The number of real values of $\lambda$ for which the system of linear equations

$2x+4y-\lambda z=0$

$4x+\lambda y+2z=0$

$\lambda x+2y+2z=0$

has infinitely many solutions, is :

1

If (27)999 is divided by 7, then the remainder is :

Topic: JEE Main 2017 (8 April Morning Shift)

2

Let $A$ be any $3\times 3$ invertible matrix. Then which one of the following is not always true?

Topic: JEE Main 2017 (8 April Morning Shift)

3

Let p(x) be a quadratic polynomial such that p(0)=1. If p(x) leaves remainder 4 when divided by x-1 and it leaves remai…

Topic: JEE Main 2017 (8 April Morning Shift)

4

If the arithmetic mean of two numbers a and b, a>b>0, is five times their geometric mean, then $\dfrac{a+b}{a-b}$ is eq…

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5

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in Engli…

Topic: JEE Main 2017 (8 April Morning Shift)

6

Let f(x) = 210.x + 1 and g(x)=310.x $-$ 1. If (fog) (x) = x, then x is equal to :

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7

Let $z\in\mathbb{C}$, the set of complex numbers. Then the equation $2|z+3i|-|z-i|=0$ represents :

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8

Consider an ellipse, whose center is at the origin and its major axis is along the $x$-axis. If its eccentricity is $\d…

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9

The value of $\tan^{-1}\left[\dfrac{\sqrt{1+x^{2}}+\sqrt{1-x^{2}}}{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}}\right]$, $|x|

Topic: JEE Main 2017 (8 April Morning Shift)

10

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :

Topic: JEE Main 2017 (8 April Morning Shift)