$ \text{Let } S_K=\dfrac{1+2+\cdots+K}{K} \text{ and } \displaystyle\sum_{j=1}^{n} S_j^{2}=\dfrac{n}{A}\big(Bn^{2}+Cn+D\big),\ \text{where } A,B,C,D\in\mathbb{N} \text{ and } A \text{ has least value. Then:} $
Previous 10 Questions — JEE Main 2023 (8 April Morning Shift)
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Let the number of elements in sets and be five and two respectively. Then the number of subsets o…
Topic: JEE Main 2023 (8 April Morning Shift)
$ \text{Let } \alpha,\beta,\gamma \text{ be the three roots of } x^{3}+bx+c=0. \text{ If } \beta\gamma=1=-\alpha,\ \tex…
Topic: JEE Main 2023 (8 April Morning Shift)
$ \text{Let } I(x)=\int \frac{x+1}{x,(1+x e^{x})^{2}},dx,; x>0.\ \text{If } \lim_{x\to\infty} I(x)=0,\ \text{then } I(1…
Topic: JEE Main 2023 (8 April Morning Shift)
$ \text{Let } C(\alpha,\beta) \text{ be the circumcenter of the triangle formed by the lines } 4x+3y=69,; 4y-3x=17,; x+…
Topic: JEE Main 2023 (8 April Morning Shift)
$ \text{The area of the region } {(x,y): x^{2}\le y \le 8-x^{2},; y\le 7} \text{ is:} $
Topic: JEE Main 2023 (8 April Morning Shift)
$ \text{Let } R \text{ be the focus of the parabola } y^{2}=20x \text{ and the line } y=mx+c \text{ intersect the parab…
Topic: JEE Main 2023 (8 April Morning Shift)
$ \text{The shortest distance between the lines } \dfrac{x-4}{4}=\dfrac{y+2}{5}=\dfrac{z+3}{3} \text{ and } \dfrac{x-1}…
Topic: JEE Main 2023 (8 April Morning Shift)
$ \text{The number of ways in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together…
Topic: JEE Main 2023 (8 April Morning Shift)
In a bolt factory, machines $A, B$ and $C$ manufacture respectively $20 \%, 30 \%$ and $50 \%$ of the total bolts. Of t…
Topic: JEE Main 2023 (8 April Morning Shift)
Let $f(x)=\frac{\sin x+\cos x-\sqrt{2}}{\sin x-\cos x}, x \in[0, \pi]-\left\{\frac{\pi}{4}\right\}$. Then $f\left(\frac…
Topic: JEE Main 2023 (8 April Morning Shift)
Next 10 Questions — JEE Main 2023 (8 April Morning Shift)
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Let $P=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right], …
Topic: JEE Main 2023 (8 April Morning Shift)
If for $z=\alpha+i \beta,|z+2|=z+4(1+i)$, then $\alpha+\beta$ and $\alpha \beta$ are the roots of the equation :
Topic: JEE Main 2023 (8 April Morning Shift)
$ \text{If the points with position vectors } \alpha\hat{i}+10\hat{j}+13\hat{k},; 6\hat{i}+11\hat{j}+11\hat{k},; \dfrac…
Topic: JEE Main 2023 (8 April Morning Shift)
