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Mathematics Quiz - Class 10 Mathematics Medium Level 69 Quiz

Question 1/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी में पहला पद (3), सार्व अंतर (5) और पदों की संख्या (20) है। पहले (20) पदों का योग क्या होगा?

In an AP, the first term is (3), common difference is (5), and number of terms is (20). What is the sum of the first (20) terms?

Explanation opens after your attempt

Correct Answer

A. (1010)

Step 1

Concept

Using (S_n=\frac{n}{2}[2a+(n-1)d]), the sum is (1010). In exams, handle (n-1) carefully.

Step 2

Why this answer is correct

The correct answer is A. (1010). Using (S_n=\frac{n}{2}[2a+(n-1)d]), the sum is (1010). In exams, handle (n-1) carefully.

Step 3

Exam Tip

सूत्र (S_n=\frac{n}{2}[2a+(n-1)d]) लगाने पर योग (1010) आता है। परीक्षा में (n-1) को ध्यान से रखें।

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Question 2/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

यदि किसी समांतर श्रेढ़ी में (a=12), (d=-2) और (n=15), तो $S_{15}$ का मान ज्ञात कीजिए।

If an AP has (a=12), (d=-2), and (n=15), find the value of $S_{15}$.

Explanation opens after your attempt

Correct Answer

B. (-30)

Step 1

Concept

This is a decreasing AP, and the formula gives $S_{15}=-30$. Do not forget the sign of the negative common difference.

Step 2

Why this answer is correct

The correct answer is B. (-30). This is a decreasing AP, and the formula gives $S_{15}=-30$. Do not forget the sign of the negative common difference.

Step 3

Exam Tip

यह घटती हुई श्रेढ़ी है और सूत्र से $S_{15}=-30$ मिलता है। ऋणात्मक सार्व अंतर का संकेत न भूलें।

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Question 3/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

पहली (25) धनात्मक विषम संख्याओं का योग कितना है?

What is the sum of the first (25) positive odd numbers?

Explanation opens after your attempt

Correct Answer

C. (625)

Step 1

Concept

The sum of the first (n) odd numbers is $n^2$, so $25^2=625$. This result is useful for quick calculation.

Step 2

Why this answer is correct

The correct answer is C. (625). The sum of the first (n) odd numbers is $n^2$, so $25^2=625$. This result is useful for quick calculation.

Step 3

Exam Tip

पहली (n) विषम संख्याओं का योग $n^2$ होता है, इसलिए $25^2=625$। यह परिणाम तेज गणना में उपयोगी है।

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Question 4/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

(7) से (140) तक (7) के सभी धनात्मक गुणजों का योग ज्ञात कीजिए।

Find the sum of all positive multiples of (7) from (7) to (140).

Explanation opens after your attempt

Correct Answer

D. (1470)

Step 1

Concept

The AP is $7,14,\ldots,140$ with (20) terms, and its sum is (1470). Finding (n) from the last term is an easy method.

Step 2

Why this answer is correct

The correct answer is D. (1470). The AP is $7,14,\ldots,140$ with (20) terms, and its sum is (1470). Finding (n) from the last term is an easy method.

Step 3

Exam Tip

यह श्रेढ़ी $7,14,\ldots,140$ है जिसमें (20) पद हैं और योग (1470) है। अंतिम पद से (n) निकालना आसान तरीका है।

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Question 5/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $-5,-2,1,\ldots$ के पहले (30) पदों का योग क्या है?

What is the sum of the first (30) terms of the AP $-5,-2,1,\ldots$?

Explanation opens after your attempt

Correct Answer

A. (1155)

Step 1

Concept

Here (a=-5), (d=3), (n=30), so the sum is (1155). The same formula works even with a negative first term.

Step 2

Why this answer is correct

The correct answer is A. (1155). Here (a=-5), (d=3), (n=30), so the sum is (1155). The same formula works even with a negative first term.

Step 3

Exam Tip

यहाँ (a=-5), (d=3), (n=30), इसलिए योग (1155) है। ऋणात्मक पहले पद के साथ भी वही सूत्र लागू होता है।

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Question 6/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

किसी समांतर श्रेढ़ी का पहला पद (8), अंतिम पद (62) और पदों की संख्या (10) है। सभी पदों का योग ज्ञात कीजिए।

An AP has first term (8), last term (62), and number of terms (10). Find the sum of all terms.

Explanation opens after your attempt

Correct Answer

A. (350)

Step 1

Concept

Using (S_n=\frac{n}{2}(a+l)), the sum is (350). When the last term is given, this formula is faster.

Step 2

Why this answer is correct

The correct answer is A. (350). Using (S_n=\frac{n}{2}(a+l)), the sum is (350). When the last term is given, this formula is faster.

Step 3

Exam Tip

सूत्र (S_n=\frac{n}{2}(a+l)) से योग (350) आता है। जब अंतिम पद दिया हो तो यह सूत्र जल्दी काम करता है।

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Question 7/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

यदि $S_n=3n^2+2n$, तो पहले (12) पदों का योग क्या है?

If $S_n=3n^2+2n$, what is the sum of the first (12) terms?

Explanation opens after your attempt

Correct Answer

B. (456)

Step 1

Concept

Putting (n=12), (S_{12}=3(12)²+2(12)=456). Substitute the given value of (n) directly in the sum formula.

Step 2

Why this answer is correct

The correct answer is B. (456). Putting (n=12), (S_{12}=3(12)²+2(12)=456). Substitute the given value of (n) directly in the sum formula.

Step 3

Exam Tip

(n=12) रखने पर (S_{12}=3(12)²+2(12)=456)। दिए गए योग सूत्र में सीधे (n) का मान रखें।

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Question 8/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

एक सभागार की पंक्तियों में सीटों की संख्या $18,21,24,\ldots$ है। पहली (16) पंक्तियों में कुल सीटें कितनी होंगी?

The numbers of seats in rows of an auditorium are $18,21,24,\ldots$. How many seats are there in the first (16) rows?

Explanation opens after your attempt

Correct Answer

C. (648)

Step 1

Concept

This is an AP with (a=18), (d=3), (n=16), and the sum is (648). In word problems, identify (a,d,n) first.

Step 2

Why this answer is correct

The correct answer is C. (648). This is an AP with (a=18), (d=3), (n=16), and the sum is (648). In word problems, identify (a,d,n) first.

Step 3

Exam Tip

यह (a=18), (d=3), (n=16) वाली समांतर श्रेढ़ी है और योग (648) है। शब्द-प्रश्न में पहले (a,d,n) पहचानें।

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Question 9/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $50,47,44,\ldots$ के पहले (18) पदों का योग ज्ञात कीजिए।

Find the sum of the first (18) terms of the AP $50,47,44,\ldots$.

Explanation opens after your attempt

Correct Answer

A. (441)

Step 1

Concept

Here (d=-3), and the formula gives $S_{18}=441$. In a decreasing AP, write the common difference as negative.

Step 2

Why this answer is correct

The correct answer is A. (441). Here (d=-3), and the formula gives $S_{18}=441$. In a decreasing AP, write the common difference as negative.

Step 3

Exam Tip

यहाँ (d=-3) है और सूत्र से $S_{18}=441$ मिलता है। घटती श्रेढ़ी में सार्व अंतर ऋणात्मक लिखें।

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Question 10/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

यदि किसी समांतर श्रेढ़ी में (a=4), (l=100) और $S_n=1040$, तो पदों की संख्या (n) क्या है?

If an AP has (a=4), (l=100), and $S_n=1040$, what is the number of terms (n)?

Explanation opens after your attempt

Correct Answer

B. (20)

Step 1

Concept

From (\frac{n}{2}(4+100)=1040), (n=20). When last term and sum are given, use (S_n=\frac{n}{2}(a+l)).

Step 2

Why this answer is correct

The correct answer is B. (20). From (\frac{n}{2}(4+100)=1040), (n=20). When last term and sum are given, use (S_n=\frac{n}{2}(a+l)).

Step 3

Exam Tip

(\frac{n}{2}(4+100)=1040) से (n=20) आता है। अंतिम पद और योग दिए हों तो (S_n=\frac{n}{2}(a+l)) लगाएँ।

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Question 11/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

पहले (40) धनात्मक सम संख्याओं का योग क्या है?

What is the sum of the first (40) positive even numbers?

Explanation opens after your attempt

Correct Answer

C. (1640)

Step 1

Concept

The sum of the first (n) even numbers is (n(n+1)), so $40\times41=1640$. Remember it for even-number AP questions.

Step 2

Why this answer is correct

The correct answer is C. (1640). The sum of the first (n) even numbers is (n(n+1)), so $40\times41=1640$. Remember it for even-number AP questions.

Step 3

Exam Tip

पहली (n) सम संख्याओं का योग (n(n+1)) होता है, इसलिए $40\times41=1640$। इसे सम संख्या वाले प्रश्नों में याद रखें।

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Question 12/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

एक समांतर श्रेढ़ी में (a=9), (d=6) है। यदि $S_n=525$, तो (n) का मान क्या होगा?

In an AP, (a=9) and (d=6). If $S_n=525$, what is the value of (n)?

Explanation opens after your attempt

Correct Answer

A. (10)

Step 1

Concept

Solving (\frac{n}{2}[18+6(n-1)]=525) gives (n=10). For (n), a quadratic may appear, so choose the positive value.

Step 2

Why this answer is correct

The correct answer is A. (10). Solving (\frac{n}{2}[18+6(n-1)]=525) gives (n=10). For (n), a quadratic may appear, so choose the positive value.

Step 3

Exam Tip

(\frac{n}{2}[18+6(n-1)]=525) हल करने पर (n=10) मिलता है। (n) के लिए द्विघात बन सकता है, सही धनात्मक मान चुनें।

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Question 13/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $2,7,12,\ldots$ के कितने शुरुआती पदों का योग (287) होगा?

How many initial terms of the AP $2,7,12,\ldots$ have sum (287)?

Explanation opens after your attempt

Correct Answer

C. (11)

Step 1

Concept

From (\frac{n}{2}[4+5(n-1)]=287), (n=11). When finding the number of terms from sum, reject the negative root.

Step 2

Why this answer is correct

The correct answer is C. (11). From (\frac{n}{2}[4+5(n-1)]=287), (n=11). When finding the number of terms from sum, reject the negative root.

Step 3

Exam Tip

(\frac{n}{2}[4+5(n-1)]=287) से (n=11) मिलता है। योग से पदों की संख्या निकालते समय ऋणात्मक हल छोड़ दें।

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Question 14/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

यदि $S_{10}=250$ और $S_9=207$, तो (10)वाँ पद क्या है?

If $S_{10}=250$ and $S_9=207$, what is the (10)th term?

Explanation opens after your attempt

Correct Answer

C. (43)

Step 1

Concept

$a_{10}=S_{10}-S_9=43$. The difference of consecutive sums gives the corresponding term.

Step 2

Why this answer is correct

The correct answer is C. (43). $a_{10}=S_{10}-S_9=43$. The difference of consecutive sums gives the corresponding term.

Step 3

Exam Tip

$a_{10}=S_{10}-S_9=43$। लगातार योगों का अंतर संबंधित पद देता है।

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Question 15/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $6,11,16,\ldots$ के पहले (n) पदों का योग (660) है। (n) ज्ञात कीजिए।

The sum of the first (n) terms of the AP $6,11,16,\ldots$ is (660). Find (n).

Explanation opens after your attempt

Correct Answer

B. (15)

Step 1

Concept

Solving (\frac{n}{2}[12+5(n-1)]=660) gives (n=15). Simplify the bracket first, then solve the equation.

Step 2

Why this answer is correct

The correct answer is B. (15). Solving (\frac{n}{2}[12+5(n-1)]=660) gives (n=15). Simplify the bracket first, then solve the equation.

Step 3

Exam Tip

(\frac{n}{2}[12+5(n-1)]=660) हल करने पर (n=15) आता है। पहले कोष्ठक सरल करें, फिर समीकरण हल करें।

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Question 16/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

यदि किसी समांतर श्रेढ़ी के पहले (20) पदों का योग (780) और पहला पद (5) है, तो सार्व अंतर (d) क्या होगा?

If the sum of the first (20) terms of an AP is (780) and the first term is (5), what is the common difference (d)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

From (780=10[10+19d]), (d=4). When sum and first term are given, the common difference can be found directly.

Step 2

Why this answer is correct

The correct answer is B. (4). From (780=10[10+19d]), (d=4). When sum and first term are given, the common difference can be found directly.

Step 3

Exam Tip

(780=10[10+19d]) से (d=4) मिलता है। योग और पहला पद दिए हों तो सार्व अंतर सीधे निकाला जा सकता है।

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Question 17/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

एक बचत योजना में रवि पहले महीने (500) रुपये और हर अगले महीने (100) रुपये अधिक जमा करता है। (12) महीनों में कुल जमा राशि कितनी होगी?

In a saving plan, Ravi deposits (500) rupees in the first month and (100) rupees more each next month. What is the total deposit in (12) months?

Explanation opens after your attempt

Correct Answer

A. (12600)

Step 1

Concept

This is an AP with (a=500), (d=100), (n=12), and the total is (12600). In real-life questions, treat each amount as a term.

Step 2

Why this answer is correct

The correct answer is A. (12600). This is an AP with (a=500), (d=100), (n=12), and the total is (12600). In real-life questions, treat each amount as a term.

Step 3

Exam Tip

यह (a=500), (d=100), (n=12) वाली श्रेढ़ी है और कुल योग (12600) है। वास्तविक जीवन प्रश्नों में राशि को पद मानें।

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Question 18/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $15,19,23,\ldots$ के पहले (18) पदों का योग ज्ञात कीजिए।

Find the sum of the first (18) terms of the AP $15,19,23,\ldots$.

Explanation opens after your attempt

Correct Answer

B. (882)

Step 1

Concept

Putting (a=15), (d=4), (n=18) in the formula gives $S_{18}=882$. Always check (d) from the first three terms.

Step 2

Why this answer is correct

The correct answer is B. (882). Putting (a=15), (d=4), (n=18) in the formula gives $S_{18}=882$. Always check (d) from the first three terms.

Step 3

Exam Tip

सूत्र में (a=15), (d=4), (n=18) रखने पर $S_{18}=882$ मिलता है। पहले तीन पदों से (d) जरूर जाँचें।

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Question 19/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

(3) अंकों वाली उन संख्याओं का योग ज्ञात कीजिए जो (9) से विभाज्य हैं।

Find the sum of all (3)-digit numbers that are divisible by (9).

Explanation opens after your attempt

Correct Answer

A. (60984)

Step 1

Concept

The AP is $108,117,\ldots,999$ with (100) terms, so the sum is (55350), not (60984). Find the last term and number of terms carefully.

Step 2

Why this answer is correct

The correct answer is A. (60984). The AP is $108,117,\ldots,999$ with (100) terms, so the sum is (55350), not (60984). Find the last term and number of terms carefully.

Step 3

Exam Tip

श्रेढ़ी $108,117,\ldots,999$ है जिसमें (100) पद हैं, इसलिए योग (55350) नहीं बल्कि (55350) होगा। अंतिम पद और पदों की संख्या सावधानी से निकालें।

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Question 20/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

किसी समांतर श्रेढ़ी में $S_n=2n^2+5n$ है। पहले (8) पदों का योग क्या होगा?

In an AP, $S_n=2n^2+5n$. What is the sum of the first (8) terms?

Explanation opens after your attempt

Correct Answer

A. (168)

Step 1

Concept

(S_8=2(8)²+5(8)=168). Put (n=8) directly in the given $S_n$.

Step 2

Why this answer is correct

The correct answer is A. (168). (S_8=2(8)²+5(8)=168). Put (n=8) directly in the given $S_n$.

Step 3

Exam Tip

(S_8=2(8)²+5(8)=168)। दिए गए $S_n$ में सीधे (n=8) रखें।

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Question 21/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

यदि समांतर श्रेढ़ी का (a=20), (d=-1) और (n=25), तो $S_{25}$ कितना होगा?

If an AP has (a=20), (d=-1), and (n=25), what is $S_{25}$?

Explanation opens after your attempt

Correct Answer

B. (200)

Step 1

Concept

The formula gives $S_{25}=\frac{25}{2}[40-24]=200$. In a decreasing AP, the last term may be smaller.

Step 2

Why this answer is correct

The correct answer is B. (200). The formula gives $S_{25}=\frac{25}{2}[40-24]=200$. In a decreasing AP, the last term may be smaller.

Step 3

Exam Tip

सूत्र से $S_{25}=\frac{25}{2}[40-24]=200$ मिलता है। घटती श्रेढ़ी में अंतिम पद छोटा हो सकता है।

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Question 22/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $4,10,16,\ldots$ के पहले (14) पदों का योग क्या है?

What is the sum of the first (14) terms of the AP $4,10,16,\ldots$?

Explanation opens after your attempt

Correct Answer

B. (602)

Step 1

Concept

Here (a=4), (d=6), (n=14), so the sum is (602). Calculate (2a) and ((n-1)d) separately.

Step 2

Why this answer is correct

The correct answer is B. (602). Here (a=4), (d=6), (n=14), so the sum is (602). Calculate (2a) and ((n-1)d) separately.

Step 3

Exam Tip

यहाँ (a=4), (d=6), (n=14), इसलिए योग (602) है। (2a) और ((n-1)d) को अलग-अलग निकालें।

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Question 23/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

एक कारखाने में रोज उत्पादन $120,135,150,\ldots$ वस्तुओं का है। (10) दिनों में कुल उत्पादन कितना होगा?

A factory produces $120,135,150,\ldots$ items per day. What is the total production in (10) days?

Explanation opens after your attempt

Correct Answer

A. (1875)

Step 1

Concept

The production forms an AP, and $S_{10}=1875$. Treat the daily increase as the common difference.

Step 2

Why this answer is correct

The correct answer is A. (1875). The production forms an AP, and $S_{10}=1875$. Treat the daily increase as the common difference.

Step 3

Exam Tip

यह उत्पादन समांतर श्रेढ़ी बनाता है और $S_{10}=1875$ है। दैनिक वृद्धि को सार्व अंतर मानें।

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Question 24/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

यदि किसी समांतर श्रेढ़ी का पहला पद (11), अंतिम पद (71) और योग (574) है, तो पदों की संख्या क्या है?

If an AP has first term (11), last term (71), and sum (574), what is the number of terms?

Explanation opens after your attempt

Correct Answer

C. (14)

Step 1

Concept

From (\frac{n}{2}(11+71)=574), (n=14). When the last term is given, the common difference is not needed.

Step 2

Why this answer is correct

The correct answer is C. (14). From (\frac{n}{2}(11+71)=574), (n=14). When the last term is given, the common difference is not needed.

Step 3

Exam Tip

(\frac{n}{2}(11+71)=574) से (n=14) मिलता है। अंतिम पद दिए होने पर सार्व अंतर की जरूरत नहीं होती।

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Question 25/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $31,28,25,\ldots$ के पहले (20) पदों का योग ज्ञात कीजिए।

Find the sum of the first (20) terms of the AP $31,28,25,\ldots$.

Explanation opens after your attempt

Correct Answer

A. (50)

Step 1

Concept

Here the last term is (-26), and $S_{20}=50$. In a decreasing AP, the sum can become quite small.

Step 2

Why this answer is correct

The correct answer is A. (50). Here the last term is (-26), and $S_{20}=50$. In a decreasing AP, the sum can become quite small.

Step 3

Exam Tip

यहाँ अंतिम पद (-26) है और $S_{20}=50$ मिलता है। घटती श्रेढ़ी में योग बहुत छोटा भी हो सकता है।

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Question 26/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

पहले (18) पदों का योग (441) और पहला पद (3) है। यदि श्रेढ़ी समांतर है, तो सार्व अंतर (d) क्या होगा?

The sum of the first (18) terms is (441), and the first term is (3). If the sequence is an AP, what is the common difference (d)?

Explanation opens after your attempt

Correct Answer

B. (3)

Step 1

Concept

From (441=9[6+17d]), (d=3). In questions with unknown (d), simplify both sides first.

Step 2

Why this answer is correct

The correct answer is B. (3). From (441=9[6+17d]), (d=3). In questions with unknown (d), simplify both sides first.

Step 3

Exam Tip

(441=9[6+17d]) से (d=3) आता है। अज्ञात (d) वाले प्रश्नों में पहले दोनों पक्षों को सरल करें।

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Question 27/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

किसी समांतर श्रेढ़ी में $S_{16}=816$ और (a=6) है। यदि (d) धनात्मक है, तो (d) ज्ञात कीजिए।

In an AP, $S_{16}=816$ and (a=6). If (d) is positive, find (d).

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

From (816=8[12+15d]), (d=6). Divide the given sum by $\frac{n}{2}$ to solve faster.

Step 2

Why this answer is correct

The correct answer is A. (6). From (816=8[12+15d]), (d=6). Divide the given sum by $\frac{n}{2}$ to solve faster.

Step 3

Exam Tip

(816=8[12+15d]) से (d=6) मिलता है। दिए गए योग को $\frac{n}{2}$ से बाँटकर जल्दी हल करें।

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Question 28/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

(100) से (200) के बीच (5) से विभाज्य सभी संख्याओं का योग ज्ञात कीजिए।

Find the sum of all numbers divisible by (5) between (100) and (200).

Explanation opens after your attempt

Correct Answer

A. (3150)

Step 1

Concept

The numbers are $105,110,\ldots,195$, and the sum of (19) terms is (2850). The word between often excludes endpoints.

Step 2

Why this answer is correct

The correct answer is A. (3150). The numbers are $105,110,\ldots,195$, and the sum of (19) terms is (2850). The word between often excludes endpoints.

Step 3

Exam Tip

संख्याएँ $105,110,\ldots,195$ हैं और (19) पदों का योग (2850) है। बीच का अर्थ अक्सर सिरों को शामिल नहीं करता।

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Question 29/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

यदि समांतर श्रेढ़ी $13,18,23,\ldots$ में पहले (n) पदों का योग (253) है, तो (n) क्या है?

If the sum of the first (n) terms of the AP $13,18,23,\ldots$ is (253), what is (n)?

Explanation opens after your attempt

Correct Answer

D. (11)

Step 1

Concept

From (\frac{n}{2}[26+5(n-1)]=253), (n=11). Only the correct positive integer can be the number of terms.

Step 2

Why this answer is correct

The correct answer is D. (11). From (\frac{n}{2}[26+5(n-1)]=253), (n=11). Only the correct positive integer can be the number of terms.

Step 3

Exam Tip

(\frac{n}{2}[26+5(n-1)]=253) से (n=11) मिलता है। सही धनात्मक पूर्णांक ही पदों की संख्या हो सकता है।

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Question 30/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $1,4,7,\ldots$ के पहले (30) पदों का योग कितना है?

What is the sum of the first (30) terms of the AP $1,4,7,\ldots$?

Explanation opens after your attempt

Correct Answer

C. (1335)

Step 1

Concept

Here (a=1), (d=3), (n=30), so $S_{30}=1335$. Even with a small first term, the sum can be large.

Step 2

Why this answer is correct

The correct answer is C. (1335). Here (a=1), (d=3), (n=30), so $S_{30}=1335$. Even with a small first term, the sum can be large.

Step 3

Exam Tip

यहाँ (a=1), (d=3), (n=30), इसलिए $S_{30}=1335$। छोटे पहले पद के कारण भी योग बड़ा हो सकता है।

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Question 31/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

एक सीढ़ी में डंडों की लंबाइयाँ $40,43,46,\ldots$ सेंटीमीटर हैं। पहले (15) डंडों की कुल लंबाई क्या होगी?

The lengths of rods in a ladder are $40,43,46,\ldots$ cm. What is the total length of the first (15) rods?

Explanation opens after your attempt

Correct Answer

B. (915)

Step 1

Concept

Putting (a=40), (d=3), (n=15), the sum is (915) cm. Keep the unit in mind in the answer.

Step 2

Why this answer is correct

The correct answer is B. (915). Putting (a=40), (d=3), (n=15), the sum is (915) cm. Keep the unit in mind in the answer.

Step 3

Exam Tip

(a=40), (d=3), (n=15) रखने पर योग (915) सेंटीमीटर है। इकाई को उत्तर में ध्यान रखें।

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Question 32/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

यदि $S_n=n^2+4n$, तो $S_{20}$ का मान क्या होगा?

If $S_n=n^2+4n$, what is the value of $S_{20}$?

Explanation opens after your attempt

Correct Answer

C. (480)

Step 1

Concept

(S_{20}=20²+4(20)=480). In such a question, there is no need to find (a) and (d) separately.

Step 2

Why this answer is correct

The correct answer is C. (480). (S_{20}=20²+4(20)=480). In such a question, there is no need to find (a) and (d) separately.

Step 3

Exam Tip

(S_{20}=20²+4(20)=480)। ऐसे प्रश्न में अलग से (a) और (d) निकालने की जरूरत नहीं है।

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Question 33/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

किसी समांतर श्रेढ़ी में (a=17), (d=2) और $S_n=580$ है। (n) ज्ञात कीजिए।

In an AP, (a=17), (d=2), and $S_n=580$. Find (n).

Explanation opens after your attempt

Correct Answer

C. (20)

Step 1

Concept

From (\frac{n}{2}[34+2(n-1)]=580), (n=20). After forming the equation, you can also check using options.

Step 2

Why this answer is correct

The correct answer is C. (20). From (\frac{n}{2}[34+2(n-1)]=580), (n=20). After forming the equation, you can also check using options.

Step 3

Exam Tip

(\frac{n}{2}[34+2(n-1)]=580) से (n=20) मिलता है। समीकरण बनने के बाद विकल्पों से भी जाँच कर सकते हैं।

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Question 34/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $100,95,90,\ldots$ के पहले (12) पदों का योग ज्ञात कीजिए।

Find the sum of the first (12) terms of the AP $100,95,90,\ldots$.

Explanation opens after your attempt

Correct Answer

A. (870)

Step 1

Concept

The last term is (45), so (S_{12}=\frac{12}{2}(100+45)=870). Once the last term is found, the sum is quick.

Step 2

Why this answer is correct

The correct answer is A. (870). The last term is (45), so (S_{12}=\frac{12}{2}(100+45)=870). Once the last term is found, the sum is quick.

Step 3

Exam Tip

अंतिम पद (45) है, इसलिए (S_{12}=\frac{12}{2}(100+45)=870)। अंतिम पद मिल जाए तो योग तेजी से निकलेगा।

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Question 35/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

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)?

Explanation opens after your attempt

Correct Answer

C. (30)

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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Question 36/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $8,13,18,\ldots,83$ का योग ज्ञात कीजिए।

Find the sum of the AP $8,13,18,\ldots,83$.

Explanation opens after your attempt

Correct Answer

B. (728)

Step 1

Concept

First find (n): (83=8+(n-1)5), so (n=16) and the sum is (728). When the last term is given, find the number of terms first.

Step 2

Why this answer is correct

The correct answer is B. (728). First find (n): (83=8+(n-1)5), so (n=16) and the sum is (728). When the last term is given, find the number of terms first.

Step 3

Exam Tip

पहले (n) निकालें: (83=8+(n-1)5), इसलिए (n=16) और योग (728) है। अंतिम पद होने पर पहले पदों की संख्या निकालें।

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Question 37/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

एक छात्र प्रतिदिन (15) मिनट से शुरू करके हर दिन (5) मिनट अधिक अभ्यास करता है। (14) दिनों में कुल अभ्यास समय कितना होगा?

A student starts with (15) minutes of practice per day and increases it by (5) minutes every day. What is the total practice time in (14) days?

Explanation opens after your attempt

Correct Answer

C. (665)

Step 1

Concept

This is the AP $15,20,25,\ldots$, and the sum for (14) days is (665) minutes. In word problems, treat days as the number of terms.

Step 2

Why this answer is correct

The correct answer is C. (665). This is the AP $15,20,25,\ldots$, and the sum for (14) days is (665) minutes. In word problems, treat days as the number of terms.

Step 3

Exam Tip

यह $15,20,25,\ldots$ श्रेढ़ी है और (14) दिनों का योग (665) मिनट है। शब्द-प्रश्न में दिन को पदों की संख्या मानें।

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Question 38/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

यदि $S_{25}=1225$ और $S_{24}=1128$, तो (25)वाँ पद क्या है?

If $S_{25}=1225$ and $S_{24}=1128$, what is the (25)th term?

Explanation opens after your attempt

Correct Answer

C. (97)

Step 1

Concept

$a_{25}=S_{25}-S_{24}=97$. The difference of total sums gives the newly added last term.

Step 2

Why this answer is correct

The correct answer is C. (97). $a_{25}=S_{25}-S_{24}=97$. The difference of total sums gives the newly added last term.

Step 3

Exam Tip

$a_{25}=S_{25}-S_{24}=97$। कुल योगों का अंतर अंतिम नया पद देता है।

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Question 39/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $24,21,18,\ldots$ के पहले (16) पदों का योग कितना है?

What is the sum of the first (16) terms of the AP $24,21,18,\ldots$?

Explanation opens after your attempt

Correct Answer

C. (24)

Step 1

Concept

The last term is (-21), and (S_{16}=\frac{16}{2}(24-21)=24). Positive and negative terms can greatly reduce the sum.

Step 2

Why this answer is correct

The correct answer is C. (24). The last term is (-21), and (S_{16}=\frac{16}{2}(24-21)=24). Positive and negative terms can greatly reduce the sum.

Step 3

Exam Tip

अंतिम पद (-21) है और (S_{16}=\frac{16}{2}(24-21)=24)। धनात्मक और ऋणात्मक पद एक-दूसरे को काफी घटा सकते हैं।

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Question 40/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

यदि किसी समांतर श्रेढ़ी में $S_{12}=390$ और (d=5), तो पहला पद (a) क्या होगा?

If an AP has $S_{12}=390$ and (d=5), what is the first term (a)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

From (390=6[2a+55]), (a=5). For an unknown first term, keep (2a) separate.

Step 2

Why this answer is correct

The correct answer is B. (5). From (390=6[2a+55]), (a=5). For an unknown first term, keep (2a) separate.

Step 3

Exam Tip

(390=6[2a+55]) से (a=5) मिलता है। अज्ञात पहले पद के लिए (2a) को अलग रखें।

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Question 41/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

(50) से कम (4) के सभी धनात्मक गुणजों का योग कितना है?

What is the sum of all positive multiples of (4) less than (50)?

Explanation opens after your attempt

Correct Answer

C. (312)

Step 1

Concept

The AP is $4,8,\ldots,48$ with (12) terms, and the sum is (312). Identifying the last allowed multiple is important.

Step 2

Why this answer is correct

The correct answer is C. (312). The AP is $4,8,\ldots,48$ with (12) terms, and the sum is (312). Identifying the last allowed multiple is important.

Step 3

Exam Tip

श्रेढ़ी $4,8,\ldots,48$ है जिसमें (12) पद हैं और योग (312) है। अंतिम स्वीकार्य गुणज पहचानना जरूरी है।

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Question 42/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $5,9,13,\ldots$ में पहले कितने पदों का योग (425) होगा?

In the AP $5,9,13,\ldots$, how many first terms have sum (425)?

Explanation opens after your attempt

Correct Answer

C. (17)

Step 1

Concept

From (\frac{n}{2}[10+4(n-1)]=425), (n=17). You can also verify by substituting options.

Step 2

Why this answer is correct

The correct answer is C. (17). From (\frac{n}{2}[10+4(n-1)]=425), (n=17). You can also verify by substituting options.

Step 3

Exam Tip

(\frac{n}{2}[10+4(n-1)]=425) से (n=17) मिलता है। विकल्पों में मान रखकर भी जाँच कर सकते हैं।

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Question 43/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

एक सड़क पर खंभों की दूरी के क्रम $6,12,18,\ldots$ मीटर हैं। पहले (25) अंतरालों की कुल दूरी कितनी होगी?

On a road, the distances of intervals are $6,12,18,\ldots$ meters. What is the total distance of the first (25) intervals?

Explanation opens after your attempt

Correct Answer

C. (1950)

Step 1

Concept

This is the sum of the first (25) multiples of (6), so the total distance is (1950) meters. In sums of multiples, (a=d).

Step 2

Why this answer is correct

The correct answer is C. (1950). This is the sum of the first (25) multiples of (6), so the total distance is (1950) meters. In sums of multiples, (a=d).

Step 3

Exam Tip

यह (6) के पहले (25) गुणजों का योग है, इसलिए कुल दूरी (1950) मीटर है। गुणजों के योग में (a=d) होता है।

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Question 44/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

यदि $S_n=5n^2-n$, तो $S_{9}$ का मान क्या है?

If $S_n=5n^2-n$, what is the value of $S_9$?

Explanation opens after your attempt

Correct Answer

A. (396)

Step 1

Concept

(S_9=5(9)²-9=396). Pay attention to the sign because subtraction is involved.

Step 2

Why this answer is correct

The correct answer is A. (396). (S_9=5(9)²-9=396). Pay attention to the sign because subtraction is involved.

Step 3

Exam Tip

(S_9=5(9)²-9=396)। संकेत का ध्यान रखें क्योंकि यहाँ घटाव है।

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Question 45/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $7,12,17,\ldots,82$ का योग ज्ञात कीजिए।

Find the sum of the AP $7,12,17,\ldots,82$.

Explanation opens after your attempt

Correct Answer

B. (712)

Step 1

Concept

From (82=7+(n-1)5), (n=16), and then the sum is (712). Finding (n) from the last term is the first step.

Step 2

Why this answer is correct

The correct answer is B. (712). From (82=7+(n-1)5), (n=16), and then the sum is (712). Finding (n) from the last term is the first step.

Step 3

Exam Tip

(82=7+(n-1)5) से (n=16), फिर योग (712) है। अंतिम पद से (n) निकालना पहला कदम है।

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Question 46/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

यदि (a=25), (d=-4) और $S_n=105$, तो (n) का सही धनात्मक मान क्या है?

If (a=25), (d=-4), and $S_n=105$, what is the correct positive value of (n)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

From (\frac{n}{2}[50-4(n-1)]=105), (n=7). Even in a decreasing AP, (n) must be a positive integer.

Step 2

Why this answer is correct

The correct answer is C. (7). From (\frac{n}{2}[50-4(n-1)]=105), (n=7). Even in a decreasing AP, (n) must be a positive integer.

Step 3

Exam Tip

(\frac{n}{2}[50-4(n-1)]=105) से (n=7) मिलता है। घटती श्रेढ़ी में भी (n) धनात्मक पूर्णांक होता है।

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Question 47/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

पहले (32) प्राकृतिक संख्याओं का योग ज्ञात कीजिए।

Find the sum of the first (32) natural numbers.

Explanation opens after your attempt

Correct Answer

B. (528)

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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Question 48/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $9,16,23,\ldots$ के पहले (13) पदों का योग क्या है?

What is the sum of the first (13) terms of the AP $9,16,23,\ldots$?

Explanation opens after your attempt

Correct Answer

C. (663)

Step 1

Concept

Here (a=9), (d=7), (n=13), so $S_{13}=663$. Do not worry about $\frac{n}{2}$ when (n) is odd.

Step 2

Why this answer is correct

The correct answer is C. (663). Here (a=9), (d=7), (n=13), so $S_{13}=663$. Do not worry about $\frac{n}{2}$ when (n) is odd.

Step 3

Exam Tip

यहाँ (a=9), (d=7), (n=13), इसलिए $S_{13}=663$। विषम (n) होने पर $\frac{n}{2}$ से डरें नहीं।

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Question 49/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

यदि किसी समांतर श्रेढ़ी का $S_{14}=511$ और (a=4) है, तो (d) क्या होगा?

If an AP has $S_{14}=511$ and (a=4), what is (d)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

From (511=7[8+13d]), (d=5). First divide $S_n$ by $\frac{n}{2}$.

Step 2

Why this answer is correct

The correct answer is B. (5). From (511=7[8+13d]), (d=5). First divide $S_n$ by $\frac{n}{2}$.

Step 3

Exam Tip

(511=7[8+13d]) से (d=5) मिलता है। पहले $S_n$ को $\frac{n}{2}$ से विभाजित करें।

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Question 50/50 Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

किसी समांतर श्रेढ़ी में पहला पद (14), अंतिम पद (104) और पदों की संख्या (19) है। योग कितना होगा?

In an AP, the first term is (14), the last term is (104), and the number of terms is (19). What is the sum?

Explanation opens after your attempt

Correct Answer

C. (1121)

Step 1

Concept

(S_{19}=\frac{19}{2}(14+104)=1121). When first and last terms are given, finding (d) is not necessary.

Step 2

Why this answer is correct

The correct answer is C. (1121). (S_{19}=\frac{19}{2}(14+104)=1121). When first and last terms are given, finding (d) is not necessary.

Step 3

Exam Tip

(S_{19}=\frac{19}{2}(14+104)=1121)। पहला और अंतिम पद दिए हों तो (d) निकालना जरूरी नहीं है।

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Class 10 Mathematics Medium Quiz

समांतर श्रेढ़ी में पहला पद (3), सार्व अंतर (5) और पदों की संख्या (20) है। पहले (20) पदों का योग क्या होगा?

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Why this answer is correct

Exam Tip

यदि किसी समांतर श्रेढ़ी में (a=12), (d=-2) और (n=15), तो \(S_{15}\) का मान ज्ञात कीजिए।

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पहली (25) धनात्मक विषम संख्याओं का योग कितना है?

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(7) से (140) तक (7) के सभी धनात्मक गुणजों का योग ज्ञात कीजिए।

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समांतर श्रेढ़ी \(-5,-2,1,\ldots\) के पहले (30) पदों का योग क्या है?

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Exam Tip

किसी समांतर श्रेढ़ी का पहला पद (8), अंतिम पद (62) और पदों की संख्या (10) है। सभी पदों का योग ज्ञात कीजिए।

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यदि \(S_n=3n^2+2n\), तो पहले (12) पदों का योग क्या है?

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एक सभागार की पंक्तियों में सीटों की संख्या \(18,21,24,\ldots\) है। पहली (16) पंक्तियों में कुल सीटें कितनी होंगी?

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समांतर श्रेढ़ी \(50,47,44,\ldots\) के पहले (18) पदों का योग ज्ञात कीजिए।

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यदि किसी समांतर श्रेढ़ी में (a=4), (l=100) और \(S_n=1040\), तो पदों की संख्या (n) क्या है?

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पहले (40) धनात्मक सम संख्याओं का योग क्या है?

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एक समांतर श्रेढ़ी में (a=9), (d=6) है। यदि \(S_n=525\), तो (n) का मान क्या होगा?

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समांतर श्रेढ़ी \(2,7,12,\ldots\) के कितने शुरुआती पदों का योग (287) होगा?

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यदि \(S_{10}=250\) और \(S_9=207\), तो (10)वाँ पद क्या है?

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समांतर श्रेढ़ी \(6,11,16,\ldots\) के पहले (n) पदों का योग (660) है। (n) ज्ञात कीजिए।

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यदि किसी समांतर श्रेढ़ी के पहले (20) पदों का योग (780) और पहला पद (5) है, तो सार्व अंतर (d) क्या होगा?

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समांतर श्रेढ़ी \(15,19,23,\ldots\) के पहले (18) पदों का योग ज्ञात कीजिए।

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(3) अंकों वाली उन संख्याओं का योग ज्ञात कीजिए जो (9) से विभाज्य हैं।

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किसी समांतर श्रेढ़ी में \(S_n=2n^2+5n\) है। पहले (8) पदों का योग क्या होगा?

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