Ncert Solutions Maths class 11th

An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that the most three of them are red is(Combinations)

Let the normal at a point $P$ $$ on the curve ${}^{}{}^{}$ $y^2-3x^2+y+10=0$ intersect the $$ $y-axis$ at $\left(0,\frac{3}{2}\right)$ $\left(\frac{}{}\right)$ . If $m$ $$ is the slope of the tangent at $P$ $$ to the curve, then $$ $\left|m\right|$ is equal to(2D)

Let the line $y=mx$ $$ and the ellipse $2x^2+y^2=1$ ${}^{}{}^{}$ intersect at a point $$ $P$ in the first quadrant. If the normal to this ellipse at $P$ $$ meets the co - ordinate axes at $\left(\frac{}{\text{exception 25:}}\right)$ $\left(-\frac{1}{3\sqrt[]{2}},0\right)$ and $$ $(0,\beta )$ then $\beta$ $$ is equal to:

Let $f:R\to R$ $$ be such that for all $x\in R\left(2^{1+x}+2^{1-x}\right),f\left(x\right)$ $\left({}^{}{}^{}\right)$ and $\left(3^x+3^{-x}\right)$ $\left({}^{}{}^{}\right)$ are in A.P., then the minimum value of $f\left(x\right)$ $$ is:

Let $A,B,C$ and $D$ be four non - empty sets. The contrapositive statement of "If $A\subseteq B$ and $B\subseteq D$ , then $A\subseteq C$  " is:

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 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 $\frac{3+\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{n}\theta }{4-\mathrm{i}\mathrm{c}\mathrm{o}\mathrm{s}\theta },\theta \in \left[\mathrm{0,2}\pi \right]$ , 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?