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If $y=e^{-x}\cos 2x$ then which of the following differential equations is satisfied?

The feasible solution for a LPP is shown in following figure. Let Z=3x-4y be the objective funciton. Minimum of Z occurs at

(a)(0,0)
(b)(0,8)
(c)(5,0)
(d)(4,10)

If $A^{-1}=\left[\begin{array}{ccc}3& -1& 1\\ -15& 6& -5\\ 5& -2& 2\end{array}\right]$ and $B=\left[\begin{array}{ccc}1& 2& -2\\ -1& 3& 0\\ 0& -2& 1\end{array}\right]$, find $(AB{)}^{-1}$.

In the following question, there is a blank in each sentence. Four alternatives are suggested for each blank. Choose the correct one.
Rahul has spent ………... money he had.

Sketch the graph of y = |x + 3| and evaluate ${\int }_{-6}^0|x+3|dx$

Find the probability distribution of the number of successes in two tosses of a die, where a succeess is defined as

six appears on the die.

Let f,g and h be functions from R to R. Show that (f+g)oh =foh+goh

Using elementary transformations, find the inverse of the followng matrix.

$\left[\begin{array}{cc}3& -1\\ -4& 2\end{array}\right]$

The circle circumscribing the triangle formed by three tangents to a parabola passes through _____

Let $z=\left(\frac{\cos \theta +i\sin \theta }{\cos \theta -i\sin \theta }\right),\frac{\pi }{4}<\theta <\frac{\pi }{2},$ then $\arg \left(z\right)$ will be

Prove that

sin⁶x .- tan⁶ x - 3 sec²x •

tan²x = 1

Find sum and order of the differential equation (d^2y/dx^2)^3/2=x

A student multiplied a number by 4/5 instead of 5/4.What is the percentage error in the calculation?

A vector A is along the positive x axis .If B is another vector such that A×B is zero ,then B could be : a) 4j . b)-4j c) -( i+ j) d)(i+ k)

A line L is perpendicular to the line 5x-y=1 and the area of the triangle formed by the line L and coordinate axes is 5. The equation of the line L is

The equation of the circle passing through the point (–2, 4) and through the points of intersection of the circle $x^2+y^2-2x-6y+6=0$ and the line 3x + 2y - 5 = 0, is

If alpha and beta are the zeroes of the polynomial f(x)=Kx²+4x+4 such that alpha square + beta square is 24.Find the value of K.

If $|z_1+z_2{|}^2$ = $|z_1-z_2{|}^2$ where $z_1$ and $z_2$ are non-zero complex numbers, then :

The value of $2^{\frac{1}{4}}\cdot 4^{\frac{1}{8}}\cdot 8^{\frac{1}{16}}\cdot {16}^{\frac{1}{32}}\dots \dots$ is

If A = {2, 4, 6, 8} and U = {1, 2, 3, 4, 5, 6, 7, 8, 9,}, then A'=

The area bounded by $xy=1,x=1,x=e$ and $x$ axis is

How is 'over' written in a code language?

I. 'Over and again' is written as 'ka ja ha' in that code language.

II. 'Came and go' is written as 'ja pa na' in that code language

If $f\left(x\right)=\{\begin{array}{cc}x& \text{if}x\text{is rational}\\ 1-x& \text{if}x\text{is irrational}\end{array}$, then the number of points for $xϵR$ where $f\left(f\right(x\left)\right)$ is/are discontinuous

If A, B, C are angles of a triangles, then cos A + cos B + cos C is equal to

Triangle is formed by the coordinates (0, 0), (0, 21) and (21, 0). Find the number of integral coordinates strictly inside triangle (integral coordinates has both x and y):

The value of the determinant $\left|\begin{array}{ccc}1& 1& 1\\ {}^n{C}_{n-1}& {}^{n+1}{C}_n& {}^{n+2}{C}_1\\ {}^n{C}_{n-2}& {}^{n+1}{C}_{n-1}& {}^{n+2}{C}_2\end{array}\right|$

If the point $P(\alpha ,-\alpha )$ lies inside the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1,$ then

A line with direction cosines proportional to 2,1, 2 meets each of the lines and . The co-ordinates of each of the points of intersection are given by
[AIEEE 2004]

All the values of $m$ for which both the roots of $x^2-2mx+m^2-1=0$ are greater than $-2$ but less than $4$, lies in the interval

Let a, b, c be such that (b+c) ≠0. If

Then, the value of 'n' is

The line joining the origin to the points of intersection of the curves
$a{x}^2+2hxy+b{y}^2+2gx=0$ and $a^{{}^{\prime }}{x}^2+2h^{{}^{\prime }}xy+b^{{}^{\prime }}{y}^2+2g^{{}^{\prime }}x=0$
will be mutually perpendicular, if

Let n(U) = 700, n(A) = 200, n(B) = 300 and n(A ∩ B) = 100,

Then n$(A^c\cap B^c)$ =

If the letters of the word Krisna are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word Krisna is

Suppose the tube in the previous problem is kept vertical with B upward. Water enters through B at the rate of 1 $c{m}^3{s}^{-1}$. Repeat parts (a), (b) and (c). Note that the speed decreases as the water falls down.

If ABC is an acute-angled triangle with circumcenter O and Orthocenter H. If AO = AH, then angle A = .

Let $I={\int }_1^3\sqrt{3+x^3}dx$, then the value of I lies in the interval

The tangents PA and PB are drawn from any point P of the circle $x^2+y^2=2a^2$ to the circle $x^2+y^2=a^2.$ The chord of contact AB on extending meets again the first circle at the point A’ and B’. The locus of point of intersection of tangents at A’ and B’ may be given as

Given 3 points given by position vectors $\overline{a}=\hat{i}+\hat{j},\overline{b}=\hat{j}+\hat{k},\overline{c}=-\hat{i}-\hat{j}-\hat{k}$. Find the plane passing through these 3 points.