Class 11th

The ${}_{}^{}$ $\mathrm{s}\mathrm{u}\mathrm{m}?{\sum }_{\mathrm{k}=1}^{20}?(1+2+3+\dots .\mathrm{k})$ is(Series)

The least positive value of ' $$ $a$ ' for which the equation, $2x^2+(a-10)x+\frac{33}{2}=2a$ ${}^{}\frac{}{}$ has real root is

(Quadratic Equations)

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:

If $a,b$ $$ and $c$ $$ are the greatest values of ${}^{}{}_{}{}^{}{}_{}$ ${}^{19}{\mathrm{C}}_{\mathrm{p}},{}^{20}{\mathrm{C}}_{\mathrm{q}}$ and ${}^{21}{\mathrm{C}}_{\mathrm{r}}$ ${}^{}{}_{}$ respectively, then:

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