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The equation of the plane which contains the lines $L_1:x+y+z-6=0=x-z+6$ and $L_2:\frac{x}{2}=\frac{y}{1}=\frac{z-6}{2}$ is

Arrange the following multiplication statements such that the lowest product at the top.

The product of the first $100$ odd natural numbers is

The eigen values of matrix$A=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$ are

P (a,
b) is the mid-point of a line segment between axes. Show that
equation of the line is

Question 93

Solve the following question:

Using distributive law, find the squares of

a) 101

b) 72

What is the expression for Fourier transform of a periodic signal x(t) with exponential Fourier series coefficient as $C_n$?

The angle of elevation of the top of a vertical tower from a point A, due east of it is ${45}^{\circ }$. The angle of elevation of the top of the same tower from a point B, due south of A is ${30}^{\circ }$. If the distance between A and B is $54\sqrt{2}$ m, then the height of the tower (in metres), is

Write the sets for the following

a. {3}

{6, 11}

If $PSQ$ is the focal chord of the parabola $y^2=8x$ such that $SP=6$ then the lenght of $SQ$ is, where $S$ is the focus of the parabola

Find the multiplicative inverse of the complex number

Let f(x) be a function such that $f\text{'}\left(x\right)={\log }_{1/3}\left({\log }_3\left(\sin x+a\right)\right]$. If f(x) is decreasing for all real values of x, then .

If two sides of a triangle are the roots of $x^2-7x+8=0$ and the angle between these sides is $\frac{\pi }{3},$ then the product of inradius and circumradius of the triangle is

Choose the correct option of general solutions -

$$\begin{array}{cc}TrigonometricEquations& GeneralSolutions\\ 1.si{n}^2\theta =si{n}^{2}x& A.2n\pi \pm \alpha \\ 2.co{s}^2\theta =co{s}^{2}x& B.n\pi +(-1{)}^n\alpha \\ 3.ta{n}^2\theta =ta{n}^{2}x& C.n\pi \pm \alpha \\ & \end{array}$$

The range of $f\left(x\right)=\left[x\right]-x.$ Where $\left[x\right]$ is the greatest integer function.

1. 1

If $sin\alpha ,sin\beta ,cos\alpha$ are in GP, then roots of equation $x^{2}sin\beta +2xcos\beta +sin\beta =0$ are

The length of the latus rectum of the hyperbola $9x^2-16y^2-72x-32y-16=0$ is

The value of ${\int }_0^{si{n}^{2}x}si{n}^{-1}\left(\sqrt{t}\right)dt+{\int }_0^{co{s}^{2}x}co{s}^{-1}\left(\sqrt{t}\right)dt$ is

The value of the integral $\int \frac{x^2+1}{x^2-5x+6}dx$

(where $C$ is integration constant)

Find the maximum value of $|z|$ when $|z-\frac{3}{z}|=2$, $z$ being a complex number.

If $f\left(x\right)=\sin x-ax$ is decreasing $\forall x\in R,$ then

The equation of the image of the circle $x^2+y^2-6x-4y=0$ in the bisector of $2^{\text{nd}}$ and $4^{\text{th}}$ quadrant is

Let $L=\left[\begin{array}{ccc}2& 3& 5\\ 4& 1& 2\\ 1& 2& 1\end{array}\right]=P+Q,$ where $P$ is a symmetric matrix & $Q$ is a skew-symmetric matrix, then $P$ is equal to

Determine order and degree (when defined) of differential equations.
y'+y=$e^x$

1. -0.06

The points
on the curve 9y² = x³, where the
normal to the curve makes equal intercepts with the axes are

(A) (B)

(C) (D)