NTA JEE Main 9th April 2017 Online

The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points $$(4, -1)$$ and $$(-2, 2)$$ is

The contrapositive of the statement 'If two numbers are not equal, then their squares are not equal', is

The sum of 100 observations and the sum of their squares are 400 & 2475, respectively. Later on, three observations 3, 4 & 5 were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is

For two $$3 \times 3$$ matrices $$A$$ and $$B$$, let $$A + B = 2B'$$ and $$3A + 2B = I_3$$, where $$B'$$ is the transpose of $$B$$ and $$I_3$$ is $$3 \times 3$$ identity matrix. Then:

If $$x = a$$, $$y = b$$, $$z = c$$ is a solution of the system of linear equations
$$x + 8y + 7z = 0$$
$$9x + 2y + 3z = 0$$
$$x + y + z = 0$$
Such that the point $$(a, b, c)$$ lies on the plane $$x + 2y + z = 6$$, then $$2a + b + c$$ equals:

A value of $$x$$ satisfying the equation $$\sin\left[\cot^{-1}(1 + x)\right] = \cos\left[\tan^{-1}x\right]$$, is:

The function $$f : N \to I$$ defined by $$f(x) = x - 5\left[\frac{x}{5}\right]$$, where $$N$$ is the set of natural numbers and $$[x]$$ denotes the greatest integer less than or equal to $$x$$, is:

The value of $$k$$ which the function $$f(x) = \begin{cases} \left(\frac{4}{5}\right)^{\frac{\tan 4x}{\tan 5x}}, & 0 < x < \frac{\pi}{2} \\ k + \frac{2}{5}, & x = \frac{\pi}{2} \end{cases}$$ is continuous at $$x = \frac{\pi}{2}$$, is

If $$2x = y^{\frac{1}{5}} + y^{-\frac{1}{5}}$$ and $$(x^2 - 1)\frac{d^2y}{dx^2} + \lambda x \frac{dy}{dx} + ky = 0$$, then $$\lambda + k$$ is equal to

The function $$f$$ defined by $$f(x) = x^3 - 3x^2 + 5x + 7$$ is: