) है। चरण 2: बड़ी घात (4) है, लेकिन \(\frac{43}{400}=0.1075\) में चार स्थान आते हैं। चरण 3: इसलिए सही संख्या (4) स्थान है।
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(400) को (31) से भाग देने पर सही यूक्लिडीय रूप कौन-सा है?
Which is the correct Euclidean form when (400) is divided by (31)?
#real-numbers
#euclidean-form
#standard-form
A \(400=31 \times 12+28\)
B \(400=31 \times 13-3\)
C \(400=31 \times 11+59\)
D \(400=31 \times 10+90\)
Explanation opens after your attempt
Correct Answer
A. \(400=31 \times 12+28\)
Step 1
Concept
\(31 \times 12=372\) and \(31 \times 13=403\).
Step 2
Why this answer is correct
Since (403) is greater, \(400=31 \times 12+28\).
Step 3
Exam Tip
A form with a negative remainder is not the standard Euclidean form. चरण 1: \(31 \times 12=372\) और \(31 \times 13=403\)। चरण 2: (403) बड़ा है, इसलिए \(400=31 \times 12+28\)। चरण 3: ऋणात्मक शेषफल वाला रूप मानक यूक्लिडीय रूप नहीं है।
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एक वर्ग का क्षेत्रफल \(225 cm^2\) है। यदि उसकी भुजा (x cm) बढ़ाकर नया क्षेत्रफल (400 cm\(^2) कर दिया जाए, तो (x) क्या है\)?
The area of a square is (225 cm\(^2). If its side is increased by (x\) cm) and the new area becomes (400 cm\(^2), what is (x)\)?
#quadratic equations
#square area
#application
A (3 cm)
B (4 cm)
C (5 cm)
D (6 cm)
Explanation opens after your attempt
Step 1
Concept
The original side is \(\sqrt{225}=15\), and the new side is \(\sqrt{400}=20\). Hence (x=20-15=5).
Step 2
Why this answer is correct
The correct answer is C. (5 cm\(). The original side is (\sqrt{225}=15), and the new side is (\sqrt{400}=20). Hence (x=20-15=5).\)
Step 3
Exam Tip
मूल भुजा \(\sqrt{225}=15\) है और नई भुजा \(\sqrt{400}=20\) है। अतः (x=20-15=5)।
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^4\times5^2\) है, तो वह संख्या कौन सी है?
If the prime factorisation of a number is \(2^4\times5^2\), which number is it?
#evaluate-factorisation
#number-400
#easy
A 400
B 200
C 800
D 100
Explanation opens after your attempt
Step 1
Concept
Calculate \(2^4=16\) and \(5^2=25\).
Step 2
Why this answer is correct
\(16\times25=400\).
Step 3
Exam Tip
Finding powers first makes the calculation easier. चरण 1: \(2^4=16\) और \(5^2=25\) निकालें। चरण 2: \(16\times25=400\)। चरण 3: घातों का मान पहले निकालना आसान रहता है।
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