NTA JEE Main 11th April 2015 Online

If a circle passing through the point $$(-1, 0)$$ touches y-axis at $$(0, 2)$$, then the x-intercept of the circle is

If the incentre of an equilateral triangle is $$(1, 1)$$ and the equation of its one side is $$3x + 4y + 3 = 0$$, then the equation of the circumcircle of this triangle is:

If $$PQ$$ be a double ordinate of the parabola, $$y^2 = -4x$$, where $$P$$ lies in the second quadrant. If $$R$$ divides $$PQ$$ in the ratio 2 : 1, then the locus of $$R$$ is

If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is:

Consider the following statements:
P: Suman is brilliant
Q: Suman is rich
R: Suman is honest

The negation of the statement, "Suman is brilliant and dishonest if and only if Suman is rich" can be equivalently expressed as

Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation $$\alpha$$ at a point $$O$$ on this line and all the poles are on the same side of $$O$$. If the height of the longest pole is $$h$$ and the distance of the foot of the smallest pole from $$O$$ is $$a$$; then the distance between two consecutive poles, is

If $$A$$ is a $$3 \times 3$$ matrix such that $$|5 \cdot adj A| = 5$$, then $$|A|$$ is equal to

If $$\begin{vmatrix} x^2+x & x+1 & x-2 \\ 2x^2+3x-1 & 3x & 3x-3 \\ x^2+2x+3 & 2x-1 & 2x-1 \end{vmatrix} = ax - 12$$, then $$a$$ is equal to:

Let $$k$$ be a non-zero real number. If $$f(x) = \begin{cases} \frac{(e^x - 1)^2}{\sin\left(\frac{x}{k}\right)\log\left(1 + \frac{x}{4}\right)}, & x \neq 0 \\ 12, & x = 0 \end{cases}$$ is a continuous function at $$x = 0$$, then the value of $$k$$ is

The equation of a normal to the curve, $$\sin y = x\sin\left(\frac{\pi}{3} + y\right)$$ at $$x = 0$$, is: