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The area under the curve $y=x^2–3x+2$ with boundaries as x-axis and the ordinates x = 0, x = 3 is

If ${\sin }^{2}mx+{\cos }^{2}ny=a^2$ where $m,n(\ne 0),a$ are constants, then $\frac{dy}{dx}=$

Find the equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y - 4x + 3 = 0.

The value of determinant $△=\left|\begin{array}{ccc}-2& 3& 10\\ 3& -4& -1\\ 8& -12& -40\end{array}\right|$ is equal to

The diagram shows three circles externally tangent to each other and to a semicircle.The shaded area is 120 sq.units. The area of the unshaded parts of the semi circle in square units is

The period of the function $f\left(x\right)=3\sin 2\sqrt{3}x+2\cos 5\sqrt{3}x$ is

Consider a parabola $y^2=4x$, Let $A$ be the vertex of parabola, $P$ be any point on the parabola and $B$ is a point on the axis of parabola, if $PA\perp PB$, then the locus of centroid of $△PAB$ is

An equation of a tangent drawn to the curve $y=x^2-3x+2$ from the point $(1,-1)$ is

Which of the following can be the parametric equation of $x^2=4ay$

The locus of the point which divides the double ordinate of the parabola $y^2=6ax$ in the ratio $5:6,$ is

The fraction exceeding its pth power by the greatest number possible, where p $\ge$ 2, is

The solution set of the equation $x^{lo{g}_x(1-x{)}^2}=9$ is

The equation of the plane which contains the line of intersection of planes $x+2y+3z-4=0$ and $2x+y-z+5=0$ which is perpandicular to the plane $5x+3y-6z+8=0$

Solve the following systems of inequalities graphically:

2x-y > 1, x -2y < -1

The $2^n$ vertices of graph G correspond to all subsets a set of size n, for $n\ge 6.$ Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements.



The maximum degree of a vertex in G is

What is integral and differential calculus?

How it can be used in numericals?

Please explain with an example each.

Is it very necessary to learn more detailed about them keeping in mind the AIIMS UG examination?

In a town, 25% of the persons earned more than Rs 45,000 whereas 75% earned more than 18,000. Calculate the absolute and relative values of dispersion.

The slope
of the tangent to the curveat
the point (2, −1) is

(A) (B) (C) (D)

The range of $f\left(x\right)=|x|+5$ is

Let the algebric sum of the perpendicular distances from the points (2, 0), (0, 2), (1, 1) to a variable straight line be zero, then the line passes through a fixed point whose co-ordinates are

(I.I.T 1991)

The volume of tetrahedron whose vertices are

A = (3, 2, 1) ,~B = (1, 2, 4),~ C = (4, 0, 3),~ D = (1, 1, 7)~will be $\underset{–}{}$cubic units

If $a,b,c$ are in geometric progression with common ratio $r(r>1)$ such that $abc=216$ and $ab+bc+ca=156,$ then

If $\alpha ,\beta ,\gamma$ are the roots of $x^3+lx+m=0$, then the value of ${\alpha }^3+{\beta }^3+{\gamma }^3$ is

If the value of determinant $\left|\begin{array}{ccc}1& sin(x+\alpha )& cos(x+\alpha )\\ 1& sin(x+\beta )& cos(x+\beta )\\ 1& sin(x+\gamma )& cos(x+\gamma )\end{array}\right|$ is

If $\tan A=\text{cosec}{5}^{\circ }-\cot 5^{\circ }$, where $A$ is an acute angle, then the value of $\tan 24A+\tan 12A+\tan 6A$ is

Differentiate between budget and procedure.

If two ordered pairs are related as
$(\frac{a}{4},a-2b)=(0,6+b)$, then $a+b$ is

If ${\log }_3(3x-8)=2-x,$ then the value of $x$ is

The distance between the orthocentre and circumcentre of the triangle with vertices $(1,2)(2,1)$ and $(\frac{3+\sqrt{3}}{2},\frac{3+\sqrt{3}}{2})$ is

Find the slope of the normal to the
curve x = acos³θ, y =
asin³θ at.