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If $\overrightarrow{A}$ + $\overrightarrow{B}$ = $\overrightarrow{P}$ and $\overrightarrow{A}$ $\times$ $\overrightarrow{B}$ = $\overrightarrow{Q}$ then

The x-coordinate of the incentre of the triangle that has the coordinates of mid-points of its sides as (0,1), (1, 1) and (1, 0) is

In $SI$ units, the dimensions of $\sqrt{\frac{{ϵ}_0}{{\mu }_0}}$ is

The characteristic of $27.321$ is

The edge of a cube is increasing at the rate of 5cm/sec.How fast is the volume of the cube increasing when the edge is 12cm long

If f(x) = ax + b and g(x) = cx + d, then f[g(x)] – g[f(x)] is equivalent to

Statements: V $ W, W T, T # H
Conclusions:

a) V © T

b) H % W

The value of ‘$c$’ such that the line joining $(0,3),(5,–2)$ is a tangent to $y=\frac{c}{x+1}$ is

${lim}_{x\to a}\frac{logx-loga}{x-a}$

Write the value of ${lim}_{x\to \pi }\frac{sinx}{x-\pi }$

$\underset{x\to 0}{lim}\frac{(1+x{)}^{\frac{1}{3}}-(1-x{)}^{\frac{1}{3}}}{x}=$

By using properties of definite integrals, evaluate the integrals
${\int }_0^{\frac{\pi }{2}}(2logsinx-logsin2x)dx.$

Find $(x+1{)}^6+(x-1{)}^6$. Hence, or otherwise evaluate $(\sqrt{2}+1{)}^6+(\sqrt{2}-1{)}^6$.

If a, b and c are real numbers and $\Delta =\left|\begin{array}{ccc}b+c& c+a& a+b\\ c+a& a+b& b+c\\ a+b& b+c& c+a\end{array}\right|=0$, Show that either a+b+c=0 or a=b=c.

A furniture shop has six identical steel cabinets of brand A and four identical steel cabinets of brand B. Three customers buy one cabinet each. Then the probability that two or more cabinets of brand A have been sold

Tangents are drawn to the circle $x^2+y^2=50$ from a point $P$ lying on the $x-$axis. These tangents meet the $y-$axis at points $P_1$ and $P_2$. Possible coordinates of $P$ so that area of $△P{P}_1{P}_2$ is minimum, are

If $p$ be the perpendicular distance of a focal chord $PQ$ of length $l$ from the vertex $A$ of the parabola $y^2=4ax$, then $l$ varies inversely as

The value of x for which $si{n}^{-1}\left\{sin\left(\frac{2x^2+4}{1+x^2}\right)\right\}<\pi -3$ is

If m be the slope of a tangent to the curve $e^{2y}=1+4x^2$, then

If $|z-i|=1$ and arg $\left(z\right)=\theta$ where $\theta \in (0,\frac{\pi }{2})$, then
$cot\theta -\frac{2}{z}$

Let f(x) be a function defined on [0, 1] such that $f\left(x\right)=\{\begin{array}{ccc}x,& ifxϵQ& \\ 1-x,& ifx\text{/}ϵQ& \end{array}$
Then, for all $xϵ[0,1],f\left(f\right(x\left)\right)=$

The cosine of the angle between the tangents from the origin to the circle $x^2+y^2-14x+2y+25$ = 0 is

Find the eccentricity, coordinates of foci, length of the latus-rectum of the following ellipse:
(i)$4x^2+9y^2=1$
(ii)$5x^2+4y^2=1$
(iii)$4x^2+3y^2=1$
(iv)$25x^2+16y^2=1600$
(v)$9x^2+25y^2=225$

For the parabola $y^2+6y-2x+5=0$ (i) The vertex is $(-2,-3)$ (ii) The directrix is $y+3=0$ which of the following is correct?

The direction angles of the line $x=4z+3,y=2-3z$ are $\alpha ,\beta$ and $\gamma$, then $\cos \alpha +\cos \beta +\cos \gamma =$____

The $3^{rd}$ and $6^{th}$ term of a G.P. is 12 and 96 respectively. If the sum of all terms is 1533, find the number of terms in the G.P.

Let the line
$\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}$
lies in the plane $x+3y-\alpha z+\beta =0.$ Then $(\alpha ,\beta )$ equals

Two parabola $y^2=4a(x-{\lambda }_1),$ and $x^2=4a(y-{\lambda }_2)$ always touch each other, where ${\lambda }_1$ and ${\lambda }_2$ being variable parameters. Then their points of contact lie on a

Question 3(c)

See the figure and find the ratio of:

The number of circles to all the figures inside the rectangle.

Though this is a non academic question I just wanted to ask whether u provide extra questions to solve after I have done solving the ones in the byjus app.

A discrete random variable X has the probability distribution as given below

$\begin{array}{ccccc}X& 0.5& 1& 1.5& 2\\ P\left(X\right)& k& k^2& 2k^2& k\end{array}$

(i) Find the value of k.

(ii) Determine the mean of the distribution.

For the given differential equation find the general solution.

$\frac{dy}{dx}+3y=e^{-2x}$

Compute the indicated products.
$\left(i\right)\left[\begin{array}{cc}a& b\\ -b& a\end{array}\right]\left[\begin{array}{cc}a& -b\\ b& a\end{array}\right]$

$\left(ii\right)\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]\left[234\right]$

$\left(iii\right)\left[\begin{array}{cc}1& -2\\ 2& 3\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\end{array}\right]$

$\left(iv\right)\left[\begin{array}{ccc}2& 3& 4\\ 3& 4& 5\\ 4& 5& 6\end{array}\right]\left[\begin{array}{ccc}1& -3& 5\\ 0& 2& 4\\ 3& 0& 5\end{array}\right]$

$\left(v\right)\left[\begin{array}{cc}2& 1\\ 3& 2\\ -1& 1\end{array}\right]\left[\begin{array}{ccc}1& 0& 1\\ -1& 2& 1\end{array}\right]$

$\left(vi\right)\left[\begin{array}{ccc}3& -1& 3\\ -1& 0& 2\end{array}\right]\left[\begin{array}{cc}2& -3\\ 1& 0\\ 3& 1\end{array}\right]$

Find $\frac{dy}{dx}$, if x and y are connected parametrically by the equations given in questions without eliminating the parameter.

$x=\frac{si{n}^{3}t}{\sqrt{cost2t}},y=\frac{co{s}^{3}t}{\sqrt{cos2t}}$

The angle between any two diagonals of a cube is:

A bag contains 3 white, 3 black and 2 red balls. One by one, three balls are drawn without replacing them. Then the probability that the third ball is red , is given by

If sin$\theta$ and cos$\theta$ are the roots of the equation $a{x}^2-bx+c=0$, then a, b and c satisfy the relation

The solution of the differential equation $\text{log}\left(\frac{dy}{dx}\right)=4x-2y-2$, y = 1 when x = 1 is:

Area of parallelogram formed by lines y=mx,y=mx+1,y=nx,y=nx+1 (in form of m and n)?

The general solution of the equation ${\sin }^2\theta ={\sin }^2\alpha$ is/are

In $R^3$, Let $L$ be a straight line passing through the origin. Suppose that all the points on $L$ are at a constant distance from the two planes $P_1:x+2y-z+1=0$ and $P_2:2x-y+z-1=0.$ Let $M$ be the locus of the feet of the perpendiculars drawn from the points on $L$ on the plane $P_1.$ Which of the following points lie(s) on $M?$