1
JEE Main 2023 (Online) 8th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\alpha, \beta, \gamma$$ be the three roots of the equation $$x^{3}+b x+c=0$$. If $$\beta \gamma=1=-\alpha$$, then $$b^{3}+2 c^{3}-3 \alpha^{3}-6 \beta^{3}-8 \gamma^{3}$$ is equal to :

A
21
B
19
C
$$\frac{169}{8}$$
D
$$\frac{155}{8}$$
2
JEE Main 2023 (Online) 8th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the number of elements in sets $$A$$ and $$B$$ be five and two respectively. Then the number of subsets of $$A \times B$$ each having at least 3 and at most 6 elements is :

A
782
B
772
C
752
D
792
3
JEE Main 2023 (Online) 8th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

If the coefficients of three consecutive terms in the expansion of $$(1+x)^{n}$$ are in the ratio $$1: 5: 20$$, then the coefficient of the fourth term is

A
3654
B
1827
C
5481
D
2436
4
JEE Main 2023 (Online) 8th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$S_{K}=\frac{1+2+\ldots+K}{K}$$ and $$\sum_\limits{j=1}^{n} S_{j}^{2}=\frac{n}{A}\left(B n^{2}+C n+D\right)$$, where $$A, B, C, D \in \mathbb{N}$$ and $$A$$ has least value. Then

A
$$A+B+C+D$$ is divisible by 5
B
$$A+C+D$$ is not divisible by $$B$$
C
$$A+B=5(D-C)$$
D
$$A+B$$ is divisible by $$\mathrm{D}$$
JEE Main Papers
2023
2021
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12