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A rigid bod y in the shape of a “V” has two equal arms made of uniform rods. What must the angle between the two rods be so that when the body is suspended from one end, the other arm is horizontal?

If a curve passing through P(4, 2) and satisfies the differential equation $\frac{dy}{dx}=\frac{y}{x-y^2}$ is a conic then which of the following is correct?

R=$(5\sqrt{5}+11{)}^{2n+1}$ and $f=R-\left[R\right]$, where [] denotes the greatest integer function. Then the value of $Rf$ is

If the mean deviation about the median of the numbers $k,3k,7k,9k,11k,13k$ is $11,$ then $k$ is equal to $(k>0)$

The vertices of $△ABC$ lie on a rectangular hyperbola such that the orthocentre of the triangle is $(3,2)$ and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. If two perpendicular tangents of the hyperbola intersect at the point $(1,1)$,then combined equation of the asymptotes is

Determine order and degree(if defined)
of differential equation

The graph of a quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$ is shown below





Which of the following options is/are true for the graph?

The horizontal asymptote of the curve $y=e^{\frac{1}{x}}$ is

Let a function $f\left(x\right)=\{\begin{array}{cc}{a}^2-2a-3+5x^3,& x<0\\ -2x^2,& x\ge 0\end{array}$ has a local maximum at $x=0.$ Then set of values of $a$ is

In the world of matrices if null matrix represents a zero ,then ______ represents a one.

let g(x) be a function satisfying g(0)=2, g(1)=3, g(x+2)=2g(x) - g(x+1), then find out g(5)

In the circle given below which point(s) has/have a chord of contact.

Let the observations $x_i(1\le i\le 10)$ satisfy the equations, $\sum _{i=1}^{10}(x_i-5)=10$ and $\sum _{i=1}^{10}(x_i-5{)}^2=40$. If $\mu$ and $\lambda$ are the mean and the variance of observations, $(x_1-3),(x_2-3),...,(x_{10}-3)$, then the ordered pair $(\mu ,\lambda )$ is equal to :

The eigen values of the matrix $\left[\begin{array}{cc}a& 1\\ a& 1\end{array}\right]$ are

Using differentials, find the approximate value of the following up to 3 places of decimal.
$(0.009{)}^{\frac{1}{3}}$

Probability of a fraudster being caught is $\frac{1}{2}$ and commiting a fraud is $\frac{3}{5}$. What is his chances of not going to jail?

If a, b, c, are in H.P. then

Let $△PQR$ be a triangle. Let $\overrightarrow{a}=\overrightarrow{QR},\overrightarrow{b}=\overrightarrow{RP}$ and $\overrightarrow{c}=\overrightarrow{PQ}.$ If $|\overrightarrow{a}|=12,|\overrightarrow{b}|=4\sqrt{3}$ and $\overrightarrow{b}.\overrightarrow{c}=24,$ then which of the following is (are) true?

Let $q\in N$ and $p\in (-\frac{\pi }{2},\frac{\pi }{2})$. Then, the value of $\underset{0}{\overset{p+q\pi }{\int }}|\cos x|dx$ is

Evaluate $\int \frac{dx}{x(x^n+1)}$

(where $C$ is constant of integration)

The value of $I=\underset{0}{\overset{\pi /2}{\int }}\frac{{\tan }^{7}x}{{\cot }^{7}x+{\tan }^{7}x}dx$ equals to

The sum $\sum _{k=1}^{20}k\frac{1}{2^k}$ is equal to :

If equation of a plane is given as 4x + 2y + 12z = 7, then the x, y and z intercepts by the given plane will be .

Consider the differential equation $y^{2}dx+(x-\frac{1}{y})dy=0.$ If $y\left(1\right)=1,$ then $x$ is equal to

A binary tree with n > 1 nodes has $n_1,n_2$ and $n_3$ nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbours.



$n_3$ can be expressed as: