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The coordinates of the point(s) on $x+y+3=0$, whose distance from $x+2y+2=0$ is $\sqrt{5}$ units, is/are

Mode of the distribution

$\begin{array}{cccccc}\text{Marks}& 4& 5& 6& 7& 8\\ \text{No. of students}& 3& 5& 10& 6& 1\end{array}$

If the tangents to the parabola $x=y^2+c$ from origin are perpendicular, then $c$ is equal to

The image of the point $(1,2,-1)$ with respect to the plane containing the line $\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$ and the point $(0,7,-7),$ is

The solution of the inequality ${\log }_{\frac{25-x^2}{16}}\left(\frac{24-2x-x^2}{14}\right)>1$ is

Graph of $y=e^x\cos x$ is:

Find the values of $x$ and $y$ for the system of equations, $x+y=2$ and $3x-y=6$ using Cramer's Rule.

If two tangents to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$ make angles $\alpha$ and $\beta$ with the major axis such that $\tan \alpha +\tan \beta =\lambda ,$ then the locus of their point of intersection is

If the line $\frac{x}{a}+\frac{y}{b}=1$touches the circle $2(x^2+y^2)=a^2$ then

If the point $(a,a^2)$ lies inside the triangle formed by the lines $2x+3y-1=0,x+2y-1=0$ and $-8x+8y+2=0$ then

If the point $P$ on the curve, $4x^2+5y^2=20$ is farthest from the point $Q(0,-4)$, then $P{Q}^2$ is equal to:

If length of the side $BC$ of a $\Delta ABC$ is $4$ cm and $\angle BAC={120}^{\circ },$ then the distance between the incenter and excentre of the circle touching the side $BC$ is:

Evaluate $\int \frac{e^x(2-x^2)}{(1-x)\sqrt{1-x^2}}dx$

The ellipse $x^2+4y^2=4$ is inscribed in a rectangle touches its side and aligned with the coordinates axes, which is turn in inscribed in another ellipse which passes through that passes through the point $(4,0).$ Then , the equation of ellipse is

If $\underset{x\to \infty }{Lim}[\frac{x^2+1}{x+1}-ax-b]=b$, where a, b are constants, then the value of a+b, is

If A is an invertible matrix of order 2, then det $\left(A^{-1}\right)$ is equal to
a) $det\left(A\right)$
(b) $\frac{1}{det\left(A\right)}$
c) 1
d) zero

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is:

Which among the following pairs of linear equations has unique solution?

If the circle $x^2+y^2+4x+22y+c=0$ bisects the circumference of the circle $x^2+y^2-2x+8y-d=0(c,d>0),$ then the maximum possible value of $cd$ is

The equation of tangent to the curve $y=3x^2+4x+8-\ln (x+1)$ at $x=0$ is

If cos A + cos² A = 1, then sin² A + sin⁴ A is

If the arithmetic and geometric mean of two positive real numbers $a$ and $b(a>b)$ are $13$ and $12$ respectively, then the value of $a-b$ is

If $|2x-1|+|3x-4|=|5x-5|$, then complete set of values of $x$ is

The point (4, 1)undergoes the following two successive transformation

(i) Reflection about the line y=x

(ii) Translation through a distance 2 units along the positive x-axis

Then the final coordinates of the point are

How to prove dimensions for the equation v²=u²+2ax

Find the value of $\lambda$ which will make the vectors $\overrightarrow{a},\overrightarrow{b}\text{and}\overrightarrow{c}$ coplanar, where $\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k},\overrightarrow{b}=\hat{i}+2\hat{j}-3\hat{k}\text{and}\overrightarrow{c}=3\hat{i}-\lambda \hat{j}+5\hat{k}$ .

The value of $\cos \frac{\pi }{4}\times (\cos \frac{\pi }{12}-\sin \frac{\pi }{12})$ is

Smaller area enclosed by the circle x²
+ y² = 4 and the line x + y = 2 is

A. 2 (π
– 2)

B. π
– 2

C. 2π
– 1

D. 2 (π
+ 2)

Profit earned from Product X is shown below. Another Product Y also has the same profit but it started selling 1.5 years after start of sale of Product X. What will be the new set of input values for the Product Y?

$a_1,a_2,\dots \dots .a_n$ are A.P. Where $a_1$ > 0 for all i, then $\frac{1}{\sqrt{a_1}+\sqrt{a_2}}+\frac{1}{\sqrt{a_2}+\sqrt{a_3}}+....+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_n}}$