NTA JEE Main 9th April 2019 Shift 2

If $$m$$ is chosen in the quadratic equation $$(m^2 + 1)x^2 - 3x + (m^2 + 1)^2 = 0$$ such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is:

Let $$z \in C$$ be such that $$|z| \lt 1$$. If $$\omega = \frac{5 + 3z}{5(1 - z)}$$, then:

The sum of the series $$1 + 2 \times 3 + 3 \times 5 + 4 \times 7 + \ldots$$ upto 11th term is:

Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If 99 more identical balls are added to the total number of balls used in forming the equilateral triangle, then all these balls can be arranged in a square, whose each side contains exactly 2 balls less than the number of balls each side of the triangle contains. Then the number of balls used to form the equilateral triangle is:

If the sum and product of the first three terms in an A.P. are 33 and 1155, respectively, then a value of its 11th term is:

If some three consecutive coefficients in the binomial expansion of $$(x + 1)^n$$ in powers of $$x$$ are in the ratio 2 : 15 : 70, then the average of these three coefficients is:

The value of $$\sin 10° \sin 30° \sin 50° \sin 70°$$ is:

If the two lines $$x + (a-1)y = 1$$ and $$2x + a^2y = 1$$, $$(a \in R - \{0, 1\})$$ are perpendicular, then the distance of their point of intersection from the origin is:

A rectangle is inscribed in a circle with a diameter lying along the line $$3y = x + 7$$. If the two adjacent vertices of the rectangle are $$(-8, 5)$$ and $$(6, 5)$$, then the area of the rectangle (in sq. units) is:

The common tangent to the circles $$x^2 + y^2 = 4$$ and $$x^2 + y^2 + 6x + 8y - 24 = 0$$ also passes through the point: