Maths

If the lines x+y=a and x-y=b touch the curve y=x²-3x+2 at the points where the curve intersects the x-axis, then a/b is equal to

Let the tangents drawn from the origin to the circle, $x^2+y^2-8x-4y+16=0$ touch it at the points $A$ and $B$ . Then $(AB{)}^2$  is equal to:

The coefficient of x⁴ in the expansion of (1+x+x²+x³)⁶ in powers of x, is

Let A=(a,b,c) and B=(1,2,3,4). Then the number of elements in the set C={f: A→B | 2∈f(A) and f is not one-one} is

The locus of a point which divides the line segment joining the point $(0,-1)$ $$ and a point on the parabola, $x^2=4y$ ${}^{}$ , internally in the ratio $1:2$ $$ , is

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is $\frac{1}{4}$ . If the probability that at most two machines will be out of service on the same day is ${\left(\frac{3}{4}\right)}^{3}k$ , then $k$  is equal to:

If x=1 is a critical point of the function f(x)=(3x²+ax-2-a)eˣ, then

Let $A$ $$ and $$ $B$ be two independent events such that $P\left(A\right)=\frac{1}{3}$ $\frac{}{}$ and $P\left(B\right)=\frac{1}{6}$ $\frac{}{}$ . Then, which of the following is TRUE?

If the mean and standard deviation of the data 3,5,7,a,b are 5 and 2 respectively, then a and b are the roots of the equation:

If $\frac{3+\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{n}\theta }{4-\mathrm{i}\mathrm{c}\mathrm{o}\mathrm{s}\theta },\theta \in \left[\mathrm{0,2}\pi \right]$ , is a real number, then an argument of $\mathrm{s}\mathrm{i}\mathrm{n}?\theta +\mathrm{i}\mathrm{c}\mathrm{o}\mathrm{s}?\theta$  is: