100 results found for "decreasing interval" in Class 10.
एक घटती समान्तर श्रेणी में प्रथम पद (72) और सार्व अंतर (-4) है। पहले (24) पदों का योग कितना होगा?
In a decreasing arithmetic progression the first term is (72) and the common difference is (-4). What is the sum of the first (24) terms?
#ap
#decreasing-ap
#expert
A (576)
B (600)
C (612)
D (624)
Explanation opens after your attempt
Step 1
Concept
(S_{24}=\frac{24}{2}[144+23(-4)]=624). Exam tip: handle the negative common difference carefully.
Step 2
Why this answer is correct
The correct answer is D. (624). (S_{24}=\frac{24}{2}[144+23(-4)]=624). Exam tip: handle the negative common difference carefully.
Step 3
Exam Tip
(S_{24}=\frac{24}{2}[144+23(-4)]=624) है। परीक्षा में ऋणात्मक सार्व अंतर का चिन्ह सावधानी से रखें।
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एक घटती समान्तर श्रेणी में प्रथम पद (65) और सार्व अंतर (-5) है। पहले (15) पदों का योग कितना होगा?
In a decreasing arithmetic progression the first term is (65) and the common difference is (-5). What is the sum of the first (15) terms?
#ap
#decreasing-ap
#expert
A (450)
B (475)
C (500)
D (525)
Explanation opens after your attempt
Step 1
Concept
(S_{15}=\frac{15}{2}[130+14(-5)]=450). Exam tip: handle the negative common difference carefully.
Step 2
Why this answer is correct
The correct answer is A. (450). (S_{15}=\frac{15}{2}[130+14(-5)]=450). Exam tip: handle the negative common difference carefully.
Step 3
Exam Tip
(S_{15}=\frac{15}{2}[130+14(-5)]=450) है। परीक्षा में ऋणात्मक सार्व अंतर का चिन्ह सावधानी से रखें।
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किस अनुक्रम में पद समान मात्रा से घट रहे हैं लेकिन (d=-4) नहीं है?
In which sequence are terms decreasing by an equal amount but (d) is not (-4)?
#ap
#decreasing sequence
#negative difference
#medium
A \(30,26,22,18,\ldots\)
B \(45,40,35,30,\ldots\)
C \(16,12,8,4,\ldots\)
D \(9,5,1,-3,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(45,40,35,30,\ldots\)
Step 1
Concept
In \(45,40,35,30,\ldots\), (d=-5), not (-4). Check both value and sign in the options.
Step 2
Why this answer is correct
The correct answer is B. \(45,40,35,30,\ldots\). In \(45,40,35,30,\ldots\), (d=-5), not (-4). Check both value and sign in the options.
Step 3
Exam Tip
\(45,40,35,30,\ldots\) में (d=-5) है, (-4) नहीं। विकल्पों में मान और चिह्न दोनों जांचें।
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किस अनुक्रम में पद समान मात्रा से घट रहे हैं लेकिन (d=-2) नहीं है?
In which sequence are the terms decreasing by an equal amount but (d) is not (-2)?
#ap
#decreasing sequence
#negative difference
#medium
A \(20,17,14,11,\ldots\)
B \(9,7,5,3,\ldots\)
C \(8,6,4,2,\ldots\)
D \(5,3,1,-1,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(20,17,14,11,\ldots\)
Step 1
Concept
In \(20,17,14,11,\ldots\), (d=-3), not (-2). Check both sign and value in options.
Step 2
Why this answer is correct
The correct answer is A. \(20,17,14,11,\ldots\). In \(20,17,14,11,\ldots\), (d=-3), not (-2). Check both sign and value in options.
Step 3
Exam Tip
\(20,17,14,11,\ldots\) में (d=-3) है, (-2) नहीं। विकल्पों में चिह्न और मान दोनों जांचें।
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निम्न में से कौन सा अनुक्रम घटती अंकगणितीय श्रेणी है?
Which of the following is a decreasing arithmetic progression?
#ap
#decreasing ap
#negative difference
#easy
A \(50,45,40,35,\ldots\)
B \(2,4,8,16,\ldots\)
C \(5,5,5,5,\ldots\)
D \(1,4,9,16,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(50,45,40,35,\ldots\)
Step 1
Concept
In \(50,45,40,35,\ldots\), the equal difference is (-5). A decreasing arithmetic progression has negative (d).
Step 2
Why this answer is correct
The correct answer is A. \(50,45,40,35,\ldots\). In \(50,45,40,35,\ldots\), the equal difference is (-5). A decreasing arithmetic progression has negative (d).
Step 3
Exam Tip
\(50,45,40,35,\ldots\) में समान अंतर (-5) है। घटती अंकगणितीय श्रेणी का (d) ऋणात्मक होता है।
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किस विकल्प में समांतर श्रेणी घट रही है?
Which option shows a decreasing AP?
#ap
#decreasing_ap
#negative_difference
A \(4,9,14,19,\ldots\)
B \(8,8,8,8,\ldots\)
C \(20,17,14,11,\ldots\)
D \(-5,-1,3,7,\ldots\)
Explanation opens after your attempt
Correct Answer
C. \(20,17,14,11,\ldots\)
Step 1
Concept
Here the common difference is (-3), so the terms are decreasing. In exams, a decreasing AP has negative (d).
Step 2
Why this answer is correct
The correct answer is C. \(20,17,14,11,\ldots\). Here the common difference is (-3), so the terms are decreasing. In exams, a decreasing AP has negative (d).
Step 3
Exam Tip
यहां सामान्य अंतर (-3) है, इसलिए पद घट रहे हैं। परीक्षा में घटती समांतर श्रेणी का (d) ऋणात्मक होता है।
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यदि संख्या रेखा पर \(u=-\sqrt{27}-3\), तो (u) किस अंतराल में है?
If \(u=-\sqrt{27}-3\) on the number line, in which interval does (u) lie?
#number-line
#negative-expression
#interval
A ( -7 ) और ( -6 ) के बीच / Between ( -7 ) and ( -6 )
B ( -8 ) और ( -7 ) के बीच / Between ( -8 ) and ( -7 )
C ( -9 ) और ( -8 ) के बीच / Between ( -9 ) and ( -8 )
D (6) और (7) के बीच / Between (6) and (7)
Explanation opens after your attempt
Correct Answer
B. ( -8 ) और ( -7 ) के बीच / Between ( -8 ) and ( -7 )
Step 1
Concept
\( -\sqrt{27}\approx-5.196 \), so \( -\sqrt{27}-3\approx-8.196 \). Therefore it lies between (-9) and (-8).
Step 2
Why this answer is correct
The correct answer is B. ( -8 ) और ( -7 ) के बीच / Between ( -8 ) and ( -7 ). \( -\sqrt{27}\approx-5.196 \), so \( -\sqrt{27}-3\approx-8.196 \). Therefore it lies between (-9) and (-8).
Step 3
Exam Tip
\( -\sqrt{27}-3\approx-8.196 \) नहीं, बल्कि \( -\sqrt{27}\approx-5.196 \) होने से योग लगभग (-8.196) है। इसलिए यह (-9) और (-8) के बीच है।
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संख्या रेखा पर \(6-\sqrt{39}\) का सही स्थान किस अंतराल में है?
In which interval is \(6-\sqrt{39}\) correctly located on the number line?
#number-line
#root-expression
#interval
A ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
B (0) और (1) के बीच / Between (0) and (1)
C (1) और (2) के बीच / Between (1) and (2)
D ( -2 ) और ( -1 ) के बीच / Between ( -2 ) and ( -1 )
Explanation opens after your attempt
Correct Answer
A. ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
Step 1
Concept
\( \sqrt{39}\approx6.245 \), so \(6-\sqrt{39}\approx-0.245\). Always check the sign in root subtraction.
Step 2
Why this answer is correct
The correct answer is A. ( -1 ) और (0) के बीच / Between ( -1 ) and (0). \( \sqrt{39}\approx6.245 \), so \(6-\sqrt{39}\approx-0.245\). Always check the sign in root subtraction.
Step 3
Exam Tip
\( \sqrt{39}\approx6.245 \), इसलिए \(6-\sqrt{39}\approx-0.245\) है। घटाव वाले मूल में चिह्न जरूर जाँचें।
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यदि संख्या रेखा पर \(u=-\sqrt{18}-2\), तो (u) किस अंतराल में है?
If \(u=-\sqrt{18}-2\) on the number line, in which interval does (u) lie?
#number-line
#negative-expression
#interval
A ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 )
B ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 )
C ( -7 ) और ( -6 ) के बीच / Between ( -7 ) and ( -6 )
D (4) और (5) के बीच / Between (4) and (5)
Explanation opens after your attempt
Correct Answer
C. ( -7 ) और ( -6 ) के बीच / Between ( -7 ) and ( -6 )
Step 1
Concept
\( -\sqrt{18}-2\approx-6.243 \), so it lies between (-7) and (-6). Estimate negative sums carefully.
Step 2
Why this answer is correct
The correct answer is C. ( -7 ) और ( -6 ) के बीच / Between ( -7 ) and ( -6 ). \( -\sqrt{18}-2\approx-6.243 \), so it lies between (-7) and (-6). Estimate negative sums carefully.
Step 3
Exam Tip
\( -\sqrt{18}-2\approx-6.243 \), इसलिए यह (-7) और (-6) के बीच है। ऋणात्मक योगों में अनुमान सावधानी से करें।
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संख्या रेखा पर \(5-\sqrt{31}\) का सही स्थान किस अंतराल में है?
In which interval is \(5-\sqrt{31}\) correctly located on the number line?
#number-line
#root-expression
#interval
A (0) और (1) के बीच / Between (0) and (1)
B ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
C (1) और (2) के बीच / Between (1) and (2)
D ( -2 ) और ( -1 ) के बीच / Between ( -2 ) and ( -1 )
Explanation opens after your attempt
Correct Answer
B. ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
Step 1
Concept
\( \sqrt{31}\approx5.568 \), so \(5-\sqrt{31}\approx-0.568\). Always check the sign in root subtraction.
Step 2
Why this answer is correct
The correct answer is B. ( -1 ) और (0) के बीच / Between ( -1 ) and (0). \( \sqrt{31}\approx5.568 \), so \(5-\sqrt{31}\approx-0.568\). Always check the sign in root subtraction.
Step 3
Exam Tip
\( \sqrt{31}\approx5.568 \), इसलिए \(5-\sqrt{31}\approx-0.568\) है। घटाव वाले मूलों में चिह्न अवश्य जाँचें।
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यदि संख्या रेखा पर \(u=-2-\sqrt{7}\), तो (u) किस अंतराल में स्थित है?
If \(u=-2-\sqrt{7}\), in which interval is (u) located on the number line?
#number-line
#negative-expression
#interval
A ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 )
B ( -4 ) और ( -3 ) के बीच / Between ( -4 ) and ( -3 )
C ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 )
D (2) और (3) के बीच / Between (2) and (3)
Explanation opens after your attempt
Correct Answer
C. ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 )
Step 1
Concept
\( \sqrt{7}\approx2.646 \), so \(u\approx-4.646\). Therefore it lies between (-5) and (-4).
Step 2
Why this answer is correct
The correct answer is C. ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 ). \( \sqrt{7}\approx2.646 \), so \(u\approx-4.646\). Therefore it lies between (-5) and (-4).
Step 3
Exam Tip
\( \sqrt{7}\approx2.646 \), इसलिए \(u\approx-4.646\) है। अतः यह (-5) और (-4) के बीच होगा।
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यदि \(x=-5+\sqrt{22}\), तो संख्या रेखा पर (x) किस अंतराल में है?
If \(x=-5+\sqrt{22}\), in which interval is (x) on the number line?
#number-line
#root-expression
#interval
A ( -2 ) और ( -1 ) के बीच / Between ( -2 ) and ( -1 )
B (0) और (1) के बीच / Between (0) and (1)
C ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
D (1) और (2) के बीच / Between (1) and (2)
Explanation opens after your attempt
Correct Answer
C. ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
Step 1
Concept
Since \(4<\sqrt{22}<5\), \(-1<-5+\sqrt{22}<0\). Add bounds carefully in mixed expressions.
Step 2
Why this answer is correct
The correct answer is C. ( -1 ) और (0) के बीच / Between ( -1 ) and (0). Since \(4<\sqrt{22}<5\), \(-1<-5+\sqrt{22}<0\). Add bounds carefully in mixed expressions.
Step 3
Exam Tip
\(4<\sqrt{22}<5\), इसलिए \(-1<-5+\sqrt{22}<0\)। मिश्रित अभिव्यक्ति में सीमा जोड़ें।
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यदि संख्या रेखा पर \(x=-\sqrt{29}\), तो (x) किस अंतराल में होगा?
If \(x=-\sqrt{29}\) on the number line, in which interval will (x) lie?
#number-line
#negative-square-root
#interval
A ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 )
B ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 )
C (4) और (5) के बीच / Between (4) and (5)
D (5) और (6) के बीच / Between (5) and (6)
Explanation opens after your attempt
Correct Answer
B. ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 )
Step 1
Concept
Since \(5<\sqrt{29}<6\), \(-6<-\sqrt{29}<-5\). For negative roots, write the reversed interval carefully.
Step 2
Why this answer is correct
The correct answer is B. ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 ). Since \(5<\sqrt{29}<6\), \(-6<-\sqrt{29}<-5\). For negative roots, write the reversed interval carefully.
Step 3
Exam Tip
क्योंकि \(5<\sqrt{29}<6\), इसलिए \(-6<-\sqrt{29}<-5\)। ऋणात्मक मूलों में क्रम उलटकर लिखें।
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यदि संख्या रेखा पर \(u=-\sqrt{2}-1\), तो (u) किस अंतराल में है?
If \(u=-\sqrt{2}-1\) on the number line, in which interval does (u) lie?
#number-line
#negative-expression
#interval
A ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 )
B ( -2 ) और ( -1 ) के बीच / Between ( -2 ) and ( -1 )
C ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
D (2) और (3) के बीच / Between (2) and (3)
Explanation opens after your attempt
Correct Answer
A. ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 )
Step 1
Concept
\( -\sqrt{2}-1\approx-2.414 \), so it lies between (-3) and (-2). Estimate negative sums carefully.
Step 2
Why this answer is correct
The correct answer is A. ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 ). \( -\sqrt{2}-1\approx-2.414 \), so it lies between (-3) and (-2). Estimate negative sums carefully.
Step 3
Exam Tip
\( -\sqrt{2}-1\approx-2.414 \), इसलिए यह (-3) और (-2) के बीच है। ऋणात्मक योगों में अनुमान सावधानी से करें।
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संख्या रेखा पर \(2-\sqrt{10}\) का सही स्थान किस अंतराल में है?
In which interval is \(2-\sqrt{10}\) correctly located on the number line?
#number-line
#root-expression
#interval
A (-2) और (-1) के बीच / Between (-2) and (-1)
B (-1) और (0) के बीच / Between (-1) and (0)
C (0) और (1) के बीच / Between (0) and (1)
D (1) और (2) के बीच / Between (1) and (2)
Explanation opens after your attempt
Correct Answer
A. (-2) और (-1) के बीच / Between (-2) and (-1)
Step 1
Concept
\( \sqrt{10}\approx3.162 \), so \(2-\sqrt{10}\approx-1.162\). Estimation is important in root subtraction.
Step 2
Why this answer is correct
The correct answer is A. (-2) और (-1) के बीच / Between (-2) and (-1). \( \sqrt{10}\approx3.162 \), so \(2-\sqrt{10}\approx-1.162\). Estimation is important in root subtraction.
Step 3
Exam Tip
\( \sqrt{10}\approx3.162 \) इसलिए \(2-\sqrt{10}\approx-1.162\) है। घटाव वाले मूल में अनुमान जरूरी है।
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संख्या रेखा पर (x) का स्थान ( -4 ) से \( \sqrt{13} \) इकाई दाईं ओर है। (x) किस अंतराल में है?
The point (x) is \( \sqrt{13} \) units to the right of (-4) on the number line. In which interval does (x) lie?
#number-line
#interval
#root-expression
A (-1) और (0) के बीच / Between (-1) and (0)
B (0) और (1) के बीच / Between (0) and (1)
C (-2) और (-1) के बीच / Between (-2) and (-1)
D (-4) और (-3) के बीच / Between (-4) and (-3)
Explanation opens after your attempt
Correct Answer
A. (-1) और (0) के बीच / Between (-1) and (0)
Step 1
Concept
\(x=-4+\sqrt{13}\), and \(3<\sqrt{13}<4\), so (-1<x<0). Add bounds in combined expressions.
Step 2
Why this answer is correct
The correct answer is A. (-1) और (0) के बीच / Between (-1) and (0). \(x=-4+\sqrt{13}\), and \(3<\sqrt{13}<4\), so (-1<x<0). Add bounds in combined expressions.
Step 3
Exam Tip
\(x=-4+\sqrt{13}\) और \(3<\sqrt{13}<4\), इसलिए (-1<x<0)। संयुक्त अभिव्यक्ति में सीमा जोड़ें।
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संख्या रेखा पर \(\sqrt{5}-\sqrt{2}\) किस अंतराल में स्थित होगा?
On the number line, in which interval will \(\sqrt{5}-\sqrt{2}\) lie?
#polynomials
#number-line
#irrational-difference
#interval
A ((0,1))
B ((1,2))
C ((2,3))
D ((-1,0))
Explanation opens after your attempt
Correct Answer
A. ((0,1))
Step 1
Concept
\(\sqrt{5}\approx2.236\) and \(\sqrt{2}\approx1.414\), so the difference is about (0.822). Use short approximations to locate differences of irrationals.
Step 2
Why this answer is correct
The correct answer is A. ((0,1)). \(\sqrt{5}\approx2.236\) and \(\sqrt{2}\approx1.414\), so the difference is about (0.822). Use short approximations to locate differences of irrationals.
Step 3
Exam Tip
\(\sqrt{5}\approx2.236\) और \(\sqrt{2}\approx1.414\), इसलिए अंतर लगभग (0.822) है। अपरिमेयों के अंतर का स्थान निकालने के लिए छोटे अनुमान उपयोग करें।
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किस विकल्प में संख्या रेखा पर \(-\sqrt{12}\) का सही सरल अंतराल है?
Which option gives the correct simple interval for \(-\sqrt{12}\) on the number line?
#polynomials
#number-line
#negative-surd
#interval
A ((-4,-3))
B ((-3,-2))
C ((3,4))
D ((-5,-4))
Explanation opens after your attempt
Correct Answer
A. ((-4,-3))
Step 1
Concept
Since \(3<\sqrt{12}<4\), \(-4<-\sqrt{12}<-3\). Multiplying by a negative reverses the inequality.
Step 2
Why this answer is correct
The correct answer is A. ((-4,-3)). Since \(3<\sqrt{12}<4\), \(-4<-\sqrt{12}<-3\). Multiplying by a negative reverses the inequality.
Step 3
Exam Tip
क्योंकि \(3<\sqrt{12}<4\), इसलिए \(-4<-\sqrt{12}<-3\)। ऋणात्मक करने पर असमानता की दिशा बदलती है।
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संख्या रेखा पर \(\sqrt{2}+\sqrt{3}\) किस अंतराल में होगा?
On the number line, in which interval will \(\sqrt{2}+\sqrt{3}\) lie?
#polynomials
#number-line
#surd-addition
#interval
A ((3,4))
B ((2,3))
C ((4,5))
D ((1,2))
Explanation opens after your attempt
Correct Answer
A. ((3,4))
Step 1
Concept
\(\sqrt{2}\approx1.414\) and \(\sqrt{3}\approx1.732\), so the sum is about (3.146). Add approximate values for sums.
Step 2
Why this answer is correct
The correct answer is A. ((3,4)). \(\sqrt{2}\approx1.414\) and \(\sqrt{3}\approx1.732\), so the sum is about (3.146). Add approximate values for sums.
Step 3
Exam Tip
\(\sqrt{2}\approx1.414\) और \(\sqrt{3}\approx1.732\), इसलिए योग लगभग (3.146) है। योग के लिए अनुमानित मान जोड़ें।
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किस विकल्प में संख्या रेखा पर \(-1+\sqrt{5}\) का सही अंतराल है?
Which option gives the correct interval of \(-1+\sqrt{5}\) on the number line?
#polynomials
#number-line
#irrational-expression
#interval
A ((1,2))
B ((0,1))
C ((2,3))
D ((-1,0))
Explanation opens after your attempt
Correct Answer
A. ((1,2))
Step 1
Concept
Since \(2<\sqrt{5}<3\), \(1<-1+\sqrt{5}<2\). When adding or subtracting a constant, adjust the whole inequality.
Step 2
Why this answer is correct
The correct answer is A. ((1,2)). Since \(2<\sqrt{5}<3\), \(1<-1+\sqrt{5}<2\). When adding or subtracting a constant, adjust the whole inequality.
Step 3
Exam Tip
क्योंकि \(2<\sqrt{5}<3\), इसलिए \(1<-1+\sqrt{5}<2\)। स्थिर संख्या जोड़ने या घटाने पर पूरी असमानता बदलें।
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संख्या रेखा पर \(2-\sqrt{3}\) किस अंतराल में स्थित होगा?
On the number line, in which interval will \(2-\sqrt{3}\) lie?
#polynomials
#number-line
#irrational-expression
#interval
A ((0,1))
B ((1,2))
C ((-1,0))
D ((2,3))
Explanation opens after your attempt
Correct Answer
A. ((0,1))
Step 1
Concept
Since \(1<\sqrt{3}<2\), \(0<2-\sqrt{3}<1\). Be careful with inequalities when subtracting.
Step 2
Why this answer is correct
The correct answer is A. ((0,1)). Since \(1<\sqrt{3}<2\), \(0<2-\sqrt{3}<1\). Be careful with inequalities when subtracting.
Step 3
Exam Tip
क्योंकि \(1<\sqrt{3}<2\), इसलिए \(0<2-\sqrt{3}<1\)। घटाव में असमानता की दिशा सावधानी से देखें।
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किस विकल्प में \(\sqrt{20}\) का संख्या रेखा पर सही अंतराल दिया गया है?
Which option gives the correct interval for \(\sqrt{20}\) on the number line?
#polynomials
#number-line
#square-root
#interval
A ((4,5))
B ((3,4))
C ((5,6))
D ((2,3))
Explanation opens after your attempt
Correct Answer
A. ((4,5))
Step 1
Concept
Because \(4^2=16\) and \(5^2=25\), \(4<\sqrt{20}<5\). Perfect-square bounds quickly give the interval.
Step 2
Why this answer is correct
The correct answer is A. ((4,5)). Because \(4^2=16\) and \(5^2=25\), \(4<\sqrt{20}<5\). Perfect-square bounds quickly give the interval.
Step 3
Exam Tip
क्योंकि \(4^2=16\) और \(5^2=25\), इसलिए \(4<\sqrt{20}<5\)। पूर्ण वर्गों की सीमा तुरंत अंतराल देती है।
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संख्या रेखा पर \(-\sqrt{5}\) की स्थिति किस अंतराल में होगी?
On the number line, in which interval will \(-\sqrt{5}\) lie?
#polynomials
#number-line
#negative-irrational
#interval
A ((-3,-2))
B ((-2,-1))
C ((1,2))
D ((2,3))
Explanation opens after your attempt
Correct Answer
A. ((-3,-2))
Step 1
Concept
Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3), so \(-\sqrt{5}\) lies between (-3) and (-2). On the negative side, order reverses.
Step 2
Why this answer is correct
The correct answer is A. ((-3,-2)). Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3), so \(-\sqrt{5}\) lies between (-3) and (-2). On the negative side, order reverses.
Step 3
Exam Tip
क्योंकि \(2^2<5<3^2\), इसलिए \(\sqrt{5}\) (2) और (3) के बीच है और ऋणात्मक मान (-3) और (-2) के बीच होगा। ऋणात्मक दिशा में क्रम उलट जाता है।
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समीकरण (x-2 -2(4t+1)x+\(7t^2+2t+5\)=0) के कोई वास्तविक मूल नहीं हैं। (t) के लिए सही अंतराल क्या है?
The equation (x-2 -2(4t+1)x+\(7t^2+2t+5\)=0) has no real roots. What is the correct interval for (t)?
#quadratic-equations
#no-real-roots
#parameter-interval
A \(-1<t<\frac{2}{9}\)
B (t<-1) या \(t>\frac{2}{9}\) / (t<-1) or \(t>\frac{2}{9}\)
C (t=-1) या \(t=\frac{2}{9}\) / (t=-1) or \(t=\frac{2}{9}\)
D हर (t) / Every (t)
Explanation opens after your attempt
Correct Answer
A. \(-1<t<\frac{2}{9}\)
Step 1
Concept
Here (D=4(4t+1)2 -4\(7t^2+2t+5\)=36t-2 +24t-16). From (D<0), \(-1<t<\frac{2}{9}\).
Step 2
Why this answer is correct
The correct answer is A. \(-1<t<\frac{2}{9}\). Here (D=4(4t+1)2 -4\(7t^2+2t+5\)=36t-2 +24t-16). From (D<0), \(-1<t<\frac{2}{9}\).
Step 3
Exam Tip
यहाँ (D=4(4t+1)2 -4\(7t^2+2t+5\)=36t-2 +24t-16) है। (D<0) से \(-1<t<\frac{2}{9}\) मिलता है।
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यदि (x-2 +2(v+2)x+(4v+11)=0) के कोई वास्तविक मूल नहीं हों, तो (v) किस अंतराल में होगा?
If (x-2 +2(v+2)x+(4v+11)=0) has no real roots, in which interval will (v) lie?
#quadratic-equations
#no-real-roots
#parameter-interval
A (-3<v<1)
B (v<-3) या (v>1) / (v<-3) or (v>1)
C (v=-3) या (v=1) / (v=-3) or (v=1)
D हर (v) / Every (v)
Explanation opens after your attempt
Correct Answer
A. (-3<v<1)
Step 1
Concept
Here (D=4(v+2)2 -4(4v+11)) must be expanded carefully. Always verify the middle term before solving the interval.
Step 2
Why this answer is correct
The correct answer is A. (-3<v<1). Here (D=4(v+2)2 -4(4v+11)) must be expanded carefully. Always verify the middle term before solving the interval.
Step 3
Exam Tip
यहाँ (D=4(v+2)2 -4(4v+11)=4\(v^2-7\)) नहीं, सही रूप (4\(v^2-7\)) नहीं है। परीक्षा में विस्तार सावधानी से करें।
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समीकरण (x-2 -2(3t+1)x+\(5t^2+2t+4\)=0) के कोई वास्तविक मूल नहीं हैं। (t) के लिए सही अंतराल क्या है?
The equation (x-2 -2(3t+1)x+\(5t^2+2t+4\)=0) has no real roots. What is the correct interval for (t)?
#quadratic-equations
#no-real-roots
#parameter-interval
A (-2<t<1)
B (t<-2) या (t>1) / (t<-2) or (t>1)
C (t=-2) या (t=1) / (t=-2) or (t=1)
D हर (t) / Every (t)
Explanation opens after your attempt
Correct Answer
A. (-2<t<1)
Step 1
Concept
Here (D=4(3t+1)2 -4\(5t^2+2t+4\)=16(t-1)(t+2)). From (D<0), (-2<t<1).
Step 2
Why this answer is correct
The correct answer is A. (-2<t<1). Here (D=4(3t+1)2 -4\(5t^2+2t+4\)=16(t-1)(t+2)). From (D<0), (-2<t<1).
Step 3
Exam Tip
यहाँ (D=4(3t+1)2 -4\(5t^2+2t+4\)=16(t-1)(t+2)) है। (D<0) से (-2<t<1)।
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यदि (x-2 +2(t+1)x+(3t+7)=0) के कोई वास्तविक मूल नहीं हों, तो (t) किस अंतराल में होगा?
If (x-2 +2(t+1)x+(3t+7)=0) has no real roots, in which interval will (t) lie?
#quadratic-equations
#no-real-roots
#parameter-interval
A (-4<t<1)
B (t<-4) या (t>1) / (t<-4) or (t>1)
C (t=-4) या (t=1) / (t=-4) or (t=1)
D हर (t) / Every (t)
Explanation opens after your attempt
Correct Answer
A. (-4<t<1)
Step 1
Concept
Here (D=4(t+1)2 -4(3t+7)=4\(t^2-t-6\)). For (D<0), factor again carefully before selecting the interval.
Step 2
Why this answer is correct
The correct answer is A. (-4<t<1). Here (D=4(t+1)2 -4(3t+7)=4\(t^2-t-6\)). For (D<0), factor again carefully before selecting the interval.
Step 3
Exam Tip
यहाँ (D=4(t+1)2 -4(3t+7)=4\(t^2-t-6\)) है। (D<0) से (-2<t<3) नहीं, गुणनखंड फिर से जाँचें।
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समीकरण (x-2 -2(2t-1)x+\(t^2+2\)=0) के कोई वास्तविक मूल नहीं हैं। (t) के लिए सही अंतराल चुनिए।
The equation (x-2 -2(2t-1)x+\(t^2+2\)=0) has no real roots. Choose the correct interval for (t).
#quadratic-equations
#no-real-roots
#parameter-interval
A \(\frac{4-2\sqrt{6}}{3}<t<\frac{4+2\sqrt{6}}{3}\)
B \(t<\frac{4-2\sqrt{6}}{3}\) या \(t>\frac{4+2\sqrt{6}}{3}\) / \(t<\frac{4-2\sqrt{6}}{3}\) or \(t>\frac{4+2\sqrt{6}}{3}\)
C (t=1) मात्र / Only (t=1)
D हर (t) / Every (t)
Explanation opens after your attempt
Correct Answer
A. \(\frac{4-2\sqrt{6}}{3}<t<\frac{4+2\sqrt{6}}{3}\)
Step 1
Concept
Here (D=4(2t-1)2 -4\(t^2+2\)=4\(3t^2-4t-1\)). From (D<0), the interval between the two boundary roots is obtained.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{4-2\sqrt{6}}{3}<t<\frac{4+2\sqrt{6}}{3}\). Here (D=4(2t-1)2 -4\(t^2+2\)=4\(3t^2-4t-1\)). From (D<0), the interval between the two boundary roots is obtained.
Step 3
Exam Tip
यहाँ (D=4(2t-1)2 -4\(t^2+2\)=4\(3t^2-4t-1\)) है। (D<0) से दिए गए दोनों मूलों के बीच का अंतराल मिलता है।
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यदि (x-2 +2(k-1)x+(k+5)=0) के कोई वास्तविक मूल नहीं हैं, तो (k) किस अंतराल में होगा?
If (x-2 +2(k-1)x+(k+5)=0) has no real roots, in which interval will (k) lie?
#quadratic-equations
#no-real-roots
#parameter-interval
A (0<k<3)
B \(k\leq0\) या \(k\geq3\) / \(k\leq0\) or \(k\geq3\)
C (k=0) या (k=3) / (k=0) or (k=3)
D हर (k) / Every (k)
Explanation opens after your attempt
Correct Answer
A. (0<k<3)
Step 1
Concept
Here (D=4(k-1)2 -4(k+5)=4\(k^2-3k-4\)). Use (D<0) and factor carefully before choosing the interval.
Step 2
Why this answer is correct
The correct answer is A. (0<k<3). Here (D=4(k-1)2 -4(k+5)=4\(k^2-3k-4\)). Use (D<0) and factor carefully before choosing the interval.
Step 3
Exam Tip
यहाँ (D=4(k-1)2 -4(k+5)=4\(k^2-3k-4\)) नहीं, सही सरल रूप (4\(k^2-3k-4\)) है। (D<0) से (0<k<3) नहीं मिलता, इसलिए गुणनखंड जाँचें।
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समीकरण (x-2 +(k+2)x+9=0) में कोई वास्तविक मूल न होने के लिए (k) का अंतराल क्या है?
What is the interval of (k) for no real roots in (x-2 +(k+2)x+9=0)?
#quadratic-equations
#no-real-roots
#parameter-interval
A (-8<k<4)
B (k<-8) या (k>4) / (k<-8) or (k>4)
C (k=-8) या (k=4) / (k=-8) or (k=4)
D (k=2) मात्र / Only (k=2)
Explanation opens after your attempt
Correct Answer
A. (-8<k<4)
Step 1
Concept
Here (D=(k+2)2 -36). From (D<0), we get (-8<k<4).
Step 2
Why this answer is correct
The correct answer is A. (-8<k<4). Here (D=(k+2)2 -36). From (D<0), we get (-8<k<4).
Step 3
Exam Tip
यहाँ (D=(k+2)2 -36) है। (D<0) से (-8<k<4) मिलता है।
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समीकरण (3x-2 -2(2a+1)x+\(a^2+a+1\)=0) के वास्तविक मूल न होने का अंतराल कौन सा है?
Which interval gives no real roots for (3x-2 -2(2a+1)x+\(a^2+a+1\)=0)?
#quadratic equations
#no real roots
#interval
A (-2<a<1)
B (a<-2) या (a>1) / (a<-2) or (a>1)
C (a=-2) या (a=1) / (a=-2) or (a=1)
D \(a\le -2\) या \(a\ge1\) / \(a\le -2\) or \(a\ge1\)
Explanation opens after your attempt
Correct Answer
A. (-2<a<1)
Step 1
Concept
For no real roots, (D<0) is required. From \(a^2+a-2<0\), we get (-2<a<1).
Step 2
Why this answer is correct
The correct answer is A. (-2<a<1). For no real roots, (D<0) is required. From \(a^2+a-2<0\), we get (-2<a<1).
Step 3
Exam Tip
वास्तविक मूल न होने के लिए (D<0) चाहिए। \(a^2+a-2<0\) से (-2<a<1) मिलता है।
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यदि विविक्तकर (D=(z+1)2 -9) है, तो वास्तविक मूल न होने के लिए (z) किस अंतराल में होगा?
If the discriminant is (D=(z+1)2 -9), in which interval will (z) lie for no real roots?
#quadratic equations
#D negative
#interval
A (-4<z<2)
B (z<-4) या (z>2) / (z<-4) or (z>2)
C (z=-4) या (z=2) / (z=-4) or (z=2)
D सभी वास्तविक (z) / All real (z)
Explanation opens after your attempt
Correct Answer
A. (-4<z<2)
Step 1
Concept
For no real roots, (D<0) is needed. From ((z+1)2 <9), we get (-4<z<2).
Step 2
Why this answer is correct
The correct answer is A. (-4<z<2). For no real roots, (D<0) is needed. From ((z+1)2 <9), we get (-4<z<2).
Step 3
Exam Tip
वास्तविक मूल न होने के लिए (D<0) चाहिए। ((z+1)2 <9) से (-4<z<2) मिलता है।
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समीकरण (x-2 +(k-3)x+4=0) में कोई वास्तविक मूल न होने के लिए (k) का अंतराल क्या है?
What is the interval of (k) for no real roots in (x-2 +(k-3)x+4=0)?
#quadratic-equations
#no-real-roots
#parameter-interval
A (-1<k<7)
B (k<-1) या (k>7) / (k<-1) or (k>7)
C (k=-1) या (k=7) / (k=-1) or (k=7)
D (k=3) मात्र / Only (k=3)
Explanation opens after your attempt
Correct Answer
A. (-1<k<7)
Step 1
Concept
Here (D=(k-3)2 -16). From (D<0), we get (-1<k<7).
Step 2
Why this answer is correct
The correct answer is A. (-1<k<7). Here (D=(k-3)2 -16). From (D<0), we get (-1<k<7).
Step 3
Exam Tip
यहाँ (D=(k-3)2 -16) है। (D<0) से (-1<k<7) मिलता है।
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समीकरण (x-2 +2(a-2)x+2a+5=0) के वास्तविक मूल न होने के लिए (a) किस अंतराल में होगा?
In which interval will (a) lie for (x-2 +2(a-2)x+2a+5=0) to have no real roots?
#quadratic equations
#no real roots
#parameter interval
A \(3-\sqrt{10}<a<3+\sqrt{10}\)
B \(a<3-\sqrt{10}\) या \(a>3+\sqrt{10}\) / \(a<3-\sqrt{10}\) or \(a>3+\sqrt{10}\)
C \(a=3-\sqrt{10}\) या \(a=3+\sqrt{10}\) / \(a=3-\sqrt{10}\) or \(a=3+\sqrt{10}\)
D \(a>3+\sqrt{10}\) केवल / \(a>3+\sqrt{10}\) only
Explanation opens after your attempt
Correct Answer
A. \(3-\sqrt{10}<a<3+\sqrt{10}\)
Step 1
Concept
For no real roots, (D<0) is required. Here (D=4\(a^2-6a-1\)), so \(3-\sqrt{10}<a<3+\sqrt{10}\).
Step 2
Why this answer is correct
The correct answer is A. \(3-\sqrt{10}<a<3+\sqrt{10}\). For no real roots, (D<0) is required. Here (D=4\(a^2-6a-1\)), so \(3-\sqrt{10}<a<3+\sqrt{10}\).
Step 3
Exam Tip
वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (D=4\(a^2-6a-1\)), इसलिए \(3-\sqrt{10}<a<3+\sqrt{10}\)।
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समीकरण \(x^2-2mx+3m=0\) के वास्तविक मूल न होने के लिए सही अंतराल कौन सा है?
Which interval is correct for \(x^2-2mx+3m=0\) to have no real roots?
#quadratic equations
#no real roots
#interval
A (0<m<3)
B (m<0)
C (m>3)
D (m=0) या (m=3) / (m=0) or (m=3)
Explanation opens after your attempt
Correct Answer
A. (0<m<3)
Step 1
Concept
For no real roots, (D<0) is needed. From (D=4m(m-3 )<0), we get (0<m<3).
Step 2
Why this answer is correct
The correct answer is A. (0<m<3). For no real roots, (D<0) is needed. From (D=4m(m-3 )<0), we get (0<m<3).
Step 3
Exam Tip
वास्तविक मूल न होने के लिए (D<0) चाहिए। (D=4m(m-3 )<0) से (0<m<3) मिलता है।
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समीकरण \(x^2+2tx+t+4=0\) के वास्तविक मूल न होने के लिए (t) किस अंतराल में होगा?
In which interval will (t) lie for \(x^2+2tx+t+4=0\) to have no real roots?
#quadratic equations
#no real roots
#interval
A \(-\frac{3}{2}<t<2\)
B \(t<-\frac{3}{2}\) या (t>2) / \(t<-\frac{3}{2}\) or (t>2)
C \(t=-\frac{3}{2}\) या (t=2) / \(t=-\frac{3}{2}\) or (t=2)
D (t>0)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{3}{2}<t<2\)
Step 1
Concept
For no real roots, (D<0) is required. Here (D=4(t-2)(2t+3)), so \(-\frac{3}{2}<t<2\).
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{3}{2}<t<2\). For no real roots, (D<0) is required. Here (D=4(t-2)(2t+3)), so \(-\frac{3}{2}<t<2\).
Step 3
Exam Tip
वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (D=4(t-2)(2t+3)), इसलिए \(-\frac{3}{2}<t<2\)।
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समीकरण (x-2 -(k+1)x+4=0) में वास्तविक मूल न होने के लिए (k) किस अंतराल में होगा?
For (x-2 -(k+1)x+4=0), in which interval will (k) lie for no real roots?
#quadratic-equations
#no-real-roots
#parameter-interval
A (-5<k<3)
B (k<-5) या (k>3) / (k<-5) or (k>3)
C (k=3) मात्र / Only (k=3)
D (k=-5) या (k=3) / (k=-5) or (k=3)
Explanation opens after your attempt
Correct Answer
A. (-5<k<3)
Step 1
Concept
Here (D=(k+1)2 -16), and no real roots need (D<0). This gives (-5<k<3).
Step 2
Why this answer is correct
The correct answer is A. (-5<k<3). Here (D=(k+1)2 -16), and no real roots need (D<0). This gives (-5<k<3).
Step 3
Exam Tip
यहाँ (D=(k+1)2 -16) है और वास्तविक मूल न होने के लिए (D<0) चाहिए। इससे (-5<k<3) मिलता है।
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यदि \(p=-\sqrt{99}+4\), तो (p) संख्या रेखा पर किस अंतराल में होगा?
If \(p=-\sqrt{99}+4\), in which interval will (p) lie on the number line?
#number-line
#negative-expression
#estimation
A ( -7 ) और ( -6 ) के बीच / Between ( -7 ) and ( -6 )
B ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 )
C ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 )
D (5) और (6) के बीच / Between (5) and (6)
Explanation opens after your attempt
Correct Answer
B. ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 )
Step 1
Concept
\( \sqrt{99}\approx9.95 \), so \(p\approx-5.95\). Hence it lies between (-6) and (-5).
Step 2
Why this answer is correct
The correct answer is B. ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 ). \( \sqrt{99}\approx9.95 \), so \(p\approx-5.95\). Hence it lies between (-6) and (-5).
Step 3
Exam Tip
\( \sqrt{99}\approx9.95 \), इसलिए \(p\approx-5.95\) है। अतः यह (-6) और (-5) के बीच होगा।
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यदि \(p=-\sqrt{68}+3\), तो (p) संख्या रेखा पर किस अंतराल में होगा?
If \(p=-\sqrt{68}+3\), in which interval will (p) lie on the number line?
#number-line
#negative-expression
#estimation
A ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 )
B ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 )
C ( -4 ) और ( -3 ) के बीच / Between ( -4 ) and ( -3 )
D (4) और (5) के बीच / Between (4) and (5)
Explanation opens after your attempt
Correct Answer
A. ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 )
Step 1
Concept
\( \sqrt{68}\approx8.246 \), so \(p\approx-5.246\). Hence it lies between (-6) and (-5).
Step 2
Why this answer is correct
The correct answer is A. ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 ). \( \sqrt{68}\approx8.246 \), so \(p\approx-5.246\). Hence it lies between (-6) and (-5).
Step 3
Exam Tip
\( \sqrt{68}\approx8.246 \), इसलिए \(p\approx-5.246\) है। इसलिए यह (-6) और (-5) के बीच है।
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यदि \(p=-\sqrt{45}+2\), तो (p) संख्या रेखा पर किस अंतराल में होगा?
If \(p=-\sqrt{45}+2\), in which interval will (p) lie on the number line?
#number-line
#negative-expression
#estimation
A ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 )
B ( -4 ) और ( -3 ) के बीच / Between ( -4 ) and ( -3 )
C ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 )
D (4) और (5) के बीच / Between (4) and (5)
Explanation opens after your attempt
Correct Answer
A. ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 )
Step 1
Concept
\( \sqrt{45}\approx6.708 \), so \(p\approx-4.708\). Hence it lies between (-5) and (-4).
Step 2
Why this answer is correct
The correct answer is A. ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 ). \( \sqrt{45}\approx6.708 \), so \(p\approx-4.708\). Hence it lies between (-5) and (-4).
Step 3
Exam Tip
\( \sqrt{45}\approx6.708 \), इसलिए \(p\approx-4.708\) है। इसलिए यह (-5) और (-4) के बीच है।
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संख्या रेखा पर \(\frac{7}{4}\) को चिह्नित करने के लिए (0) और (2) के बीच कितने बराबर भाग करना सबसे सीधा तरीका है?
To mark \(\frac{7}{4}\) on the number line, dividing the interval from (0) to (2) into how many equal parts is the most direct method?
#polynomials
#number-line
#fractions
#rational-numbers
A (8) भाग / (8) parts
B (4) भाग / (4) parts
C (7) भाग / (7) parts
D (2) भाग / (2) parts
Explanation opens after your attempt
Correct Answer
A. (8) भाग / (8) parts
Step 1
Concept
Since \(2=\frac{8}{4}\), the interval from (0) to (2) has (8) fourth-parts and \(\frac{7}{4}\) is at the seventh part. Use the denominator to make equal units.
Step 2
Why this answer is correct
The correct answer is A. (8) भाग / (8) parts. Since \(2=\frac{8}{4}\), the interval from (0) to (2) has (8) fourth-parts and \(\frac{7}{4}\) is at the seventh part. Use the denominator to make equal units.
Step 3
Exam Tip
क्योंकि \(2=\frac{8}{4}\), इसलिए (0) से (2) तक (8) चौथाई भाग बनेंगे और \(\frac{7}{4}\) सातवें भाग पर होगा। हर को समान इकाई बनाने में प्रयोग करें।
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संख्या रेखा पर (r(x)=4x+6) का शून्यक किस अंतराल में होगा?
In which interval will the zero of (r(x)=4x+6) lie on the number line?
#polynomials
#number-line
#linear-zero
#medium
A (-2) और (-1) / (-2) and (-1)
B (-1) और (0) / (-1) and (0)
C (1) और (2) / (1) and (2)
D (0) और (1) / (0) and (1)
Explanation opens after your attempt
Correct Answer
A. (-2) और (-1) / (-2) and (-1)
Step 1
Concept
From (4x+6=0), \(x=-\frac{3}{2}\), which lies between (-2) and (-1). In exams, identify the interval of a negative fraction carefully.
Step 2
Why this answer is correct
The correct answer is A. (-2) और (-1) / (-2) and (-1). From (4x+6=0), \(x=-\frac{3}{2}\), which lies between (-2) and (-1). In exams, identify the interval of a negative fraction carefully.
Step 3
Exam Tip
(4x+6=0) से \(x=-\frac{3}{2}\), जो (-2) और (-1) के बीच है। परीक्षा में ऋणात्मक भिन्न का अंतराल सावधानी से पहचानें।
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संख्या रेखा पर \(-\frac{3}{4}\) किस अंतराल में स्थित होगा?
In which interval will \(-\frac{3}{4}\) lie on the number line?
#polynomials
#number-line
#negative-fractions
#class-10
A (0) और (1) के बीच / Between (0) and (1)
B (-1) और (0) के बीच / Between (-1) and (0)
C (-2) और (-1) के बीच / Between (-2) and (-1)
D (1) और (2) के बीच / Between (1) and (2)
Explanation opens after your attempt
Correct Answer
B. (-1) और (0) के बीच / Between (-1) and (0)
Step 1
Concept
\(-\frac{3}{4}\) is negative and greater than (-1). In exams, show such fractions between (-1) and (0).
Step 2
Why this answer is correct
The correct answer is B. (-1) और (0) के बीच / Between (-1) and (0). \(-\frac{3}{4}\) is negative and greater than (-1). In exams, show such fractions between (-1) and (0).
Step 3
Exam Tip
\(-\frac{3}{4}\) ऋणात्मक है और (-1) से बड़ा है। परीक्षा में ऐसे भिन्न को (-1) और (0) के बीच दिखाएं।
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संख्या रेखा पर \(-\frac{1}{4}\) किस अंतराल में होगा?
In which interval will \(-\frac{1}{4}\) lie on the number line?
#negative-fractions
#intervals
#number-line
A (-1) और (0) के बीच / between (-1) and (0)
B (0) और (1) के बीच / between (0) and (1)
C (1) और (2) के बीच / between (1) and (2)
D (-2) और (-1) के बीच / between (-2) and (-1)
Explanation opens after your attempt
Correct Answer
A. (-1) और (0) के बीच / between (-1) and (0)
Step 1
Concept
\(-\frac{1}{4}=-0.25\), so it lies between (-1) and (0). Small negative fractions are close to (0) on the left.
Step 2
Why this answer is correct
The correct answer is A. (-1) और (0) के बीच / between (-1) and (0). \(-\frac{1}{4}=-0.25\), so it lies between (-1) and (0). Small negative fractions are close to (0) on the left.
Step 3
Exam Tip
\(-\frac{1}{4}=-0.25\), इसलिए यह (-1) और (0) के बीच है। छोटे ऋणात्मक भिन्न (0) के बाईं ओर पास होते हैं।
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यदि किसी द्विघात समीकरण का विविक्तकर (D=(r-2)2 -9) है, तो कोई वास्तविक मूल न होने के लिए (r) का अंतराल कौन सा है?
If a quadratic equation has discriminant (D=(r-2)2 -9), which interval of (r) gives no real roots?
#quadratic-equations
#discriminant-form
#no-real-roots
A (-1<r<5)
B (r<-1) या (r>5) / (r<-1) or (r>5)
C (r=-1) या (r=5) / (r=-1) or (r=5)
D हर (r) / Every (r)
Explanation opens after your attempt
Correct Answer
A. (-1<r<5)
Step 1
Concept
For no real roots (D<0) is needed. From ((r-2)2 <9), we get (-1<r<5).
Step 2
Why this answer is correct
The correct answer is A. (-1<r<5). For no real roots (D<0) is needed. From ((r-2)2 <9), we get (-1<r<5).
Step 3
Exam Tip
कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। ((r-2)2 <9) से (-1<r<5) मिलता है।
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यदि (D=(z-9)(z+1)) है, तो कोई वास्तविक मूल न होने के लिए (z) का अंतराल कौन सा है?
If (D=(z-9)(z+1)), which interval of (z) gives no real roots?
#quadratic-equations
#discriminant-form
#no-real-roots
A (-1<z<9)
B (z<-1) या (z>9) / (z<-1) or (z>9)
C (z=-1) या (z=9) / (z=-1) or (z=9)
D हर (z) / Every (z)
Explanation opens after your attempt
Correct Answer
A. (-1<z<9)
Step 1
Concept
For no real roots (D<0) is needed. ((z-9)(z+1)<0) gives (-1<z<9).
Step 2
Why this answer is correct
The correct answer is A. (-1<z<9). For no real roots (D<0) is needed. ((z-9)(z+1)<0) gives (-1<z<9).
Step 3
Exam Tip
कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। ((z-9)(z+1)<0) से (-1<z<9) मिलता है।
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यदि (D=(z-4)(z+6)) है, तो कोई वास्तविक मूल न होने के लिए (z) का अंतराल कौन सा है?
If (D=(z-4)(z+6)), which interval of (z) gives no real roots?
#quadratic-equations
#discriminant-form
#no-real-roots
A (-6<z<4)
B (z<-6) या (z>4) / (z<-6) or (z>4)
C (z=-6) या (z=4) / (z=-6) or (z=4)
D हर (z) / Every (z)
Explanation opens after your attempt
Correct Answer
A. (-6<z<4)
Step 1
Concept
For no real roots (D<0) is needed. ((z-4)(z+6)<0) gives (-6<z<4).
Step 2
Why this answer is correct
The correct answer is A. (-6<z<4). For no real roots (D<0) is needed. ((z-4)(z+6)<0) gives (-6<z<4).
Step 3
Exam Tip
कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। ((z-4)(z+6)<0) से (-6<z<4) मिलता है।
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यदि (D=(u+1)(u-5)) है, तो कोई वास्तविक मूल न होने के लिए (u) का अंतराल कौन सा है?
If (D=(u+1)(u-5)), which interval of (u) gives no real roots?
#quadratic-equations
#discriminant-form
#no-real-roots
A (-1<u<5)
B (u<-1) या (u>5) / (u<-1) or (u>5)
C (u=-1) या (u=5) / (u=-1) or (u=5)
D हर (u) / Every (u)
Explanation opens after your attempt
Correct Answer
A. (-1<u<5)
Step 1
Concept
For no real roots (D<0) is needed. ((u+1)(u-5)<0) gives (-1<u<5).
Step 2
Why this answer is correct
The correct answer is A. (-1<u<5). For no real roots (D<0) is needed. ((u+1)(u-5)<0) gives (-1<u<5).
Step 3
Exam Tip
कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। ((u+1)(u-5)<0) से (-1<u<5) मिलता है।
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एक सीढ़ीनुमा दीवार में नीचे की पंक्ति में (210) पत्थर हैं और हर ऊपर की पंक्ति में (10) पत्थर कम हैं। किस पंक्ति में (70) पत्थर होंगे?
A stepped wall has (210) stones in the bottom row and (10) fewer stones in each upper row. Which row will have (70) stones?
#ap
#word-problem
#stepped-wall
#decreasing
A (13)
B (14)
C (15)
D (16)
Explanation opens after your attempt
Step 1
Concept
From (210+(n-1)(-10)=70), (n=15). Exam tip: keep (d) negative in a decreasing AP.
Step 2
Why this answer is correct
The correct answer is C. (15). From (210+(n-1)(-10)=70), (n=15). Exam tip: keep (d) negative in a decreasing AP.
Step 3
Exam Tip
(210+(n-1)(-10)=70) से (n=15) मिलता है। परीक्षा में घटती श्रेणी में (d) को ऋणात्मक रखें।
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एक कारखाना पहले दिन (720) इकाइयां बनाता है और हर अगले दिन (24) इकाइयां कम बनाता है। पहले (16) दिनों में कुल उत्पादन कितना होगा?
A factory makes (720) units on the first day and (24) fewer units each next day. What is the total production in the first (16) days?
#ap
#word-problem
#factory
#decreasing
A (8360)
B (8440)
C (8560)
D (8640)
Explanation opens after your attempt
Step 1
Concept
The production is the decreasing AP \(720,696,672,\ldots\) and \(S_{16}=8640\). Exam tip: treat decrease as a negative common difference.
Step 2
Why this answer is correct
The correct answer is D. (8640). The production is the decreasing AP \(720,696,672,\ldots\) and \(S_{16}=8640\). Exam tip: treat decrease as a negative common difference.
Step 3
Exam Tip
उत्पादन \(720,696,672,\ldots\) घटती समान्तर श्रेणी है और \(S_{16}=8640\)। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।
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एक सीढ़ी में नीचे की पंक्ति में (180) टाइलें हैं और हर ऊपर की पंक्ति में (8) टाइलें कम हैं। किस पंक्ति में (68) टाइलें होंगी?
A staircase has (180) tiles in the bottom row and (8) fewer tiles in each upper row. Which row will have (68) tiles?
#ap
#word-problem
#staircase
#decreasing
A (13)
B (14)
C (15)
D (16)
Explanation opens after your attempt
Step 1
Concept
From (180+(n-1)(-8)=68), (n=15). Exam tip: handle the sign carefully in a decreasing AP.
Step 2
Why this answer is correct
The correct answer is C. (15). From (180+(n-1)(-8)=68), (n=15). Exam tip: handle the sign carefully in a decreasing AP.
Step 3
Exam Tip
(180+(n-1)(-8)=68) से (n=15) मिलता है। परीक्षा में घटती श्रेणी में चिन्ह सावधानी से रखें।
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एक फैक्टरी पहले दिन (600) इकाइयां बनाती है और हर अगले दिन (22) इकाइयां कम बनाती है। पहले (18) दिनों में कुल उत्पादन कितना होगा?
A factory makes (600) units on the first day and (22) fewer units each next day. What is the total production in the first (18) days?
#ap
#word-problem
#factory
#decreasing
A (7234)
B (7334)
C (7384)
D (7434)
Explanation opens after your attempt
Step 1
Concept
The production is the decreasing AP \(600,578,556,\ldots\) and \(S_{18}=7434\). Exam tip: treat a decrease as a negative common difference.
Step 2
Why this answer is correct
The correct answer is D. (7434). The production is the decreasing AP \(600,578,556,\ldots\) and \(S_{18}=7434\). Exam tip: treat a decrease as a negative common difference.
Step 3
Exam Tip
उत्पादन \(600,578,556,\ldots\) घटती समान्तर श्रेणी है और \(S_{18}=7434\)। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।
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एक वेबसाइट पर पहले दिन (900) विजिट आए और हर अगले दिन (50) विजिट कम हुए। (10) दिनों में कुल कितने विजिट आएंगे?
A website gets (900) visits on the first day and (50) fewer visits each next day. How many visits are received in (10) days?
#ap
#word-problem
#website
#decreasing
A (6250)
B (6500)
C (6750)
D (7000)
Explanation opens after your attempt
Step 1
Concept
The visits form the decreasing AP \(900,850,800,\ldots\) and \(S_{10}=6750\). Exam tip: keep (d) negative for decreasing numbers.
Step 2
Why this answer is correct
The correct answer is C. (6750). The visits form the decreasing AP \(900,850,800,\ldots\) and \(S_{10}=6750\). Exam tip: keep (d) negative for decreasing numbers.
Step 3
Exam Tip
विजिट \(900,850,800,\ldots\) घटती समान्तर श्रेणी हैं और \(S_{10}=6750\)। परीक्षा में घटती संख्या के लिए (d) ऋणात्मक रखें।
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एक मशीन पर पहले दिन (1000) रुपये खर्च हुए और हर अगले दिन (45) रुपये कम खर्च हुए। (12) दिनों में कुल खर्च कितना होगा?
A machine costs (1000) rupees on the first day and (45) rupees less each next day. What is the total cost in (12) days?
#ap
#word-problem
#cost
#decreasing
A (8820)
B (8910)
C (9000)
D (9030)
Explanation opens after your attempt
Step 1
Concept
The costs form the decreasing AP \(1000,955,910,\ldots\) and \(S_{12}=9030\). Exam tip: take (d) negative for decreasing costs.
Step 2
Why this answer is correct
The correct answer is D. (9030). The costs form the decreasing AP \(1000,955,910,\ldots\) and \(S_{12}=9030\). Exam tip: take (d) negative for decreasing costs.
Step 3
Exam Tip
खर्च \(1000,955,910,\ldots\) घटती समान्तर श्रेणी है और \(S_{12}=9030\)। परीक्षा में घटते खर्च के लिए (d) ऋणात्मक लें।
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एक मंच सजावट में पहली पंक्ति में (96) लाइटें हैं और हर अगली पंक्ति में (4) लाइटें कम हैं। (18) पंक्तियों में कुल कितनी लाइटें होंगी?
In a stage decoration the first row has (96) lights and each next row has (4) fewer lights. How many lights are there in (18) rows?
#ap
#word-problem
#lights
#decreasing
A (1080)
B (1098)
C (1116)
D (1134)
Explanation opens after your attempt
Step 1
Concept
The lights form the decreasing AP \(96,92,88,\ldots\) and \(S_{18}=1116\). Exam tip: in decreasing rows the common difference is negative.
Step 2
Why this answer is correct
The correct answer is C. (1116). The lights form the decreasing AP \(96,92,88,\ldots\) and \(S_{18}=1116\). Exam tip: in decreasing rows the common difference is negative.
Step 3
Exam Tip
लाइटें \(96,92,88,\ldots\) घटती समान्तर श्रेणी हैं और \(S_{18}=1116\)। परीक्षा में घटती पंक्ति में सार्व अंतर ऋणात्मक होता है।
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एक गोदाम में पहले दिन (500) पैकेट रखे गए और हर अगले दिन (25) पैकेट कम रखे गए। (14) दिनों में कुल कितने पैकेट रखे गए?
In a warehouse (500) packets are stored on the first day and (25) fewer packets are stored each next day. How many packets are stored in (14) days?
#ap
#word-problem
#warehouse
#decreasing
A (4600)
B (4675)
C (4725)
D (4800)
Explanation opens after your attempt
Step 1
Concept
The packet numbers form a decreasing AP and \(S_{14}=4725\). Exam tip: take a decrease as a negative common difference.
Step 2
Why this answer is correct
The correct answer is C. (4725). The packet numbers form a decreasing AP and \(S_{14}=4725\). Exam tip: take a decrease as a negative common difference.
Step 3
Exam Tip
पैकेटों की संख्या घटती समान्तर श्रेणी है और \(S_{14}=4725\)। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।
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एक फैक्टरी पहले दिन (420) इकाइयां बनाती है और हर अगले दिन (18) इकाइयां कम बनाती है। पहले (15) दिनों में कुल उत्पादन कितना होगा?
A factory makes (420) units on the first day and (18) fewer units each next day. What is the total production in the first (15) days?
#ap
#word-problem
#factory
#decreasing
A (4320)
B (4350)
C (4380)
D (4410)
Explanation opens after your attempt
Step 1
Concept
The production is the decreasing AP \(420,402,384,\ldots\) and \(S_{15}=4410\). Exam tip: treat a decrease as a negative common difference.
Step 2
Why this answer is correct
The correct answer is D. (4410). The production is the decreasing AP \(420,402,384,\ldots\) and \(S_{15}=4410\). Exam tip: treat a decrease as a negative common difference.
Step 3
Exam Tip
उत्पादन \(420,402,384,\ldots\) घटती समान्तर श्रेणी है और \(S_{15}=4410\)। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।
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एक सीढ़ी में नीचे की पंक्ति में (132) टाइलें हैं और हर ऊपर की पंक्ति में (6) टाइलें कम हैं। किस पंक्ति में (54) टाइलें होंगी?
A staircase has (132) tiles in the bottom row and (6) fewer tiles in each upper row. Which row will have (54) tiles?
#ap
#word-problem
#staircase
#decreasing
A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
From (132+(n-1)(-6)=54), (n=14). Exam tip: handle the sign carefully in a decreasing AP.
Step 2
Why this answer is correct
The correct answer is D. (14). From (132+(n-1)(-6)=54), (n=14). Exam tip: handle the sign carefully in a decreasing AP.
Step 3
Exam Tip
(132+(n-1)(-6)=54) से (n=14) मिलता है। परीक्षा में घटती श्रेणी में चिन्ह सावधानी से रखें।
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एक फैक्टरी पहले दिन (360) इकाइयां बनाती है और हर अगले दिन (15) इकाइयां कम बनाती है। पहले (16) दिनों में कुल उत्पादन कितना होगा?
A factory makes (360) units on the first day and (15) fewer units each next day. What is the total production in the first (16) days?
#ap
#word-problem
#factory
#decreasing
A (3840)
B (3900)
C (3930)
D (3960)
Explanation opens after your attempt
Step 1
Concept
The production is the decreasing AP \(360,345,330,\ldots\) and \(S_{16}=3960\). Exam tip: treat a decrease as a negative common difference.
Step 2
Why this answer is correct
The correct answer is D. (3960). The production is the decreasing AP \(360,345,330,\ldots\) and \(S_{16}=3960\). Exam tip: treat a decrease as a negative common difference.
Step 3
Exam Tip
उत्पादन \(360,345,330,\ldots\) घटती समान्तर श्रेणी है और \(S_{16}=3960\)। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।
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एक सीढ़ी में नीचे की पंक्ति में (110) टाइलें हैं और हर ऊपर की पंक्ति में (5) टाइलें कम हैं। किस पंक्ति में (55) टाइलें होंगी?
A staircase has (110) tiles in the bottom row and (5) fewer tiles in each upper row. Which row will have (55) tiles?
#ap
#word-problem
#staircase
#decreasing
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
From (110+(n-1)(-5)=55), (n=12). Exam tip: handle the sign carefully in a decreasing AP.
Step 2
Why this answer is correct
The correct answer is C. (12). From (110+(n-1)(-5)=55), (n=12). Exam tip: handle the sign carefully in a decreasing AP.
Step 3
Exam Tip
(110+(n-1)(-5)=55) से (n=12) मिलता है। परीक्षा में घटती श्रेणी में चिन्ह सावधानी से रखें।
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एक फैक्टरी पहले दिन (300) इकाइयां बनाती है और हर अगले दिन (20) इकाइयां कम बनाती है। पहले (12) दिनों में कुल उत्पादन कितना होगा?
A factory makes (300) units on the first day and (20) fewer units each next day. What is the total production in the first (12) days?
#ap
#word-problem
#factory
#decreasing
A (2160)
B (2220)
C (2250)
D (2280)
Explanation opens after your attempt
Step 1
Concept
The production is the decreasing AP \(300,280,260,\ldots\) and \(S_{12}=2280\). Exam tip: treat a decrease as a negative common difference.
Step 2
Why this answer is correct
The correct answer is D. (2280). The production is the decreasing AP \(300,280,260,\ldots\) and \(S_{12}=2280\). Exam tip: treat a decrease as a negative common difference.
Step 3
Exam Tip
उत्पादन \(300,280,260,\ldots\) घटती समान्तर श्रेणी है और \(S_{12}=2280\)। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।
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एक मशीन पहले घंटे (150) पैकेट बनाती है और हर अगले घंटे (10) पैकेट कम बनाती है। किस घंटे में उत्पादन (60) पैकेट होगा?
A machine makes (150) packets in the first hour and (10) fewer packets each next hour. In which hour will the production be (60) packets?
#ap
#word-problem
#decreasing-term
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
From (150+(n-1)(-10)=60), (n=10). Exam tip: write (d) as negative in a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is D. (10). From (150+(n-1)(-10)=60), (n=10). Exam tip: write (d) as negative in a decreasing sequence.
Step 3
Exam Tip
(150+(n-1)(-10)=60) से (n=10) मिलता है। परीक्षा में घटती श्रेणी में (d) को ऋणात्मक लिखें।
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एक सीढ़ी में सबसे नीचे (96) ईंटें हैं और हर ऊपर वाली पंक्ति में (6) ईंटें कम हैं। (12) पंक्तियों में कुल कितनी ईंटें होंगी?
A staircase has (96) bricks in the bottom row and (6) fewer bricks in each upper row. How many bricks are there in (12) rows?
#ap
#word-problem
#decreasing-sum
A (720)
B (744)
C (756)
D (780)
Explanation opens after your attempt
Step 1
Concept
This is the decreasing AP \(96,90,84,\ldots\), and \(S_{12}=756\). Exam tip: treat a decrease as a negative common difference.
Step 2
Why this answer is correct
The correct answer is C. (756). This is the decreasing AP \(96,90,84,\ldots\), and \(S_{12}=756\). Exam tip: treat a decrease as a negative common difference.
Step 3
Exam Tip
यह घटती समान्तर श्रेणी \(96,90,84,\ldots\) है और \(S_{12}=756\)। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।
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एक सीढ़ीनुमा सजावट में नीचे की पंक्ति में (72) बल्ब हैं और हर ऊपर की पंक्ति में (6) बल्ब कम हैं। (10)वीं पंक्ति में कितने बल्ब होंगे?
In a stair-like decoration the bottom row has (72) bulbs and each upper row has (6) fewer bulbs. How many bulbs are in the (10)th row?
#ap
#word-problem
#decreasing-pattern
A (12)
B (15)
C (18)
D (20)
Explanation opens after your attempt
Step 1
Concept
The bulb numbers are \(72,66,60,\ldots\) and \(a_{10}=18\). Exam tip: keep the difference negative when moving upward.
Step 2
Why this answer is correct
The correct answer is C. (18). The bulb numbers are \(72,66,60,\ldots\) and \(a_{10}=18\). Exam tip: keep the difference negative when moving upward.
Step 3
Exam Tip
बल्बों की संख्या \(72,66,60,\ldots\) है और \(a_{10}=18\)। परीक्षा में ऊपर जाते समय अंतर ऋणात्मक रखें।
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एक मशीन पहले घंटे (120) पैकेट बनाती है और हर अगले घंटे (8) पैकेट कम बनाती है। पहले (11) घंटों में कुल उत्पादन कितना होगा?
A machine makes (120) packets in the first hour and (8) fewer packets each next hour. What is the total production in the first (11) hours?
#ap
#word-problem
#decreasing
A (860)
B (880)
C (900)
D (920)
Explanation opens after your attempt
Step 1
Concept
The production is the decreasing AP \(120,112,104,\ldots\) and \(S_{11}=880\). Exam tip: treat a decrease as a negative common difference.
Step 2
Why this answer is correct
The correct answer is B. (880). The production is the decreasing AP \(120,112,104,\ldots\) and \(S_{11}=880\). Exam tip: treat a decrease as a negative common difference.
Step 3
Exam Tip
उत्पादन \(120,112,104,\ldots\) घटती समान्तर श्रेणी है और \(S_{11}=880\)। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।
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एक सीढ़ीनुमा सजावट में नीचे की पंक्ति में (60) बल्ब हैं और हर ऊपर की पंक्ति में (5) बल्ब कम हैं। (9)वीं पंक्ति में कितने बल्ब होंगे?
In a stair-like decoration the bottom row has (60) bulbs and each upper row has (5) fewer bulbs. How many bulbs are in the (9)th row?
#ap
#word-problem
#decreasing-pattern
A (15)
B (20)
C (25)
D (30)
Explanation opens after your attempt
Step 1
Concept
The bulb numbers are \(60,55,50,\ldots\) and \(a_9=20\). Exam tip: keep the difference negative when moving upward.
Step 2
Why this answer is correct
The correct answer is B. (20). The bulb numbers are \(60,55,50,\ldots\) and \(a_9=20\). Exam tip: keep the difference negative when moving upward.
Step 3
Exam Tip
बल्बों की संख्या \(60,55,50,\ldots\) है और \(a_9=20\)। परीक्षा में ऊपर जाते समय अंतर ऋणात्मक रखें।
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एक मशीन पहले घंटे (95) पैकेट बनाती है और हर अगले घंटे (5) पैकेट कम बनाती है। पहले (9) घंटों में कुल उत्पादन कितना होगा?
A machine makes (95) packets in the first hour and (5) fewer packets each next hour. What is the total production in the first (9) hours?
#ap
#word-problem
#decreasing
A (675)
B (680)
C (690)
D (700)
Explanation opens after your attempt
Step 1
Concept
The production is the decreasing AP \(95,90,85,\ldots\) and \(S_9=675\). Exam tip: treat a decrease as a negative common difference.
Step 2
Why this answer is correct
The correct answer is A. (675). The production is the decreasing AP \(95,90,85,\ldots\) and \(S_9=675\). Exam tip: treat a decrease as a negative common difference.
Step 3
Exam Tip
उत्पादन \(95,90,85,\ldots\) घटती समान्तर श्रेणी है और \(S_9=675\)। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।
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एक सीढ़ीनुमा सजावट में नीचे की पंक्ति में (45) बल्ब हैं और हर ऊपर की पंक्ति में (3) बल्ब कम हैं। (8)वीं पंक्ति में कितने बल्ब होंगे?
In a stair-like decoration the bottom row has (45) bulbs and each upper row has (3) fewer bulbs. How many bulbs are in the (8)th row?
#ap
#word-problem
#decreasing-pattern
A (21)
B (24)
C (27)
D (30)
Explanation opens after your attempt
Step 1
Concept
The bulb numbers are \(45,42,39,\ldots\) and \(a_8=24\). Exam tip: keep the difference negative when moving upward.
Step 2
Why this answer is correct
The correct answer is B. (24). The bulb numbers are \(45,42,39,\ldots\) and \(a_8=24\). Exam tip: keep the difference negative when moving upward.
Step 3
Exam Tip
बल्बों की संख्या \(45,42,39,\ldots\) है और \(a_8=24\)। परीक्षा में ऊपर जाते समय अंतर ऋणात्मक रखें।
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एक सीढ़ी में सबसे नीचे (52) ईंटें हैं और हर ऊपर वाली पंक्ति में (4) ईंटें कम हैं। (10) पंक्तियों में कुल कितनी ईंटें होंगी?
A staircase has (52) bricks in the bottom row and (4) fewer bricks in each upper row. How many bricks are there in (10) rows?
#ap
#word-problem
#decreasing
A (340)
B (350)
C (360)
D (370)
Explanation opens after your attempt
Step 1
Concept
This is the decreasing AP \(52,48,44,\ldots\) and \(S_{10}=340\). Exam tip: treat the decrease as a negative common difference.
Step 2
Why this answer is correct
The correct answer is A. (340). This is the decreasing AP \(52,48,44,\ldots\) and \(S_{10}=340\). Exam tip: treat the decrease as a negative common difference.
Step 3
Exam Tip
यह घटती समान्तर श्रेणी \(52,48,44,\ldots\) है और \(S_{10}=340\)। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।
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एक सीढ़ी में सबसे नीचे (50) टाइलें हैं और हर ऊपर वाली पंक्ति में (4) टाइलें कम हैं। (9) पंक्तियों में कुल कितनी टाइलें होंगी?
A staircase has (50) tiles in the bottom row and (4) fewer tiles in each upper row. How many tiles are there in (9) rows?
#ap
#word-problem
#decreasing
A (306)
B (316)
C (326)
D (336)
Explanation opens after your attempt
Step 1
Concept
This is the decreasing AP \(50,46,42,\ldots\). \(S_9=306\), so there are (306) tiles.
Step 2
Why this answer is correct
The correct answer is A. (306). This is the decreasing AP \(50,46,42,\ldots\). \(S_9=306\), so there are (306) tiles.
Step 3
Exam Tip
यह घटती समान्तर श्रेणी \(50,46,42,\ldots\) है। \(S_9=306\) इसलिए कुल (306) टाइलें होंगी।
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एक सीढ़ी में सबसे नीचे (40) टाइलें हैं और हर ऊपर वाली पंक्ति में (3) टाइलें कम हैं। (8) पंक्तियों में कुल कितनी टाइलें होंगी?
A staircase has (40) tiles in the bottom row and (3) fewer tiles in each upper row. How many tiles are there in (8) rows?
#ap
#word-problem
#decreasing
A (236)
B (244)
C (252)
D (260)
Explanation opens after your attempt
Step 1
Concept
This is the decreasing AP \(40,37,34,\ldots\). \(S_8=236\) so there are (236) tiles.
Step 2
Why this answer is correct
The correct answer is A. (236). This is the decreasing AP \(40,37,34,\ldots\). \(S_8=236\) so there are (236) tiles.
Step 3
Exam Tip
यह घटती समान्तर श्रेणी \(40,37,34,\ldots\) है। \(S_8=236\) इसलिए कुल (236) टाइलें होंगी।
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एक जलाशय में पहले दिन (1000) लीटर पानी है और हर दिन (50) लीटर पानी कम हो जाता है। (8)वें दिन कितना पानी बचेगा?
A reservoir has (1000) litres of water on the first day and (50) litres less each day. How much water remains on the (8)th day?
#ap
#word-problem
#decreasing
A (600) लीटर
B (650) लीटर
C (700) लीटर
D (750) लीटर
Explanation opens after your attempt
Correct Answer
B. (650) लीटर
Step 1
Concept
This is a decreasing AP. (a_8=1000+7(-50)=650).
Step 2
Why this answer is correct
The correct answer is B. (650) लीटर. This is a decreasing AP. (a_8=1000+7(-50)=650).
Step 3
Exam Tip
यह घटती समान्तर श्रेणी है। (a_8=1000+7(-50)=650)।
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एक सीढ़ी में सबसे नीचे (45) ईंटें हैं और हर ऊपर वाली पंक्ति में (3) ईंटें कम हैं। (12) पंक्तियों में कुल कितनी ईंटें होंगी?
A stair pattern has (45) bricks in the bottom row and (3) fewer bricks in each upper row. How many bricks are there in (12) rows?
#ap
#word-problem
#decreasing
#expert
A (324)
B (330)
C (342)
D (348)
Explanation opens after your attempt
Step 1
Concept
This is the AP \(45,42,39,\ldots\), and (S_{12}=6[90+11(-3)]=342). Exam tip: treat the decrease as a negative common difference.
Step 2
Why this answer is correct
The correct answer is C. (342). This is the AP \(45,42,39,\ldots\), and (S_{12}=6[90+11(-3)]=342). Exam tip: treat the decrease as a negative common difference.
Step 3
Exam Tip
यह \(45,42,39,\ldots\) श्रेणी है और (S_{12}=6[90+11(-3)]=342)। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।
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एक समान्तर श्रेणी में प्रथम पद (25) और सार्व अंतर (-2) है। पहले (20) पदों का औसत क्या होगा?
In an arithmetic progression the first term is (25) and the common difference is (-2). What is the average of the first (20) terms?
#ap
#average
#decreasing
#expert
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
The last term is (25+19(-2)=-13), so the average is \(\frac{25-13}{2}=6\). Exam tip: the average is the average of first and last terms.
Step 2
Why this answer is correct
The correct answer is B. (6). The last term is (25+19(-2)=-13), so the average is \(\frac{25-13}{2}=6\). Exam tip: the average is the average of first and last terms.
Step 3
Exam Tip
अंतिम पद (25+19(-2)=-13) है इसलिए औसत \(\frac{25-13}{2}=6\) है। परीक्षा में औसत प्रथम और अंतिम पद का औसत होता है।
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एक समान्तर श्रेणी में (a=18) और (d=-4) है। पहले कितने पदों का योग (144) होगा?
In an arithmetic progression (a=18) and (d=-4). How many first terms have sum (144)?
#ap
#find-n
#decreasing
#expert
A (8)
B (9)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
Using the sum formula gives (n=9). Exam tip: even in a decreasing AP, take the positive value of (n).
Step 2
Why this answer is correct
The correct answer is B. (9). Using the sum formula gives (n=9). Exam tip: even in a decreasing AP, take the positive value of (n).
Step 3
Exam Tip
योग सूत्र रखने पर समीकरण से (n=9) मिलता है। परीक्षा में घटती श्रेणी में भी धनात्मक (n) ही लें।
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समान्तर श्रेणी \(81,75,69,\ldots\) के कितने आरम्भिक पदों का योग (315) होगा?
How many initial terms of the arithmetic progression \(81,75,69,\ldots\) have sum (315)?
#ap
#decreasing-ap
#expert
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
Solving (\frac{n}{2}[162-6(n-1)]=315) gives (n=7). Exam tip: the same sum formula works for decreasing progressions too.
Step 2
Why this answer is correct
The correct answer is C. (7). Solving (\frac{n}{2}[162-6(n-1)]=315) gives (n=7). Exam tip: the same sum formula works for decreasing progressions too.
Step 3
Exam Tip
(\frac{n}{2}[162-6(n-1)]=315) हल करने पर (n=7) मिलता है। परीक्षा में घटती श्रेणी में भी वही योग सूत्र लागू होता है।
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समांतर श्रेढ़ी \(250,238,226,\ldots\) के पहले (30) पदों का योग ज्ञात कीजिए।
Find the sum of the first (30) terms of the AP \(250,238,226,\ldots\).
#decreasing sequence
#last term
#sum
A (2200)
B (2240)
C (2320)
D (2280)
Explanation opens after your attempt
Step 1
Concept
The last term is (-98), and \(S_{30}=2280\). Once the last term is found, (S_n=\frac{n}{2}(a+l)) is faster.
Step 2
Why this answer is correct
The correct answer is D. (2280). The last term is (-98), and \(S_{30}=2280\). Once the last term is found, (S_n=\frac{n}{2}(a+l)) is faster.
Step 3
Exam Tip
अंतिम पद (-98) है और \(S_{30}=2280\) है। अंतिम पद मिल जाए तो (S_n=\frac{n}{2}(a+l)) तेज रहता है।
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समांतर श्रेढ़ी \(300,287,274,\ldots\) के पहले (35) पदों का योग ज्ञात कीजिए।
Find the sum of the first (35) terms of the AP \(300,287,274,\ldots\).
#decreasing ap
#negative difference
#sum
A (2715)
B (2735)
C (2755)
D (2765)
Explanation opens after your attempt
Step 1
Concept
Here (d=-13), and \(S_{35}=2765\). Do not forget the negative sign of the common difference in a decreasing AP.
Step 2
Why this answer is correct
The correct answer is D. (2765). Here (d=-13), and \(S_{35}=2765\). Do not forget the negative sign of the common difference in a decreasing AP.
Step 3
Exam Tip
यहाँ (d=-13) है और \(S_{35}=2765\) आता है। घटती श्रेढ़ी में सार्व अंतर का ऋणात्मक चिह्न न भूलें।
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समांतर श्रेढ़ी \(140,132,124,\ldots\) के पहले (25) पदों का योग ज्ञात कीजिए।
Find the sum of the first (25) terms of the AP \(140,132,124,\ldots\).
#decreasing ap
#last term
#sum
A (1040)
B (1060)
C (1080)
D (1100)
Explanation opens after your attempt
Step 1
Concept
The last term is (-52), and \(S_{25}=1100\). Even in a decreasing AP, (S_n=\frac{n}{2}(a+l)) is useful.
Step 2
Why this answer is correct
The correct answer is D. (1100). The last term is (-52), and \(S_{25}=1100\). Even in a decreasing AP, (S_n=\frac{n}{2}(a+l)) is useful.
Step 3
Exam Tip
अंतिम पद (-52) है और \(S_{25}=1100\) है। घटती श्रेढ़ी में भी (S_n=\frac{n}{2}(a+l)) उपयोगी है।
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समांतर श्रेढ़ी \(160,151,142,\ldots\) के पहले (22) पदों का योग ज्ञात कीजिए।
Find the sum of the first (22) terms of the AP \(160,151,142,\ldots\).
#decreasing ap
#negative difference
#sum
A (1397)
B (1419)
C (1463)
D (1441)
Explanation opens after your attempt
Step 1
Concept
Here (d=-9), and the formula gives \(S_{22}=1441\). In a decreasing AP, write the common difference as negative.
Step 2
Why this answer is correct
The correct answer is D. (1441). Here (d=-9), and the formula gives \(S_{22}=1441\). In a decreasing AP, write the common difference as negative.
Step 3
Exam Tip
यहाँ (d=-9) है और सूत्र से \(S_{22}=1441\) मिलता है। घटती श्रेढ़ी में सार्व अंतर ऋणात्मक लिखें।
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समांतर श्रेढ़ी \(95,89,83,\ldots\) के पहले (20) पदों का योग ज्ञात कीजिए।
Find the sum of the first (20) terms of the AP \(95,89,83,\ldots\).
#decreasing ap
#last term
#sum
A (730)
B (760)
C (790)
D (820)
Explanation opens after your attempt
Step 1
Concept
The last term is (-19), and \(S_{20}=760\). Even in a decreasing AP, (S_n=\frac{n}{2}(a+l)) is useful.
Step 2
Why this answer is correct
The correct answer is B. (760). The last term is (-19), and \(S_{20}=760\). Even in a decreasing AP, (S_n=\frac{n}{2}(a+l)) is useful.
Step 3
Exam Tip
अंतिम पद (-19) है और \(S_{20}=760\) है। घटती श्रेढ़ी में भी (S_n=\frac{n}{2}(a+l)) उपयोगी है।
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समांतर श्रेढ़ी \(120,113,106,\ldots\) के पहले (25) पदों का योग ज्ञात कीजिए।
Find the sum of the first (25) terms of the AP \(120,113,106,\ldots\).
#decreasing ap
#negative difference
#sum
A (850)
B (875)
C (900)
D (925)
Explanation opens after your attempt
Step 1
Concept
Here (d=-7), and the formula gives \(S_{25}=900\). In a decreasing AP, write the common difference as negative.
Step 2
Why this answer is correct
The correct answer is C. (900). Here (d=-7), and the formula gives \(S_{25}=900\). In a decreasing AP, write the common difference as negative.
Step 3
Exam Tip
यहाँ (d=-7) है और सूत्र से \(S_{25}=900\) मिलता है। घटती श्रेढ़ी में सार्व अंतर ऋणात्मक लिखें।
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समांतर श्रेढ़ी \(50,47,44,\ldots\) में (6)वें पद से (20)वें पद तक का योग क्या है?
In the AP \(50,47,44,\ldots\), what is the sum from the (6)th term to the (20)th term?
#decreasing ap
#middle terms
#partial sum
A (180)
B (195)
C (210)
D (225)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{20}-S_5=210\). The same partial-sum method works for a decreasing AP.
Step 2
Why this answer is correct
The correct answer is C. (210). The required sum is \(S_{20}-S_5=210\). The same partial-sum method works for a decreasing AP.
Step 3
Exam Tip
आवश्यक योग \(S_{20}-S_5=210\) है। घटती श्रेढ़ी में भी आंशिक योग का वही तरीका लागू होता है।
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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 \(24,21,18,\ldots\)?
#decreasing ap
#small sum
#ap
A (20)
B (22)
C (24)
D (26)
Explanation opens after your attempt
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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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 \(100,95,90,\ldots\).
#decreasing sequence
#last term
#sum
A (870)
B (880)
C (890)
D (900)
Explanation opens after your attempt
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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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 \(31,28,25,\ldots\).
#decreasing ap
#negative terms
#sum
A (50)
B (55)
C (60)
D (65)
Explanation opens after your attempt
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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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 \(50,47,44,\ldots\).
#decreasing ap
#ap sum
#common difference
A (441)
B (459)
C (468)
D (450)
Explanation opens after your attempt
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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यदि (S_n=\frac{n}{2}(a+l)), (a=25), (l=5), और (n=7) है, तो योग क्या होगा?
If (S_n=\frac{n}{2}(a+l)), (a=25), (l=5), and (n=7), what is the sum?
#ap_sum
#first_last
#decreasing
A (95)
B (100)
C (105)
D (110)
Explanation opens after your attempt
Step 1
Concept
(S_7=\frac{7}{2}(25+5)=105). The first term may be larger, but the formula remains the same.
Step 2
Why this answer is correct
The correct answer is C. (105). (S_7=\frac{7}{2}(25+5)=105). The first term may be larger, but the formula remains the same.
Step 3
Exam Tip
(S_7=\frac{7}{2}(25+5)=105)। पहला पद बड़ा हो सकता है, फिर भी सूत्र वही रहता है।
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समान्तर श्रेणी \(60,54,48,\ldots\) के पहले (5) पदों का योग क्या होगा?
What will be the sum of the first (5) terms of the AP \(60,54,48,\ldots\)?
#ap-sum-five-decreasing
A (230)
B (240)
C (250)
D (260)
Explanation opens after your attempt
Step 1
Concept
The fifth term is (36). (S_5=\frac{5}{2}(60+36)=240).
Step 2
Why this answer is correct
The correct answer is B. (240). The fifth term is (36). (S_5=\frac{5}{2}(60+36)=240).
Step 3
Exam Tip
पांचवां पद (36) है। (S_5=\frac{5}{2}(60+36)=240)।
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समान्तर श्रेणी \(50,45,40,\ldots\) के पहले (9) पदों का योग क्या है?
What is the sum of the first (9) terms of the AP \(50,45,40,\ldots\)?
#ap-sum-decreasing-nine
A (260)
B (270)
C (280)
D (290)
Explanation opens after your attempt
Step 1
Concept
The ninth term is (10). (S_9=\frac{9}{2}(50+10)=270).
Step 2
Why this answer is correct
The correct answer is B. (270). The ninth term is (10). (S_9=\frac{9}{2}(50+10)=270).
Step 3
Exam Tip
नौवां पद (10) है। (S_9=\frac{9}{2}(50+10)=270)।
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समान्तर श्रेणी \(100,90,80,\ldots\) के पहले (6) पदों का योग क्या है?
What is the sum of the first (6) terms of the AP \(100,90,80,\ldots\)?
#ap-sum-decreasing-six
A (430)
B (440)
C (450)
D (460)
Explanation opens after your attempt
Step 1
Concept
The sixth term is (50). (S_6=\frac{6}{2}(100+50)=450).
Step 2
Why this answer is correct
The correct answer is C. (450). The sixth term is (50). (S_6=\frac{6}{2}(100+50)=450).
Step 3
Exam Tip
छठा पद (50) है। (S_6=\frac{6}{2}(100+50)=450)।
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यदि (a=25), (d=-2), (n=15) है तो \(S_{15}\) क्या होगा?
If (a=25), (d=-2), (n=15), what is \(S_{15}\)?
#ap-sum-decreasing-values
A (155)
B (160)
C (165)
D (170)
Explanation opens after your attempt
Step 1
Concept
In a decreasing AP use (d=-2). (S_{15}=\frac{15}{2}[50+14(-2)]=165).
Step 2
Why this answer is correct
The correct answer is C. (165). In a decreasing AP use (d=-2). (S_{15}=\frac{15}{2}[50+14(-2)]=165).
Step 3
Exam Tip
घटती AP में (d=-2) रखें। (S_{15}=\frac{15}{2}[50+14(-2)]=165)।
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समान्तर श्रेणी \(20,18,16,\ldots\) के पहले (8) पदों का योग क्या है?
What is the sum of the first (8) terms of the AP \(20,18,16,\ldots\)?
#ap-sum-decreasing
A (100)
B (104)
C (108)
D (112)
Explanation opens after your attempt
Step 1
Concept
This is a decreasing AP with (d=-2). (S_8=\frac{8}{2}[40+7(-2)]=104).
Step 2
Why this answer is correct
The correct answer is B. (104). This is a decreasing AP with (d=-2). (S_8=\frac{8}{2}[40+7(-2)]=104).
Step 3
Exam Tip
यह घटती AP है जिसमें (d=-2) है। (S_8=\frac{8}{2}[40+7(-2)]=104)।
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समान्तर श्रेणी \(240,222,204,\ldots\) में (-150) से बड़ा अंतिम पद कौन-सा है?
In the AP \(240,222,204,\ldots\), which is the last term greater than (-150)?
#ap expert decreasing limit
A (-138)
B (-144)
C (-150)
D (-156)
Explanation opens after your attempt
Step 1
Concept
(d=-18). After (-144), (-162) comes, so the last term greater than (-150) is (-144).
Step 2
Why this answer is correct
The correct answer is B. (-144). (d=-18). After (-144), (-162) comes, so the last term greater than (-150) is (-144).
Step 3
Exam Tip
(d=-18) है। (-144) के बाद (-162) आता है इसलिए (-150) से बड़ा अंतिम पद (-144) है।
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समान्तर श्रेणी \(310,291,272,\ldots\) में (75) से छोटा पहला पद कौन-सा है?
In the AP \(310,291,272,\ldots\), what is the first term less than (75)?
#ap expert decreasing boundary
A (82)
B (63)
C (44)
D (25)
Explanation opens after your attempt
Step 1
Concept
Here (d=-19). After (82), (63) comes, so the first term less than (75) is (63).
Step 2
Why this answer is correct
The correct answer is B. (63). Here (d=-19). After (82), (63) comes, so the first term less than (75) is (63).
Step 3
Exam Tip
यहां (d=-19) है। (82) के बाद (63) आता है इसलिए (75) से छोटा पहला पद (63) है।
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समान्तर श्रेणी \(156,142,128,\ldots\) में (-120) से बड़ा अंतिम पद कौन-सा है?
In the AP \(156,142,128,\ldots\), which is the last term greater than (-120)?
#ap expert decreasing limit
A (-110)
B (-112)
C (-118)
D (-124)
Explanation opens after your attempt
Step 1
Concept
(d=-14). (-110) is not in this AP, while after (-112), (-126) comes.
Step 2
Why this answer is correct
The correct answer is B. (-112). (d=-14). (-110) is not in this AP, while after (-112), (-126) comes.
Step 3
Exam Tip
(d=-14) है। (-110) इस श्रेणी में नहीं है, जबकि (-112) के बाद (-126) आता है।
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समान्तर श्रेणी \(221,204,187,\ldots\) में (50) से छोटा पहला पद कौन-सा है?
In the AP \(221,204,187,\ldots\), what is the first term less than (50)?
#ap expert decreasing boundary
A (51)
B (34)
C (17)
D (0)
Explanation opens after your attempt
Step 1
Concept
Here (d=-17). After (51), (34) comes, so the first term less than (50) is (34).
Step 2
Why this answer is correct
The correct answer is B. (34). Here (d=-17). After (51), (34) comes, so the first term less than (50) is (34).
Step 3
Exam Tip
यहां (d=-17) है। (51) के बाद (34) आता है, इसलिए (50) से छोटा पहला पद (34) है।
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समान्तर श्रेणी \(121,109,97,\ldots\) में (-75) से बड़ा अंतिम पद कौन-सा है?
In the AP \(121,109,97,\ldots\), which is the last term greater than (-75)?
#ap-decreasing-limit-expert
A (-71)
B (-75)
C (-83)
D (-87)
Explanation opens after your attempt
Step 1
Concept
(d=-12). After (-71), the next term is (-83), so the last term greater than (-75) is (-71).
Step 2
Why this answer is correct
The correct answer is A. (-71). (d=-12). After (-71), the next term is (-83), so the last term greater than (-75) is (-71).
Step 3
Exam Tip
(d=-12) है। (-71) के बाद (-83) आता है, इसलिए (-75) से बड़ा अंतिम पद (-71) है।
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समान्तर श्रेणी \(169,154,139,\ldots\) में (40) से छोटा पहला पद कौन-सा है?
In the AP \(169,154,139,\ldots\), what is the first term less than (40)?
#ap-decreasing-boundary-expert
A (49)
B (34)
C (19)
D (4)
Explanation opens after your attempt
Step 1
Concept
Here (d=-15). After (49), the next term is (34), so the first term less than (40) is (34).
Step 2
Why this answer is correct
The correct answer is B. (34). Here (d=-15). After (49), the next term is (34), so the first term less than (40) is (34).
Step 3
Exam Tip
यहां (d=-15) है। (49) के बाद (34) आता है, इसलिए (40) से छोटा पहला पद (34) है।
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समान्तर श्रेणी \(104,95,86,\ldots\) में (-50) से बड़ा अंतिम पद कौन-सा है?
In the AP \(104,95,86,\ldots\), which is the last term greater than (-50)?
#ap decreasing limit hard
A (-41)
B (-45)
C (-50)
D (-59)
Explanation opens after your attempt
Step 1
Concept
(d=-9). The last term greater than (-50) is (-40) if it appears, so always verify actual terms before choosing.
Step 2
Why this answer is correct
The correct answer is A. (-41). (d=-9). The last term greater than (-50) is (-40) if it appears, so always verify actual terms before choosing.
Step 3
Exam Tip
(d=-9) है। (-50) से बड़ा अंतिम पद (-40) नहीं बल्कि (-40) श्रेणी में नहीं आता इसलिए (-40) से पहले सही पद (-40) जांचना चाहिए।
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