पहले (32) प्राकृतिक संख्याओं का योग ज्ञात कीजिए।
Find the sum of the first (32) natural numbers.
#natural numbers
#sum formula
#class 10
A (520)
B (528)
C (536)
D (544)
Explanation opens after your attempt
Step 1
Concept
\(\frac{32\times33}{2}=528\). For natural numbers, (\frac{n(n+1)}{2}) is the fastest formula.
Step 2
Why this answer is correct
The correct answer is B. (528). \(\frac{32\times33}{2}=528\). For natural numbers, (\frac{n(n+1)}{2}) is the fastest formula.
Step 3
Exam Tip
\(\frac{32\times33}{2}=528\)। प्राकृतिक संख्याओं के लिए (\frac{n(n+1)}{2}) सबसे तेज सूत्र है।
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यदि पहले (n) प्राकृतिक संख्याओं का योग (465) है, तो (n) क्या होगा?
If the sum of the first (n) natural numbers is (465), what is (n)?
#natural numbers
#sum
#ap
A (28)
B (29)
C (30)
D (31)
Explanation opens after your attempt
Step 1
Concept
From (\frac{n(n+1)}{2}=465), (n=30). The sum of natural numbers is a special case of AP.
Step 2
Why this answer is correct
The correct answer is C. (30). From (\frac{n(n+1)}{2}=465), (n=30). The sum of natural numbers is a special case of AP.
Step 3
Exam Tip
(\frac{n(n+1)}{2}=465) से (n=30) आता है। प्राकृतिक संख्याओं का योग भी समांतर श्रेढ़ी का विशेष रूप है।
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समांतर श्रेणी \(11,22,33,\ldots\) के पहले (14) पदों का योग ज्ञात कीजिए।
Find the sum of the first (14) terms of the arithmetic progression \(11,22,33,\ldots\).
#multiples
#ap_sum
#natural_numbers
A (1135)
B (1155)
C (1175)
D (1195)
Explanation opens after your attempt
Step 1
Concept
This is the sum of the first (14) multiples of (11), so \(11\times\frac{14\times15}{2}=1155\). For multiples, use the sum of natural numbers.
Step 2
Why this answer is correct
The correct answer is B. (1155). This is the sum of the first (14) multiples of (11), so \(11\times\frac{14\times15}{2}=1155\). For multiples, use the sum of natural numbers.
Step 3
Exam Tip
यह (11) के पहले (14) गुणजों का योग है, इसलिए \(11\times\frac{14\times15}{2}=1155\)। गुणजों में प्राकृतिक संख्याओं के योग का उपयोग करें।
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(4) से (100) तक (4) के गुणजों का योग कितना है?
What is the sum of the multiples of (4) from (4) to (100)?
#multiples
#ap_sum
#natural_numbers
A (1280)
B (1300)
C (1320)
D (1340)
Explanation opens after your attempt
Step 1
Concept
This is the sum of the first (25) multiples of (4), so \(4\times\frac{25\times26}{2}=1300\). Use the sum of natural numbers for multiples.
Step 2
Why this answer is correct
The correct answer is B. (1300). This is the sum of the first (25) multiples of (4), so \(4\times\frac{25\times26}{2}=1300\). Use the sum of natural numbers for multiples.
Step 3
Exam Tip
यह (4) के पहले (25) गुणजों का योग है, इसलिए \(4\times\frac{25\times26}{2}=1300\)। गुणजों में प्राकृतिक संख्याओं का योग लगाएँ।
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यदि पहले (n) प्राकृतिक संख्याओं का योग (325) है, तो (n) का मान क्या होगा?
If the sum of the first (n) natural numbers is (325), what is the value of (n)?
#natural_numbers
#find_n
#ap_sum
A (23)
B (24)
C (25)
D (26)
Explanation opens after your attempt
Step 1
Concept
From (\frac{n(n+1)}{2}=325), (n(n+1)=650), so (n=25). In such questions, look for products of consecutive numbers.
Step 2
Why this answer is correct
The correct answer is C. (25). From (\frac{n(n+1)}{2}=325), (n(n+1)=650), so (n=25). In such questions, look for products of consecutive numbers.
Step 3
Exam Tip
(\frac{n(n+1)}{2}=325) से (n(n+1)=650), इसलिए (n=25)। ऐसे प्रश्न में पास-पास की संख्याओं का गुणन देखें।
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पहले (35) प्राकृतिक संख्याओं का योग क्या होगा?
What will be the sum of the first (35) natural numbers?
#natural_numbers
#ap_sum
#formula
A (610)
B (620)
C (630)
D (640)
Explanation opens after your attempt
Step 1
Concept
\(\frac{35\times36}{2}=630\), so the sum is (630). Divide (n(n+1)) by (2).
Step 2
Why this answer is correct
The correct answer is C. (630). \(\frac{35\times36}{2}=630\), so the sum is (630). Divide (n(n+1)) by (2).
Step 3
Exam Tip
\(\frac{35\times36}{2}=630\), इसलिए योग (630) है। (n(n+1)) को (2) से भाग दें।
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पहले (28) प्राकृतिक संख्याओं का योग ज्ञात कीजिए।
Find the sum of the first (28) natural numbers.
#natural_numbers
#sum
#ap
A (386)
B (396)
C (406)
D (416)
Explanation opens after your attempt
Step 1
Concept
\(\frac{28\times29}{2}=406\), so the sum is (406). The natural-number sum formula gives a quick answer.
Step 2
Why this answer is correct
The correct answer is C. (406). \(\frac{28\times29}{2}=406\), so the sum is (406). The natural-number sum formula gives a quick answer.
Step 3
Exam Tip
\(\frac{28\times29}{2}=406\), इसलिए योग (406) है। प्राकृतिक संख्याओं का योग सूत्र जल्दी उत्तर देता है।
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पहले (22) प्राकृतिक संख्याओं का योग कितना है?
What is the sum of the first (22) natural numbers?
#natural_numbers
#ap_sum
#easy
A (243)
B (253)
C (263)
D (273)
Explanation opens after your attempt
Step 1
Concept
The sum of the first (n) natural numbers is (\frac{n(n+1)}{2}), so the answer is (253). Put the value of (n) directly in such questions.
Step 2
Why this answer is correct
The correct answer is B. (253). The sum of the first (n) natural numbers is (\frac{n(n+1)}{2}), so the answer is (253). Put the value of (n) directly in such questions.
Step 3
Exam Tip
पहले (n) प्राकृतिक संख्याओं का योग (\frac{n(n+1)}{2}) होता है, इसलिए (253) मिलेगा। ऐसे प्रश्न में सीधे (n) का मान लगाएँ।
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यदि (a=1), (d=1), और (n=50) है, तो समांतर श्रेढ़ी के पहले (50) पदों का योग कितना है?
If (a=1), (d=1), and (n=50), what is the sum of the first (50) terms of the arithmetic progression?
#natural_numbers
#ap_sum
#fifty_terms
A (1225)
B (1250)
C (1275)
D (1300)
Explanation opens after your attempt
Step 1
Concept
This is the sum of the first (50) natural numbers, which is (1275). When (d=1) and (a=1), use the natural-number sum formula.
Step 2
Why this answer is correct
The correct answer is C. (1275). This is the sum of the first (50) natural numbers, which is (1275). When (d=1) and (a=1), use the natural-number sum formula.
Step 3
Exam Tip
यह पहले (50) प्राकृतिक संख्याओं का योग है, जो (1275) है। (d=1) और (a=1) हो तो प्राकृतिक संख्या वाला सूत्र लगाएँ।
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पहले (30) प्राकृतिक संख्याओं का योग कितना है?
What is the sum of the first (30) natural numbers?
#natural_numbers
#sum
#ap
A (435)
B (445)
C (455)
D (465)
Explanation opens after your attempt
Step 1
Concept
\(\frac{30\times31}{2}=465\), so the correct sum is (465). Remember the direct formula for natural numbers.
Step 2
Why this answer is correct
The correct answer is D. (465). \(\frac{30\times31}{2}=465\), so the correct sum is (465). Remember the direct formula for natural numbers.
Step 3
Exam Tip
\(\frac{30\times31}{2}=465\), इसलिए सही योग (465) है। प्राकृतिक संख्याओं के लिए सीधा सूत्र याद रखें।
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कौन सा विकल्प प्राकृतिक संख्या भी है और परिमेय संख्या भी है?
Which option is both a natural number and a rational number?
#natural-numbers
#rational-numbers
#classification
A (14)
B \(\sqrt{14}\)
C (-14)
D (0.14)
Explanation opens after your attempt
Step 1
Concept
(14) is a natural number and \(14=\frac{14}{1}\). So it is also rational.
Step 2
Why this answer is correct
The correct answer is A. (14). (14) is a natural number and \(14=\frac{14}{1}\). So it is also rational.
Step 3
Exam Tip
(14) प्राकृतिक संख्या है और \(14=\frac{14}{1}\) भी है। इसलिए यह परिमेय भी है।
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कौन सी संख्या प्राकृतिक संख्या भी है और परिमेय संख्या भी है?
Which number is both a natural number and a rational number?
#natural-numbers
#rational-numbers
#sets
A (9)
B \(\sqrt{10}\)
C (-2.5)
D \(\pi\)
Explanation opens after your attempt
Step 1
Concept
(9) is a counting number and \(9=\frac{9}{1}\). So it is both natural and rational.
Step 2
Why this answer is correct
The correct answer is A. (9). (9) is a counting number and \(9=\frac{9}{1}\). So it is both natural and rational.
Step 3
Exam Tip
(9) गिनती की संख्या है और \(9=\frac{9}{1}\) भी है। इसलिए यह प्राकृतिक और परिमेय दोनों है।
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