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## Numerical

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