Class 11th

$X_P\left(t\right)=\alpha t+\beta t^2$

$V_P\left(t\right)=\alpha +2\beta t$ - (i)

$X_Q\left(t\right)=ft-t^2$

$V_Q\left(t\right)=f-2t$  - (ii)

(i) = (ii)

$\alpha +2\beta t=f-2t\Rightarrow t\left(2\beta +2\right)=f-\alpha$

$t=\frac{f-\alpha }{2\left(\beta +1\right)}$

$X_P\left(t\right)=\alpha t+\beta t^2$

$V_P\left(t\right)=\alpha +2\beta t$ - (i)

$X_Q\left(t\right)=ft-t^2$

$V_Q\left(t\right)=f-2t$ - (ii)

(i) = (ii)

$\alpha +2\beta t=f-2t\Rightarrow t\left(2\beta +2\right)=f-\alpha$

$t=\frac{f-\alpha }{2\left(\beta +1\right)}$

  $\frac{2}{-4}=\frac{-1}{2}$

y – 4 = 2 (x – 3)

y = 2x – 2

x² + (2x – 2)² = 25

  $5x^2-8x-21=0$

$z\left(\frac{-7}{5},\frac{-24}{5}\right)$              

x = 2t $A\left(2t,\frac{t^2}{3}\right)$ $\frac{{}^{}}{}$

$\frac{{}^{}}{}$ $y=\frac{t^2}{3}$  S (0, 3)

${\frac{}{}}^{}$  $3y={\left(\frac{x}{2}\right)}^2$ $B\left(0,\lambda \right)$ $$

$3k=\frac{t^2}{3}+3+\lambda =\frac{2t^2}{3}+3-\frac{12t^2}{9-t^2}$

$\underset{t\to 1}{lim}3k=\frac{2}{3}+3-\frac{12}{8}=3-\frac{5}{6}=\frac{13}{6}$

Assertion -> Not correct

But Reason R -> correct

[8]-Annulene

It is non-planar structure, it exists like tub shape.

 It is non-planar structure due steric hinderance 1 and 6

(A) and (C) are staggered conformation. In (A) dihedral angle is 60° and in (C) dihedral angle is 180°.

Dihedral angle is angle between two specified groups.

In (C) it has maximum angle.

O^-2 & Mg⁺² are isoelectronic with Al⁺³

First angle, 1 = $R=\frac{u^{2}sin2?}{g}$ $\frac{{}^{}}{}$

Another angle (2 = 90 - ) for which range will be

Same as that of 1 =

$R^1=\frac{u^{2}sin2\left(90??\right)}{g}=\frac{u^2}{g}sin2?=R$

at ${?}_1=?,\text{?}\text{?}\text{?}\text{?}\text{?}{h}_1=\frac{u^{2}si{n}^2?}{2g}$ ${}_{}{}_{}\frac{{}^{}{}^{}}{}$

$\&\text{?}\text{?}\text{?}{?}_2=90??,h_2=\frac{u^{2}si{n}^2{?}_2}{2g}=\frac{u^{2}co{s}^2?}{2g}$

$?h_1{h}_2=\frac{1}{4^2}{\left[\frac{u^{2}sin2?}{g}\right]}^2$

$h_1{h}_2=\frac{1}{4^2}{R}^2$

$R=4\sqrt[]{h_1{h}_2}$

So, Both statement is true & Reason is correct explanation for statement 1.

$\frac{\Delta z}{z}=\frac{2\Delta A}{A}+\frac{3\Delta B}{B}+\frac{4\Delta C}{C}$