NTA JEE Main 17th March 2021 Shift 1
For the following questions answer them individually
NTA JEE Main 17th March 2021 Shift 1 - Question 71
If $$A = \begin{bmatrix} 0 & \sin\alpha \\ \sin\alpha & 0 \end{bmatrix}$$ and $$\det\left(A^2 - \frac{1}{2}I\right) = 0$$, then a possible value of $$\alpha$$ is:
NTA JEE Main 17th March 2021 Shift 1 - Question 72
The system of equations $$kx + y + z = 1$$, $$x + ky + z = k$$ and $$x + y + zk = k^2$$ has no solution if $$k$$ is equal to:
NTA JEE Main 17th March 2021 Shift 1 - Question 73
If $$\cot^{-1}(\alpha) = \cot^{-1} 2 + \cot^{-1} 8 + \cot^{-1} 18 + \cot^{-1} 32 + \ldots$$ upto 100 terms, then $$\alpha$$ is:
NTA JEE Main 17th March 2021 Shift 1 - Question 74
The sum of possible values of $$x$$ for $$\tan^{-1}(x+1) + \cot^{-1}\left(\frac{1}{x-1}\right) = \tan^{-1}\left(\frac{8}{31}\right)$$ is:
NTA JEE Main 17th March 2021 Shift 1 - Question 75
The inverse of $$y = 5^{\log x}$$ is:
NTA JEE Main 17th March 2021 Shift 1 - Question 76
Which of the following statement is correct for the function $$g(\alpha)$$ for $$\alpha \in R$$ such that $$g(\alpha) = \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{\sin^\alpha x}{\cos^\alpha x + \sin^\alpha x} dx$$:
NTA JEE Main 17th March 2021 Shift 1 - Question 77
Which of the following is true for $$y(x)$$ that satisfies the differential equation $$\frac{dy}{dx} = xy - 1 + x - y$$; $$y(0) = 0$$:
NTA JEE Main 17th March 2021 Shift 1 - Question 78
Let $$\vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}$$ and $$\vec{b} = 7\hat{i} + \hat{j} - 6\hat{k}$$. If $$\vec{r} \times \vec{a} = \vec{r} \times \vec{b}$$, $$\vec{r} \cdot (\hat{i} + 2\hat{j} + \hat{k}) = -3$$, then $$\vec{r} \cdot (2\hat{i} - 3\hat{j} + \hat{k})$$ is equal to:
NTA JEE Main 17th March 2021 Shift 1 - Question 79
The equation of the plane which contains the $$y$$-axis and passes through the point $$(1, 2, 3)$$ is:
NTA JEE Main 17th March 2021 Shift 1 - Question 80
Two dices are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is:
