Permutations & Combinations · JEE Main previous year questions

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2025 14 questions

Q212025 · 8 Apr 2025 · Shift 2· Numerical answer
The product of the last two digits of $(1919)^{1919}$ is
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Answer: 63
Q252025 · 4 Apr 2025 · Shift 2· Numerical answer
Let m and n, $(m < n)$ , be two 2-digit numbers. Then the total numbers of pairs (m, n), such that $g cd (m, n) = 6$ , is ____ .
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Answer: 64
Q22025 · 3 Apr 2025 · Shift 1
Let $a_{1}, a_{2}, a_{3}, \dots$ be a G.P. of increasing positive numbers. If $a_{3} a_{5} = 729$ and $a_{2} + a_{4} = \frac{111}{4}$ , then $24 (a_{1} + a_{2} + a_{3})$ is equal to
1. A.128
2. B.129
3. C.131
4. D.130
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Answer: B
Q252025 · 3 Apr 2025 · Shift 1· Numerical answer
If the number of seven-digit numbers, such that the sum of their digits is even, is $m \cdot n \cdot 1 0^{n}; m, n \in {1, 2, 3, \dots, 9}$ , then $m + n$ is equal to____
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Answer: 14
Q22025 · 3 Apr 2025 · Shift 2
Line $L_{1}$ of slope $2$ and line $L_{2}$ of slope $\frac{1}{2}$ intersect at the origin $O$ . In the first quadrant, $P_{1}, P_{2}, \dots, P_{12}$ are $12$ points on line $L_{1}$ and $Q_{1}, Q_{2}, \dots, Q_{9}$ are $9$ points on line $L_{2}$ . Then the total number of triangles, that can be formed having vertices at three of the $22$ points $O, P_{1}, P_{2}, \dots, P_{12}, Q_{1}, Q_{2}, \dots, Q_{9}$ , is:
1. A. $1026$
2. B. $1188$
3. C. $1134$
4. D. $1080$
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Answer: C
Q32025 · 2 Apr 2025 · Shift 2
1. A.5880
2. B.840
3. C.960
4. D.5760
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Answer: D
Q192025 · 29 Jan 2025 · Shift 2
If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at $44 0^{th}$ position in this arrangement is :
1. A.PRNAKU
2. B.PRKAUN
3. C.PRKANU
4. D.PRNAUK
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Answer: B
Q162025 · 28 Jan 2025 · Shift 1
The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0 , 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8 , is
1. A.5720
2. B.5719
3. C.4608
4. D.4607
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Answer: D
Q252025 · 24 Jan 2025 · Shift 1· Numerical answer
The number of 3 -digit numbers, that are divisible by 2 and 3 , but not divisible by 4 and 9 , is _________.
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Answer: 125
Q162025 · 24 Jan 2025 · Shift 2
Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B, is equal to :
1. A.8925
2. B.9100
3. C.8575
4. D.8750
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Answer: A
Q162025 · 23 Jan 2025 · Shift 2
A rod of length eight units moves such that its ends $A$ and $B$ always lie on the lines $x - y + 2 = 0$ and $y + 2 = 0$ , respectively. If the locus of the point $P$ , that divides the rod $A B$ internally in the ratio $2 : 1$ is $9 (x^{2} + α y^{2} + β x y + γ x + 28 y) - 76 = 0$ , then $α - β - γ$ is equal to :
1. A.24
2. B.22
3. C.21
4. D.23
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Answer: D
Q232025 · 23 Jan 2025 · Shift 2· Numerical answer
The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is ________.
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Answer: 17280
Q82025 · 22 Jan 2025 · Shift 1
From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is ' M ', is :
1. A.6084
2. B.5148
3. C.14950
4. D.4356
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Answer: B
Q142025 · 22 Jan 2025 · Shift 1
Let $a_{1}, a_{2}, a_{3}, \dots$ be a G.P. of increasing positive terms. If $a_{1} a_{5} = 28$ and $a_{2} + a_{4} = 29$ , then $a_{6}$ is equal to:
1. A.812
2. B.784
3. C.628
4. D.526
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Answer: B