समांतर श्रेणी \(60,55,50,\ldots\) के पहले (14) पदों का योग ज्ञात करें।
Find the sum of the first (14) terms of the arithmetic progression \(60,55,50,\ldots\).
#decreasing_ap
#negative_term
#ap_sum
A (365)
B (375)
C (385)
D (395)
Explanation opens after your attempt
Step 1
Concept
The fourteenth term is (-5), so (S_{14}=\frac{14}{2}(60-5)=385). In a decreasing progression, the last term may become negative.
Step 2
Why this answer is correct
The correct answer is C. (385). The fourteenth term is (-5), so (S_{14}=\frac{14}{2}(60-5)=385). In a decreasing progression, the last term may become negative.
Step 3
Exam Tip
चौदहवाँ पद (-5) है, इसलिए (S_{14}=\frac{14}{2}(60-5)=385)। घटती श्रेणी में अंतिम पद ऋणात्मक भी हो सकता है।
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समान्तर श्रेणी \(55,51,47,\ldots\) का (n)वां पद (-17) है। (n) क्या है?
The (n)th term of the AP \(55,51,47,\ldots\) is (-17). What is (n)?
#ap
#negative-term
#term-number
#class10
A (17)
B (18)
C (19)
D (20)
Explanation opens after your attempt
Step 1
Concept
From (-17=55+(n-1)(-4)), (72=4(n-1)) so (n=19). Keep signs correct while reaching a negative term.
Step 2
Why this answer is correct
The correct answer is C. (19). From (-17=55+(n-1)(-4)), (72=4(n-1)) so (n=19). Keep signs correct while reaching a negative term.
Step 3
Exam Tip
(-17=55+(n-1)(-4)) से (72=4(n-1)) इसलिए (n=19)। ऋणात्मक पद तक जाते समय चिन्ह सही रखें।
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समान्तर श्रेणी \(27,24,21,\ldots\) का (n)वां पद (-30) है। (n) क्या है?
The (n)th term of the AP \(27,24,21,\ldots\) is (-30). What is (n)?
#ap
#negative-term
#term-number
#class10
A (18)
B (19)
C (20)
D (21)
Explanation opens after your attempt
Step 1
Concept
From (-30=27+(n-1)(-3)), (57=3(n-1)), so (n=20). Handle signs carefully with a negative target term.
Step 2
Why this answer is correct
The correct answer is C. (20). From (-30=27+(n-1)(-3)), (57=3(n-1)), so (n=20). Handle signs carefully with a negative target term.
Step 3
Exam Tip
(-30=27+(n-1)(-3)) से (57=3(n-1)), इसलिए (n=20)। ऋणात्मक लक्ष्य पद में चिन्ह सावधानी से बदलें।
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यदि (2x-3y=1) और (x=5), तो (y) का मान क्या है?
If (2x-3y=1) and (x=5), what is the value of (y)?
#linear equations
#substitution
#negative term
#easy
#class 10
A (y=3)
B (y=4)
C (y=5)
D (y=6)
Explanation opens after your attempt
Step 1
Concept
Putting (x=5) gives (10-3y=1), so (y=3). Watch the signs while solving a negative term.
Step 2
Why this answer is correct
The correct answer is A. (y=3). Putting (x=5) gives (10-3y=1), so (y=3). Watch the signs while solving a negative term.
Step 3
Exam Tip
(x=5) रखने पर (10-3y=1), इसलिए (y=3)। ऋण पद को हल करते समय चिन्हों का ध्यान रखें।
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समीकरण (x-y=2) और (x=6) में (y) का मान क्या है?
In (x-y=2) and (x=6), what is the value of (y)?
#linear equations
#substitution
#negative term
#easy
#class 10
A (y=2)
B (y=4)
C (y=6)
D (y=8)
Explanation opens after your attempt
Step 1
Concept
(6-y=2), so (y=4). Do not rush when solving a term with a negative sign.
Step 2
Why this answer is correct
The correct answer is B. (y=4). (6-y=2), so (y=4). Do not rush when solving a term with a negative sign.
Step 3
Exam Tip
(6-y=2), इसलिए (y=4)। ऋण वाले पद को हल करते समय जल्दबाजी न करें।
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