Let $\lambda $ be a real number for which the system of linear equations x + y + z = 6, 4x + $\lambda $y – $\lambda $z = $\lambda $ – 2, 3x + 2y – 4z = – 5 has infinitely many solutions. Then $\lambda $ is a root of the quadratic equation

1

The sum of the real roots of the equation $\left| {\matrix{ x & { - 6} & { - 1} \cr 2 & { - 3x} &am…

Topic: JEE Main 2019 (10 April Evening Shift)

2

The smallest natural number $n$ such that the coefficient of $x$ in the expansion of $\left(x^{2}+\dfrac{1}{x^{3}}\righ…

Topic: JEE Main 2019 (10 April Evening Shift)

3

If $5x+9=0$ is the directrix of the hyperbola $16x^{2}-9y^{2}=144$, then its corresponding focus is:

Topic: JEE Main 2019 (10 April Evening Shift)

4

If $z$ and $w$ are two complex numbers such that $|zw|=1$ and $\arg(z)-\arg(w)=\dfrac{\pi}{2}$, then:

Topic: JEE Main 2019 (10 April Evening Shift)

5

The area (in sq. units) of the region bounded by the curves $y=2^{x}$ and $y=|x+1|$, in the first quadrant, is:

Topic: JEE Main 2019 (10 April Evening Shift)

6

$\displaystyle \int_{\pi/6}^{\pi/3}\sec^{\tfrac{2}{3}}x;\csc^{\tfrac{4}{3}}x,dx$ is equal to:

Topic: JEE Main 2019 (10 April Evening Shift)

7

Suppose that $20$ pillars of the same height are erected along the boundary of a circular stadium. If the top of each p…

Topic: JEE Main 2019 (10 April Evening Shift)

8

Let $y=y(x)$ be the solution of the differential equation $\dfrac{dy}{dx}+y\tan x=2x+x^{2}\tan x,\ x\in\left(-\dfrac{\p…

Topic: JEE Main 2019 (10 April Evening Shift)

9

Lines are drawn parallel to the line $4x-3y+2=0$, at a distance $\dfrac{3}{5}$ from the origin. Then which one of the f…

Topic: JEE Main 2019 (10 April Evening Shift)

10

If both the mean and the standard deviation of $50$ observations $x_{1},x_{2},\ldots,x_{50}$ are equal to $16$, then th…

Topic: JEE Main 2019 (10 April Evening Shift)