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Find the amplitude (in cm) of a particle due to superposition of two S.H.M. along the same line.

$x_1=5sin(t-{37}^o)$

$x_2=6cost$

If the curves $x^2+p{y}^2=1andq{x}^2+y^2=1$ are orthogonal to each other then

Let the lines $y-k_{1}x-\beta =0$ and $y-k_{2}x-\beta =0,(k_1\ne k_2),k_1,k_2\in R$ intersect at $P$ and the lines $x-p_{1}y-\alpha =0$ and $x-p_{2}y-\alpha =0,(p_1\ne p_2),p_1,p_2\in R$ intersect at $Q$. If the points $P$ and $Q$ always lies on or inside the triangle formed by the lines $2x-3y-6=0,3x-y+3=0$ and $3x+4y-12=0$, then

If $(n+1)!=12\times (n-1)!$, then the value of $n$ can be

Let $\alpha ,\beta$ be two distinct roots of $a\cos \theta +b\sin \theta =c$, where $a,b$ and $c$ are three real constants and $\theta \in [0,2\pi ]$. Then $\alpha +\beta$ is also a root of the same equation if

The discriminant of the quadratic equation $2x^2-4x+3=0$ is

Which of the following represents the graph of $y=-x^2+6x+1$

The equations of the normals to the curve $f\left(x\right)=\frac{x}{1-x^2}$ at the points where the tangents make the angle of $\frac{\pi }{4}$ with the positive direction of $x$ - axis are:

If $f\left(x\right)=\sqrt{x+3}$ and $g\left(x\right)=1+x^2,$ then $fog\left(x\right)=$ ____.

A forecast is to be made of the results of five cricket matches, each of which can be a win or a draw or a loss for Indian team. Let,
$p=$ number of forecasts with exactly $1$ error
$q=$ number of forecasts with exactly $3$ error
$r=$ number of forecasts with all five error
Then the correct statement(s) is/are

If the coordinates of the vertex and the focus of a parabola are (-1,1) and (2,3) respectively,then the equation of its directrix is

Let $a_1,a_2,a_3,...,a_n$ be in A.P. If $a_3+a_7+a_{11}+a_{15}=72$, then the sum of its first $17$ terms is equal to:

An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on each executive class ticket and a profit of Rs 600 is made on each economy class ticket. The airline reserves atleast 20 seats for executive class. However atleast 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each must be sold in order to maximize the profit for the airline. What is the maximum profit?

If $5\cos \theta \sin \theta =1,$ then the value of ${\tan }^3\theta +{\cot }^3\theta$ is

Integrate the function.
$\int e^x\left(\frac{1+sinx}{1+cosx}\right)dx.$

Maximize Z = - x + 2y, subject to the constraints are x $\ge$ 3, x + y $\ge$ 5, x + 2y $\ge$ 6 and x, y $\ge$ 0.

$\int \frac{x^2}{1-x^4}dx=$

Integrate the following functions.
$\int \frac{x}{\sqrt{x}+4}dx.$

For the following question verify that the given function (explicit or implicit) is a solution of the corresponding differential equation.

$y=x^2+2x+Cand{y}^{\prime }-2x-2=0$

For the given differential equation find the particular solution satisfying the given conditions.

(x+y)dy+(x-y)dx=0, y=1 when x=1.

If $a+b+c\ne 0$ and $\left|\begin{array}{ccc}a& b& c\\ b& c& a\\ c& a& b\end{array}\right|=0$, then prove that a = b = c.

Find a unit vector in the direction of $\overrightarrow{PQ}$, where P and Q have coordinates (5, 0, 8) and (3, 3, 2), respectively.

If $y=sin\left(\sqrt{sinx+cosx}\right).Find\frac{dy}{dx}$

If the sides of a right angle triangle from an AP, the 'sine' of the acute angles are

How many months does coordinate Geometry takes to cover in class 11 (approx) ?

Find the term independent of x in the expansion of (3x²/2-1/3x)⁹

Find the values of the trigonometric function sin 765°

The length and breadth of a field are measured as : l = (120 $\pm$ 2)m, b=(100 $\pm$ 5) m. What is the absolute error in the area of the field?

Two bottles were half filled with water from Ganga ('P') and kaveri ('Q') and kept under identical airtight conditions for 5 days. The oxygen was determined to be 2$\%$ in bottle ('P') and 10$\%$ in bottle ('Q'). What could be the cause of this difference?

For a real number x, let [x] denote the largest integer less than or equal to x, and let {x} = x - [x]. The number of solutions x to be equation [x]{x} = 5 with is 0 $\le$ x $\le$ 2015 is

There are 3 white, 4 red, and 1 blue marbles in a bag. They are drawn one by one and arranged in a row. Assuming that all 8 marbles are drawn, determine the number of different arrangements if marbles of same colour are indistinguishable.

Find the direction cosines of the sides of the triangle whose vertices are (3,5,-4), (-1,1,2) and (-5,-5,-2).

Assume that each child born is equaly likely to be boy or a girl. IF a family has two children, what is the conditional probability that both are girls given that
atleast one is a girl?

Prove, $co{s}^{-1}\frac{12}{13}+si{n}^{-1}\frac{3}{5}=si{n}^{-1}\frac{56}{65}$

If $(1+ax{)}^n=1+8x+24x^2+...,$ then which of the following is/are correct?

If $f\left(x\right)={\tan }^{-1}\left[\frac{\log \left(\frac{e}{x^2}\right)}{\log \left(e{x}^2\right)}\right]+{\tan }^{-1}\left[\frac{3+2\log x}{1-6\log x}\right]$ then the value of $f^{\prime \prime }\left(x\right)$ is

If $\underset{n\to \infty }{lim}{\left(\frac{{}^{3n}{C}_n}{{}^{2n}{C}_n}\right)}^{1/n}=\frac{A}{B}$, where $A,B$ are co-prime, then $A+B$ is divisible by

If the G.P.'s 5, 10, 20, ...... and 1280, 640, 320, .... have their nth terms equal, find the value of n.

The point(s) on the ellipse $16x^2+11y^2=256$
where the common tangent to it and the circle $x^2+y^2-2x=15$ touch is

If $a_1,a_2,a_3,\cdots ,a_n$ be an AP of nonzero terms then prove that

$\frac{1}{a_1{a}_2}+\frac{1}{a_2{a}_3}+\frac{1}{a_3{a}_4}+\cdots +\frac{1}{a_{n-1}{a}_n}=\frac{(n-1)}{a_1{a}_n}$