NDA Mathematics 21 April 2024 | Quadratic Equations and Inequalities Question 51 | Mathematics

Under which one of the following conditions does the equation $\left(\cos \beta-1\right)x^2+(\cos \beta)x+\sin \beta=0$ in $x$ have a real root for $\beta \in [0, \pi]$?

$1-\cos \beta <0$

$1-\cos \beta \leq 0$

$1-\cos \beta>0$

$1-\cos \beta \geq 0$

NDA Mathematics 3 September 2023

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the following for the next items that follow:

A quadratic equation is given by (a + b) x2 - (a + b + c) x + k = 0, where a, b, c are real.

If $\rm {k}=\frac{{c}}{2},({c} \neq 0)$, then the roots of the equation are :

Real and equal

Real and unequal

Real iff a > c

Complex but not real

NDA Mathematics 3 September 2023

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the following for the next items that follow:

A quadratic equation is given by (a + b) x2 - (a + b + c) x + k = 0, where a, b, c are real.

If k = c, then the roots of the equation are:

$ \frac{a+c}{a+b}$ and $\frac{b}{a+b}$

$ \frac{a+c}{a+b} $ and $-\frac{b}{a+b} $

1 and $ \frac{c}{a+b}$

-1 and $-\frac{c}{a+b}$

NDA Mathematics 16 April 2023

MCQ (Single Correct Answer)

+2.5

-0.83

For how many integral values of k, the equation x² - 4x + k = 0, where k is an integer has real roots and both of them lie in the interval (0, 5) ?

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