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A $4\times 1$ MUX is used to implement a 3-input Boolean function as show in figure. The Boolean function P( A, B, C) implemented is

Equation of a plane at a distance $\sqrt{\frac{2}{21}}$ from the origin, which contains the line of intersection of the planes $x-y-z-1=0$ and $2x+y-3z+4=0$, is :

Equation of the common tangent to the parabola $y^2=24x$ and the circle $x^2+y^2=18$ is

The value of ${\sin }^{2}A+{\sin }^2(A+B)-2\sin A\cos B\sin (A+B)$ when $B={45}^{\circ }$ is

Which of the following can definitely be said about the elephant-keeper?

(A) He was greedy.

(B) He was insensitive.

(C) He was brave.

Find square root using long division of 1604

If ${}^{15}{C}_{3r}$ = ${}^{15}{C}_{r+3}$, then the value of r is

For $x\in R-\{0,1\},$ let $f_1\left(x\right)=\frac{1}{x}$, $f_2\left(x\right)=1-x$ and $f_3\left(x\right)=\frac{1}{1-x}$ be three given functions. If a function, $J\left(x\right)$ satisfies $\left(f_{2}oJo{f}_1\right)\left(x\right)=f_3\left(x\right)$, then $J\left(x\right)$ is equal to :

Find the
mean deviation about the median for the data

36, 72,
46, 42, 60, 45, 53, 46, 51, 49

1. 1

Out of 10 white, 9 black and 7 red balls, the number of ways in which selection of one or more balls can be made, is_______.

${\left(ta{n}^{-1}x\right)}^2+{\left(co{t}^{-1}x\right)}^2=\frac{5{\pi }^2}{8}\Rightarrow x=$

Let $z_1$ and $z_2$ be two complex numbers such that $|z_1|=|z_2|=1.$ If $C={\left[\begin{array}{cc}{\overline{z}}_1& -z_2\\ {\overline{z}}_2& z_1\end{array}\right]}^{-1}{\left[\begin{array}{cc}{z}_1& z_2\\ -{\overline{z}}_2& {\overline{z}}_1\end{array}\right]}^{-1},$ then the sum of principal diagonal entries of $C$ is

The eccentric angle of point of intersection of the ellipse $x^2+4y^2=4$ and the parabola $x^2+1=y$ is

The equation of a line inclined at an angle $\frac{\pi }{4}$ to the $x-$axis, such that the two circles $x^2+y^2=4,$ $x^2+y^2-10x-14y+65=0$ intercept equal lengths on it, is

If the system of linear equations $\left(\cos \theta \right)x+\left(\sin \theta \right)y+\cos \theta =0,$ $\left(\sin \theta \right)x+\left(\cos \theta \right)y+\sin \theta =0$ and $\left(\cos \theta \right)x+\left(\sin \theta \right)y-\cos \theta =0$ is consistent, then the possible value(s) of $\theta \in [0,2\pi ]$ is/are

Find the area under the
given curves and given lines:

(i) y =
x², x = 1, x = 2 and x-axis

(ii) y =
x⁴, x = 1, x = 5 and x –axis

If the values of $\lambda$ for which $\hat{i}+2\lambda \hat{j}-3\hat{k},2\hat{i}-2\lambda \hat{j}+\hat{k}$ and $-2\hat{i}-\hat{j}+2\lambda \hat{k}$ are linearly dependent are $\alpha$ and $\beta ,$ then which of the following is/are true

A unit vector perpendicular to the plane determined by the points P(1,-1,2), Q(2,0,-1) and R(0,2,1) is

The probability that a two digit number selected at random will be a multiple of ${}^{\prime }{3}^{\prime }$ but not a multiple of ${}^{\prime }{5}^{\prime }$ is

Determine $P\left(\frac{E}{F}\right)$
A coin is tossed three times
E: Atmost two tails F : atleast one tail

What is the minimum value of $p$ and $q$ in the equation $x^3-p{x}^2+qx-8=0$ where $p$ and $q$ are positive real numbers and roots of the equation are real?

e^x^2 and e^x^3 are odd or even or neither odd nor even

Maths byjus worksheet 11 and 12 JEE

Chapter relation and function 1

Sub topic Algebra of real function , equal or identical function , odd and even function

Q-5 d) and e)

A rectangle ABCD of dimensions r and 2r is folded along diagonal BD such that planes ABD and CBD are perpendicular to each other. Let the position of the vertex A remains unchanged and $C_1$ is the new position of C.
The distance of $C_1$ from A is equal to