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Numerical
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Let $$S=\{4,6,9\}$$ and $$T=\{9,10,11, \ldots, 1000\}$$. If $$A=\left\{a_{1}+a_{2}+\ldots+a_{k}: k \in \mathbf{N}, a_{1}...
JEE Main 2022 (Online) 29th July Morning Shift
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Let $$A=\{1,2,3,4,5,6,7\}$$ and $$B=\{3,6,7,9\}$$. Then the number of elements in the set $$\{C \subseteq A: C \cap B \n...
JEE Main 2022 (Online) 26th July Evening Shift
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Let $$A=\{1,2,3,4,5,6,7\}$$. Define $$B=\{T \subseteq A$$ : either $$1 \notin T$$ or $$2 \in T\}$$ and $$C=\{T \subseteq...
JEE Main 2022 (Online) 25th July Evening Shift
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The sum of all the elements of the set $$\{ \alpha \in \{ 1,2,.....,100\} :HCF(\alpha ,24) = 1\} $$ is __________....
JEE Main 2022 (Online) 24th June Evening Shift
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Let A = {n $$\in$$ N : H.C.F. (n, 45) = 1} and Let B = {2k : k $$\in$$ {1, 2, ......., 100}}. Then the sum of all the el...
JEE Main 2022 (Online) 26th June Morning Shift
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Let A = {1, a1, a2 ....... a18, 77} be a set of integers with 1 1 2 18 1 + a2 + ...... + a18 is equal to _____________....
JEE Main 2022 (Online) 28th June Morning Shift
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Let R1 and R2 be relations on the set {1, 2, ......., 50} such that R1 = {(p, pn) : p is a prime and n $$\ge$$ 0 is an i...
JEE Main 2022 (Online) 28th June Morning Shift
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Let S = {1, 2, 3, 4}. Then the number of elements in the set { f : S $$\times$$ S $$\to$$ S : f is onto and f (a, b) = f...
JEE Main 2022 (Online) 28th June Evening Shift
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Let A = {n$$ \in $$N: n is a 3-digit number} B = {9k + 2: k $$ \in $$ N}...
JEE Main 2021 (Online) 24th February Morning Slot
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MCQ (Single Correct Answer)
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Let R be a relation from the set $$\{1,2,3, \ldots, 60\}$$ to itself such that $$R=\{(a, b): b=p q$$, where $$p, q \geqs...
JEE Main 2022 (Online) 29th July Morning Shift
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$$ \text { Let } S=\left\{x \in[-6,3]-\{-2,2\}: \frac{|x+3|-1}{|x|-2} \geq 0\right\} \text { and } $$$$T=\left\{x \in \m...
JEE Main 2022 (Online) 28th July Evening Shift
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For $$\alpha \in \mathbf{N}$$, consider a relation $$\mathrm{R}$$ on $$\mathbf{N}$$ given by $$\mathrm{R}=\{(x, y): 3 x+...
JEE Main 2022 (Online) 28th July Morning Shift
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Let $$R_{1}$$ and $$R_{2}$$ be two relations defined on $$\mathbb{R}$$ by $$a \,R_{1} \,b \Leftrightarrow a b \geq 0$$ a...
JEE Main 2022 (Online) 27th July Morning Shift
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Let $$A = \{ x \in R:|x + 1| ...
JEE Main 2022 (Online) 25th June Evening Shift
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Let R1 = {(a, b) $$\in$$ N $$\times$$ N : |a $$-$$ b| $$\le$$ 13} and R2 = {(a, b) $$\in$$ N $$\times$$ N : |a $$-$$ b| ...
JEE Main 2022 (Online) 28th June Evening Shift
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Let a set A = A1 $$\cup$$ A2 $$\cup$$ ..... $$\cup$$ Ak, where Ai $$\cap$$ Aj = $$\phi$$ for i $$\ne$$ j, 1 $$\le$$ j, j...
JEE Main 2022 (Online) 29th June Morning Shift
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Let A, B and C be sets such that $$\phi $$ $$ \ne $$ A $$ \cap $$ B $$ \subseteq $$ C. Then which of the following stat...
JEE Main 2019 (Online) 12th April Evening Slot
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Two newspapers A and B are published in a city. It is known that 25% of the city populations reads A and 20% reads B whi...
JEE Main 2019 (Online) 9th April Evening Slot
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Let Z be the set of integers. If A = {x $$ \in $$ Z : 2(x + 2) (x2 $$-$$ 5x + 6) = 1} and B = {x $$ \in $$ Z : $$-$$...
JEE Main 2019 (Online) 12th January Evening Slot
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Let S = {1, 2, 3, … , 100}. The number of non-empty subsets A of S such that the product of elements in A is even is :
JEE Main 2019 (Online) 12th January Morning Slot
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The number of functions f from {1, 2, 3, ...., 20} onto {1, 2, 3, ...., 20} such that f(k) is a multiple of 3, whenever ...
JEE Main 2019 (Online) 11th January Evening Slot
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In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is...
JEE Main 2019 (Online) 10th January Morning Slot
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Two sets A and B are as under : A = {($$a$$, b) $$ \in $$ R $$ \times $$ R : |$$a$$ - 5| < 1 and |b - 5| < 1}; B =...
JEE Main 2018 (Offline)
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Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A $\times$...
JEE Main 2015 (Offline)
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Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y $$ \subseteq $$ X, ...
AIEEE 2012
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