Class 11th

The coefficient of $x^7$ in the expression $(1+x{)}^{10}+x(1+x{)}^9+x^2(1-x{)}^8+\dots \dots +x^{10}$ is:

In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by $p$ $$ and then reduced by $$ $q$ , where $p=0$ $$ and $q\ne 0$ $$ . If the new mean and new s.d. become half of their original values, then $q$ $$ 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

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:

If the line y=mx+c is a common tangent to the hyperbola x²/100 - y²/64 = 1 and the circle x²+y²=36, then which one of the following is true?