Jitender Gupta and Divya Malik Solutions for Exercise 6: CHALLENGERS

The linear factors of the equation $x^2+kx+1=0$ exists, if

The root of the equation $2\mathrm{sin\theta }+\frac{3}{\mathrm{sin\theta }}+7=0$ is

The equation $x^2(a^2+b^2)+2x(ac+bd)+(c^2+d^2)=0$ has no real roots, if $ad\ne$_____.

A factory kept increasing its output by the same percentage every year. Then, the percentage, if it is known that the output is doubled in the last two years, will be

A trader bought a number of articles for $₹1200$. Ten were damaged and he sold each of the rest at $₹2$ more than what he paid for it, thus getting a profit of $₹60$ on the whole transaction. If $x$ denotes the number of articles he bought, then the value of $x$ is

If the roots of the equation $x^2+2cx+ab=0$ are real and unequal, then the equation $x^2-2(a+b)x+a^2+b^2+ 2c^2=0$ has

The values of $x$ satisfying $p^2{x}^2+\left(p^2-q^2\right)x-q^2=0$ are

From a group of Sara's birds, one-fourth of the number are moving about in lotus plants, one-ninth coupled with one-fourth as well as $7$ times the square root of the total number are moving on a hill, while $56$ birds are sitting in the Bakula trees. Then, what is the total number of birds?