Previous year questions with solutions · 2024 – 2026
| Year | Questions | Papers | Avg / paper | Weightage |
|---|---|---|---|---|
| 2026 | 32 | 19 | 1.7 | 6.74% ▲ 14.3% vs last year |
| 2025 | 28 | 19 | 1.5 | 5.89% ▲ 1.1% vs last year |
| 2024 | 35 | 20 | 1.8 | 5.83% |
For the functions f( )= 2 + 2 , and g( )= 2 + 2 , > >0, let 0< < 2 f( )= 0< < g( ). If the first term of a G.P. is ( 2 ), its common ratio is ( 2 ) and the sum of its first 10 terms is mn, (m, n)=1, then m+n is equal to .
If k=1n ak=6n3, then k=16 ( ak+1-ak36 )2 is equal to .
In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms is R - (a, b), then a2 + b2 is equal to .
If r=125 ( rr4 + r2 + 1 ) = pq, where p and q are positive integers such that (p, q) = 1, then p + q is equal to .
Suppose a, b, c are in A.P. and a2, 2b2, c2 are in G.P. If a < b < c and a + b + c = 1, then 9(a2 + b2 + c2) is equal to .
Let a1 = 1 and for n 1, an+1 = 12an + n2 - 2n - 1n2(n + 1)2. Then | n=1 (an - 2n2 ) | is equal to .
If the sum of the first 10 terms of the series 4 11 + 4 14 + 4 21 + 4 24 + 4 31 + 4 34 + is mn, where (m, n) = 1, then m + n is equal to .
Let a1,a2, ,a2024 be an Arithmetic Progression such that a1+(a5+a10+a15+ +a2020)+a2024=2233. Then a1+a2+a3+ +a2024 is equal to .
The interior angles of a polygon with n sides are in an A.P. with common difference 6 . If the largest interior angle of the polygon is 219 , then n is equal to .
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 .
If ( 1 + 1 + 1 + 2 + + 1 + 1012 ) - ( 12 1 + 14 3 + 16 5 + + 12024 2023 ) = 12024, then is equal to .
Let the positive integers be written in the form : [figure] If the kth row contains exactly k numbers for every natural number k, then the row in which the number 5310 will be, is .
An arithmetic progression is written in the following way [figure] The sum of all the terms of the 10th row is .
Let the first term of a series be T1 = 6 and its rth term Tr = 3Tr-1 + 6r, r = 2, 3, , n. If the sum of the first n terms of this series is 15 (n2 - 12n + 39 ) (4 6n - 5 3n + 1 ), then n is equal to .
If S(x) = (1 + x) + 2(1 + x)2 + 3(1 + x)3 + + 60(1 + x)60, x 0, and (60)2 S(60) = a(b)b + b, where a, b N, then (a + b) equal to .
Let a1, a2, a3, be in an arithmetic progression of positive terms. Let Ak = a12 - a22 + a32 - a42 + + a2k-12 - a2k2. If A3 = -153, A5 = -435 and a12 + a22 + a32 = 66, then a17 - A7 is equal to .
If 1 + 3 - 22 3 + 5 - 2 618 + 9 3 - 11 236 3 + 49 - 20 6180 + upto = 2 + ( ba + 1 ) e ( ab ), where a and b are integers with (a, b) = 1, then 11a + 18b is equal to .
Let a=1+ 2C23!+ 3C24!+ 4C25!+ , b=1+ 1C0+1C11!+ 2C0+2C1+2C22! + 3C0+3C1+3C2+3C33!+ . Then 2ba2 is equal to .
Let 3, 7, 11, 15, , 403 and 2, 5, 8, 11, , 404 be two arithmetic progressions. Then the sum, of the common terms in them, is equal to .
If three successive terms of a G.P. with common ratio r(r>1) are the lengths of the sides of a triangle and [r] denotes the greatest integer less than or equal to r, then 3[r]+[-r] is equal to .
Let =12+42+82+132+192+262+ upto 10 terms and = n=110 n4. If 4 - =55k+40, then k is equal to .
Let Sn be the sum to n-terms of an arithmetic progression 3,7,11, . If 40< ( 6n(n+1) k=1n Sk )<42, then n equals .
If 8=3+ 14(3+p)+ 142(3+2p)+ 143(3+3p)+ , then the value of p is .