Sequences and Series

JEE Main 2025 (Online) 23rd January Evening ShiftNumericalMedium📈 Topic in 58% papers+4

Ques. 1JEE Main 2025, 23 January (Evening Shift)

The roots of the quadratic equation 3x2-px+q=0 are 10th and 11th terms of an arithmetic progression with common difference 32. If the sum of the first 11 terms of this arithmetic progression is 88, then q-2p is equal to .

Answer

474

Solution

S11=11(a+5d)=88 a+5d=8, d= 32 a= 12

Roots: T10=14, T11= 312

p3= 592 p= 1772; q3=14 312=217 q=651

q-2p=651-177=474

Answer: 474

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Ques. 2JEE Main 2025, 22 January (Morning Shift)

Let a1,a2,a3, be a G.P. of increasing positive terms. If a1a5=28 and a2+a4=29, then a6 is equal to:

Ques. 3JEE Main 2025, 22 January (Morning Shift)

If r=1nTr= (2n-1)(2n+1)(2n+3)(2n+5)64, then n r=1n ( 1Tr ) is equal to :

Ques. 4JEE Main 2025, 22 January (Evening Shift)

Suppose that the number of terms in an A.P. is 2k, k . If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55 and the last term of the A.P. exceeds the first term by 27, then k is equal to:

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