Let $A$ be a $2 \times 2$ real matrix with entries from $\{0,1\}$ and $|A|\neq 0$. Consider the following two statements: (P) If $A \neq I_2$, then $|A| = -1$ (Q) If $|A| = 1$, then $\operatorname{tr}(A) = 2$ where $I_2$ denotes $2 \times 2$ identity matrix and $\operatorname{tr}(A)$ denotes the sum of the diagonal entries of $A$.
Previous 10 Questions — JEE Main 2 September 2020 (Morning)
Nearest first
1
2
3
4
5
Let $\alpha > 0, \, \beta > 0$ be such that $\alpha^3 + \beta^2 = 4$.
If the maximum value of the term independent o…
Topic: JEE Main 2 September 2020 (Morning)
If a function $f(x)$ defined by $f(x) =
\begin{cases}
ae^x + be^{-x}, & -1 \leq x < 1 \\[6pt] cx^2, &…
Topic: JEE Main 2 September 2020 (Morning)
Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random an…
Topic: JEE Main 2 September 2020 (Morning)
Area (in sq. units) of the region outside
$\frac{|x|}{2} + \frac{|y|}{3} = 1$
and inside the ellipse
$\frac{x^2}{4}$…
Topic: JEE Main 2 September 2020 (Morning)
Let $S$ be the set of all $\lambda \in \mathbb{R}$ for which the system of linear equations
\[
2x - y + 2z = 2
\]
…
Topic: JEE Main 2 September 2020 (Morning)
Next 10 Questions — JEE Main 2 September 2020 (Morning)
Ascending by ID
1
2
3
4
5
6
7
8
The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in :
Topic: JEE Main 2 September 2020 (Morning)
If p(x) be a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2;…
Topic: JEE Main 2 September 2020 (Morning)
$\left( \dfrac{1 + \sin\frac{2\pi}{9} + i \cos\frac{2\pi}{9}}{1 + \sin\frac{2\pi}{9} - i \cos\frac{2\pi}{9}} \right)^3$
Topic: JEE Main 2 September 2020 (Morning)
The domain of the function
$f(x) = \sin^{-1}\!\left(\dfrac{|x|+5}{x^2+1}\right)$
is $(-\infty, -a] \cup [a, \infty)…
Topic: JEE Main 2 September 2020 (Morning)
Let $\alpha$ and $\beta$ be the roots of the equation
$5x^2 + 6x - 2 = 0$.
If $S_n = \alpha^n + \beta^n,\; n = 1,2,…
Topic: JEE Main 2 September 2020 (Morning)
If $R = \{(x,y) : x,y \in \mathbb{Z}, \; x^{2} + 3y^{2} \leq 8 \}$
is a relation on the set of integers $\mathbb{Z}$, …
Topic: JEE Main 2 September 2020 (Morning)
Let $X = \{x \in \mathbb{N} : 1 \leq x \leq 17\}$ and
$Y = \{ax + b : x \in X,\; a \in \mathbb{R},\; b \in \mathbb{R…
Topic: JEE Main 2 September 2020 (Morning)
Let $y = y(x)$ be the solution of the differential equation
$\dfrac{2 + \sin x}{y+1} \cdot \dfrac{dy}{dx} = -\cos x,…
Topic: JEE Main 2 September 2020 (Morning)
