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Is the study from byjus tablet also need coaching classes in physics?

A variable plane which remains at a constant distance p from the origin cuts the coordinate axes in A, B, C. The locus of the centroid of the tetrahedron OABC is $y^2{z}^2+z^2{x}^2+x^2{y}^2=k{x}^2{y}^2{z}^2$, where k is equal to

Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6 Find
P (neither A nor B)

The value of the expression $1(2-\omega )(2-{\omega }^2)+2(3-\omega )(3-{\omega }^2)+\cdots \cdots +(n-1)(n-\omega )(n-{\omega }^2)$ is where $\omega$ is an imaginary cube root of unity is

Find the equation of the ellipse for which $e=\frac{4}{5}$ and whose vertices are $(0,\pm 10).$

If $\frac{dy}{dx}=e^{-2y}$ and y=0 when x=5, then find the value of x when y=3.

If x and y are the sides of two squares such that $y=x-x^2$, then find the rate of change of the area of second square with respect to the area of first square.

If $z_1,z_2,\cdots z_n$ lie on the circle $|z|=2$ then the value of $|z_1+z_2+\cdots +z_n|-4|\frac{1}{z_1}+\frac{1}{z_2}+\cdots +\frac{1}{z_n}|=$

Let $A$ be a $3\times 3$ matrix such that $P=\left[\begin{array}{ccc}1& \alpha & 3\\ 1& 3& 3\\ 2& 4& 4\end{array}\right],$ $P=adj\left(A\right)$ and $|A|=4,$ then the value of $\alpha$ is

Let $U=\{1,2,3,4,5,6,7,8,9,10\}$. If $A=\{1,2,5\},B=\{6,7\}$, then $A\cap B^{\prime }$ is

Find the equation of the line in vector and in Cartesian form that passes through the point with position vector $2\hat{i}-\hat{j}+4\hat{k}$ and is in the direction $\hat{i}+2\hat{j}-\hat{k}$.

If A is an idempotent matrix and A + B =I, then which of the following is true?

If (x - 5) is a factor of the cubic equation $x^3-18x-35=0$ . Find the quotient.

If $2x-y+1=0$ is a tangent to the hyperbola$\frac{x^2}{a^2}-\frac{y^2}{16}=1$, then which of the following CANNOT be sides of a right triangle?

If $\underset{0}{\overset{\pi /4}{\int }}(\sqrt{\tan x}+\sqrt{\cot x})dx$ than value of $I$ is

The range of parameter ${}^{\prime }{a}^{\prime }$ for which a unique circle will pass through the points of intersection of the rectangular hyperbola $x^2-y^2=a^2$ and the parabola $y=2x^2$, is

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$, and $\overrightarrow{d},$ are the unit vectors such that $(\overrightarrow{a}\times \overrightarrow{b}).(\overrightarrow{c}\times \overrightarrow{d})=1$ and $\overrightarrow{a}.\overrightarrow{c}=\frac{1}{2},$ then

The value of $\frac{1}{2}{}^n{C}_1.{}^{n-1}{C}_1+\frac{2}{3}{}^n{C}_2+\frac{3}{4}{}^n{C}_c.{}^{n-1}{C}_3+\dots \dots$ is

Two numbers are selected randomly from the set S = {1, 2, 3, 4, 5, 6} one by one without replacement. The probability that minimum of the two numbers is less than 4 is

The equation of the parabola with its vertex at the origin, axis on the y-axis and passing through the point (6, -3) is

The value of
$\frac{{}^n{C}_0}{2}-\frac{{}^n{C}_1}{6}+\frac{{}^n{C}_2}{12}-\frac{{}^n{C}_3}{20}+\cdots +(-1{)}^n\frac{{}^n{C}_n}{n^2+3n+2}$ is

Show that the point (3, -5) lies between the parallel lines $2x+3y-7=0$ and $2x+3y+12=0$ and find the equation of lines through (3, -5) cutting the above lines at an angle of ${45}^{\circ }$.

Prove that : tan2A = (sec2A+1)(sec²A-1)^1/2

$\text{A solution of the equation}co{s}^2\theta +sin\theta +1=0,liesintheinterval$

$Ina\Delta ABC,\text{prove that}si{n}^{3}Acos(B-C)+si{n}^{3}Bcos(C-A)+si{n}^{3}Ccos(A-B)=3sinAsinBsinC$

A point on the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ at a distance equal to the mean of the lengths of the semi major axis and semi minor axis from the centre is

The value of ${\sin }^{-1}\left(\frac{2\sqrt{2}}{3}\right)+{\sin }^{-1}\left(\frac{1}{3}\right)$ is equal to

A pair of tangents are drawn from the origin to the circle $x^2+y^2+20(x+y)+20=0$. The equation of the pair of tangents is

Find the equation of the straight line passing through the point of intersection of $2x+y-1=0$ and $x+3y-2=0$ and making with the coordinate axes a triangle of area $\frac{3}{8}$ sq. units.

Integrate the following functions w.r.t. x.

$\int \frac{e^{5logx}-e^{4logx}}{e^{3logx}-e^{2logx}}dx.$

Integrate the following functions.
$\int \sqrt{sin2x}cos2xdx.$

NSE Indices
$\begin{array}{cccc}\text{Index}& \text{Current}& \text{Previous}& \text{\% Change}\\ \text{S \& P CNX Nifty}& 3641.1& 3770.55& -3.43\%\\ \text{CNX Nifty Junior}& 6458.55& 6634.85& -2.66\%\\ \text{CNX IT}& 5100.5& 5314.05& -4.02\%\\ \text{Bank Nifty}& 5039.05& 5251.55& -4.05\%\\ \text{CNX 100}& 3519.35& 3640.35& -3.32\%\end{array}$

World Markets
$\begin{array}{cccc}\text{Index}& \text{Current}& \text{Previous}& \text{\% Change}\\ \text{NYSE Cornposite}& 8926.88& 9120.93& -2.13\%\\ \text{NASDAQ Composite}& 2350.57& 2402.29& -2.15\%\\ \text{DOW Jones IA}& 12076& 12318.6& -1.97\%\\ \text{S \& P 500}& 1377.95& 1406.6& -2.04\%\\ \text{Nikkei 225}& 16676.9& 17178.8& -2.92\%\end{array}$

The above figures are taken from the website of National Stock Exchange of India. They illustrate the movement of NSE stock indices as well as world stock indices on the date indicated.

What factors affect the movement of stock indices? Elaborate on the nature of these factors.

A plane which bisects the angle between the two given planes $2x–y+2z–4=0$ and $x+2y+2z–2=0,$ passes through the point :

If $\frac{T_2}{T_3}$ in the expansion of $(a+b{)}^n$ and $\frac{T_3}{T_4}$ in the expansion of $(a+b{)}^{n+3}$ are equal, then n=

If $\frac{\pi }{2}<\theta <\pi$, then write the value of $\sqrt{\frac{1-cos2\theta }{1+cos2\theta }}$

${lim}_{x\to 0}\frac{8^x-4^x-2^x+1}{x^2}$

Let $ABCD$ be a square and $E$ be a point outside $ABCD$ such that $E,A,C$ are collinear in that order. Suppose $EB=ED=\sqrt{130}$ and the areas of triangle $EAB$ and square $ABCD$ are equal. Then the area of square $ABCD$ is

The equation of the common tangent to $x^2=6y$ and $2x^2-4y^2=9$ can be

In the Argand plane, the vector z=4-3i is turned in the clockwise sense through ${180}^o$ and stretched three times. The complex number represented by the new vector is

If $A=\{2,3,4,8,10\},$ $B=\{3,4,5,10,12\},$ $C=\{4,5,6,12,14\},$ then $(A\cup B)\cap (A\cup C)$ is

If the sums of $n$ terms of two arithmetic progressions are in the ratio $2n+5:3n+4$, then write the ratio of their $m^{th}$ terms.

A plane $\pi$ contains the line $L_1:\frac{y}{b}+\frac{z}{c}=1,x=0$ and is parallel to the line $L_2:\frac{x}{a}-\frac{z}{c}=1,y=0,$ then