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Number of ways of choosing four squares on the Chess board in such a way that all squares are on one diagonal line is

1. 1

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL are arranged in a dictionary. Then the position of the word SMALL is : -

Find the maximum profit that a company can make, if the profit function is given by $p\left(x\right)=41-72x-18x^2$.

Equation of plane passing through $(1,-3,-2)$ and perpendicular to planes $x+2y+2z=5$ and $3x+3y+2z=8$ is

Consider the parabola $y^2=4x.$ Let $P$ and $Q$ be points on the parabola where $P(4,–4)$ & $Q(9,6).$ Let $R$ be a point on the arc of the parabola between $P$ and $Q$. Then the area of $\Delta PQR$ is largest when

If the angle of elevation of a cloud from a point $P$ which is $25\text{m}$ above a lake be ${30}^{\circ }$ and the angle of depression of reflection of the cloud in the lake from $P$ be ${60}^{\circ }$, then the height of the cloud (in meters) from the surface of the lake is :

A two wheeler agent sells scooters, motorcycles. In each body pattern two capacities $100$c.c and $150$c.c available. In each capacity there are five colours. The number of choices a customer will be having to buy a vehicle is:

If $(1-y)(1+2x+4x^2+8x^3+16x^4+32x^5)=1-y^6,$ where $y\ne 1,x\ne \frac{1}{2}$, then the value of $\frac{y}{x}$ is

x sin x

Number of points where $f\left(x\right)=\{\begin{array}{cc}max(|x^2-x-2|,x^2-3x),& x\ge 0\\ max\left(\ln \right(-x),e^x),& x<0\end{array}$ is non differentiable, is:

For $|x|<<1,coth\left(x\right)$can be approximated as

The domain of $si{n}^{-1}\left[lo{g}_3\left(\frac{x}{3}\right)\right]$ is

Find the range of the function given in graph

If $f\left(x\right)=\frac{1}{x^2-17x+66}$ then $f\left(\frac{2}{x-2}\right)$ will be discontinuous at $x=$

If $a_n,a_2,a_3,\dots \dots$ are in A.P., with common difference d, then the sum of the series $sind[sec{a}_{1}sec{a}_2+sec{a}_{2}sec{a}_3+\dots \dots +sec{a}_{n-1}sec{a}_n]$, is

If for complex numbers $z_1$ and $z_2$, $\arg \left(z_1\right)-\arg \left(z_2\right)=0$, then $|z_1-z_2|$ is equal to

Find HCF of 210 and 55 and express it as a linear combination of 210 and 55

$\text{In the adjacent figure, 'P' is any arbitrary interior of the triangle ABC,}$ H_a, H_b, H_c $\text{are the length of altitudes drawn from vertices A, B and C respectively. If}$ x_a, x_b and x_c $\text{represent the distance of 'P' from sides BC, AC and AB respectively, then}$

$\frac{x_a}{H_a}+\frac{x_b}{H_b}+\frac{x_c}{H_c}\text{is always equal to}$

Centre of circle passim through (0,0)and (1,0) and touching the circir x^2+y^2=9 is

An ordered pair $(\alpha ,\beta )$ for which the system of linear equations

$(1+\alpha )x+\beta y+z=2\alpha x+(1+\beta )y+z=3\alpha x+\beta y+2z=2$

has a unique solution, is:

The point where the origin has to be shifted so that the equation $y^2+4y+8x-2=0$ will not contain $y$ and the constant term is

Which of the following is the quotient, obtained on dividing $x^3-3x^2-10x+24$ by $x-4$?

Let z be a complex number such that the imaginary part of t is non zero and a = z²+z +1 is real.Then a cannot take the value

Let $(x,y,z)$ be points with integer coordinates satisfying the system of homogeneous equations:

$3x-y-z=0-3x+z=0-3x+2y+z=0$

Then the number of such points for which

$x^2+y^2+z^2\le 100$ is ___

The underlined suffix has been used to form which part of speech?

1. Mobilise

2. Institutionalise

3. Authorise

4. Specialise

Differentiate the
functions with respect to x.

For any sets $A\&B,A\cup (B-A)=$

The eccentricity of the conic $4(2y-x-3{)}^2-9(2x+y-1{)}^2=80$ is