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A plane passes through (2,3, -1) and is perpendicular to the line having direction ratios 3, -4, 7 The perpendicular distance from the origin to this plane is

Solution of the differential equation $2ysinx\frac{dy}{dx}=2sinxcosx-y^{2}cosxsatisfyingy\left(\pi /2\right)=1$ is given by

If both the roots of $a{x}^2+bx+c=0$ are real, positive and distinct, then

(where $\Delta =b^2-4ax$)

If $p{x}^2$ + qx + r = 0 has no real roots and p, q, r are real such that p + r > 0 then

If $x=t+1$ and $y=t^3+3t,$ then $\frac{d^{2}y}{d{x}^2}$ is equal to

If the area of triangle is 6 square units and vertices of triangle are (0, k), (0, 6) and (2, 0), then the value of k is:

1. 256

For $b>a>1,$ the area enclosed by the curve $y=\ln x,y-$axis and the straight lines $y=\ln a$ and $y=\ln b$ is

The set of real values of $x$, for which $h\left(x\right)=1+2x^2+4x^4+6x^6+\cdots +100x^{100}$ is concave downward is

The p^th,
q^th and r^th terms of an A.P. are
a, b, c respectively. Show that

Find which of the following algebraic expression is a polynomial.



(i) $3x^2-5x$

(ii) $x+\frac{1}{x}$

(iii) $\sqrt{y}-8$

The number of values of 'a' for which the equation $(x-1{)}^2=|x-a|$ has exactly three solutions is

If A
is square matrix such that
then
is equal to

A. A B. I
− A C. I D. 3A

Prove the following by using the principle of mathematical induction for all n ∈ N: (2n +7) < (n + 3)²

Can a intergal questions have many correct answers? Because for some questions I get 2 answer if I use substitution method and decomposition method

Please help me in solving the questions given below

If (sin inverse x)^2 +(sin inverse y)^2+(sin inverse z)^2=3(pie)^2/4,find the value of x^2+y^2+z^2

Please solve it step wise wise with clear explanation

Let $x=my+c$ is normal to $x^2=4y$. If $k^2+mk+m=0$ is satisfies by only one real value of $k$, then value(s) of $c$ is/are

ABCD is a parallelogram. If coordinates of A, B, C are (2,3), (1,4) and (0, -2). Coordinates of D =

The equation of the curve passing through $(\frac{{\pi }^2}{4},1),$ which has a solution of the equation as $y^{2}cos\sqrt{x}dx-2\sqrt{x}{e}^{\frac{1}{y}}dy=0$

A diet is to contain atleast 80 units of vitamin A and 100 units of minerals. Two foods $F_{1}and{F}_2$ are available. Food $F_1$ costs Rs. 4 per unit and food $F_2$ costs Rs. 6 per unit. One units of food $F_1$ contains at 3 units of vitamin A and 4 units of minerals. One unit of food $F_2$ contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.

If $\left[\begin{array}{cc}\alpha & 2\\ 2& \alpha \end{array}\right]$ and $|A^3|=27$, then $\alpha$....

Find
n, if the
ratio of the fifth term from the beginning to the fifth term from the
end in the expansion of

The graph of the curve $y=\frac{(x^2+1)}{(x^2-1)}$ is:

Equation of plane which is parallel to XY-plane is

If $y^x-x^y=1,$ then the value of $\frac{dy}{dx}$ at $x=1$ is

$f\left(x\right)=\frac{a{x}^2+b}{x^2+1},{lim}_{x\to 0}f\left(x\right)=1and{lim}_{x\to \infty }f\left(x\right)=1,thenprovethatf(-2)=f\left(2\right)=1.$

The eccentricity of the ellipse represented by the equation $25x^2+16y^2-150x-175=0$ is

The difference of the radii of the two circles with centre (4, 3) and touching the circle $x^2+y^2=1$, is

Let $X\left(j\omega \right)$ denotes the Fourier transform of the signal x(t) depicted in figure below :





then ${\int }_{-\infty }^{\infty }|X\left(j\omega \right){|}^{2}d\omega$ is