Class 11th

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?

Let $\alpha$ and $\beta$ be the roots of the equation $x^2-x-1=0$ . If $P_k=(\alpha {)}^k+(\beta {)}^k,k\ge 1$ , then which one of the following statements is not true?

If the sum of the first 20 terms of the series log₇(₁/₂)x + log₇(₁/₃)x + log₇(₁/₄)x + . is 460, then x is equal to: