Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 501-510 of 601 questions.
If \(a_1=4\), \(a_2=6\), and \(a_n=a_{n-1}+3a_{n-2}+n\), what is \(a_4\)?
A. (43)
\(a_3=21\) और \(a_4=43\) है। \(a_{n-2}\) को (3) से गुणा करके वर्तमान (n) जोड़ें। / \(a_3=21\) and \(a_4=43\). Exam tip: multiply \(a_{n-2}\) by (3) and add current (n).
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In a sequence, \(a_1=3\) and \(a_n=2a_{n-1}+n+1\). What is the value of \(a_4\)?
C. उनचास(49)
\(a_2=9\), \(a_3=22\) और \(a_4=49\) मिलता है। परीक्षा में (n) का वर्तमान मान सही रखें। / We get \(a_2=9\), \(a_3=22\), and \(a_4=49\). In exams, keep the current value of (n) correct.
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In a sequence, \(b_1=6\) and \(b_n=3b_{n-1}-n\). What is the value of \(b_4\)?
B. एक सौ इकतीस(131)
\(b_2=16\), \(b_3=45\) और \(b_4=131\) मिलता है। परीक्षा में गुणा और घटाव दोनों ध्यान से करें। / We get \(b_2=16\), \(b_3=45\), and \(b_4=131\). In exams, handle both multiplication and subtraction carefully.
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In a sequence, \(c_1=1\), \(c_2=3\), and \(c_n=2c_{n-1}+c_{n-2}\). What is the value of \(c_5\)?
D. इकतालीस(41)
\(c_3=7\), \(c_4=17\) और \(c_5=41\) मिलता है। परीक्षा में पिछले दो पदों का क्रम न बदलें। / We get \(c_3=7\), \(c_4=17\), and \(c_5=41\). In exams, do not interchange the previous two terms.
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If \(d_n=d_{n-1}+2n\) and \(d_4=25\), what is the value of \(d_1\)?
A. सात(7)
\(d_4=d_1+4+6+8\), इसलिए \(d_1=7\) है। परीक्षा में पीछे की ओर भी वही नियम लागू करें। / \(d_4=d_1+4+6+8\), so \(d_1=7\). In exams, apply the same rule backward too.
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Which recursive rule is correct for the sequence (4), (9), (19), (39)?
B. नियम \(e_n=2e_{n-1}+1\)Rule \(e_n=2e_{n-1}+1\)
हर नया पद पिछले पद के दोगुने में (1) जोड़ने से मिलता है। परीक्षा में नियम को दो पदों पर जाँचें। / Each new term is obtained by doubling the previous term and adding (1). In exams, test the rule on two terms.
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If \(f_1=10\) and \(f_n=f_{n-1}-n\), which will be the first negative term?
D. पाँचवाँ पद(5)
\(f_2=8\), \(f_3=5\), \(f_4=1\) और \(f_5=-4\) है। परीक्षा में शून्य से नीचे जाने वाला पहला पद देखें। / \(f_2=8\), \(f_3=5\), \(f_4=1\), and \(f_5=-4\). In exams, find the first term that goes below zero.
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In a sequence, \(g_1=2\) and \(g_n=g_{n-1}+2n-1\). What is the value of \(g_5\)?
A. छब्बीस(26)
क्रमशः (3), (5), (7), (9) जोड़ने पर \(g_5=26\) मिलता है। परीक्षा में जोड़ी गई राशियों को अलग लिखें। / Adding (3), (5), (7), and (9) gives \(g_5=26\). In exams, write the added quantities separately.
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If \(h_1=3\) and \(h_n=n h_{n-1}\), what is the value of \(h_4\)?
C. बहत्तर(72)
\(h_2=6\), \(h_3=18\) और \(h_4=72\) होता है। परीक्षा में हर चरण में (n) से गुणा करें। / \(h_2=6\), \(h_3=18\), and \(h_4=72\). In exams, multiply by (n) at each step.
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In a sequence, \(j_1=1\) and \(j_n=j_{n-1}+n^2\). What is the value of \(j_4\)?
B. तीस(30)
\(j_4=1+4+9+16=30\) है। परीक्षा में \(n^2\) का मान पहले निकालें। / \(j_4=1+4+9+16=30\). In exams, calculate \(n^2\) first.
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