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If range of the numbers $x_1,x_2,x_3,x_4,x_5$ is $r$ where $x_i<x_{i+1}$. If each number is multiplied by $p(p>0)$ and then $k$ is subtracted from each number then range of the new numbers is

If $f\left(x\right)=xsinx$, then $f^{\prime }\left(\frac{\pi }{2}\right)=$

If the two diagonals of one of the faces of a parallelopiped are $6\hat{i}+6\hat{k}$ and $4\hat{j}+2\hat{k}$ and one of the edges not containing the given diagonals is $4\hat{j}-8\hat{k}$, then the volume of the parallelopiped is

If the line $ax+y=c,$ touches both the curves $x^2+y^2=1$ and $y^2=4\sqrt{2}x,$ then $|c|$ is equal to :

Consider the parabola $X^2+4Y=0$. Let p = (a, b) be any fixed point inside the parabola and let 'S' be the focus of the parabola. Then the minimum value SQ + PQ as point Q moves on the parabola is

The point in which the join of A(- 9, 4, 5) and B(11, 0, -1) is met by the perpendicular from the origin

The arithmetic mean of the $5$ consecutive integers starting with ${}^{\prime }{s}^{\prime }$ is ${}^{\prime }{a}^{\prime }.$ Then the arithmetic mean of $9$ consecutive integers that start with $s+2$

How many 3-digit numbers are there, with distinct digits, with each digit odd?

A tiffin contains $4$ sandwiches . How many sandwiches would be there in $8$ such tiffins?

If
such
that f(2) = 0, then f(x) is

(A) (B)

(C) (D)

A 6 sided regular polygon (hexagon) is inscribed in a circle of radius 10 cm, find area of the hexagon. [2 MARKS]

The domain of the function log2log3log4(x) is

If $\alpha$ and $\beta$ are two distinct complex numbers satisfying $|\alpha {|}^2\beta -|{\beta }^2|\alpha =\alpha -\beta ,$ then
(Here, $\arg \left(z\right)$ denotes the principal argument with $-\pi <\arg \left(z\right)\le \pi$)

If $\pi <\theta <\frac{3\pi }{2}$, then write the value of

$\sqrt{\frac{1-cos2\theta }{1+cos2\theta }}$

If $A$ and $B$ are two sets such that $(A-B)\cup B=A$, then

Let $a,b,c$ be the sides of a triangle opposite to angles $A,B,C$ respectively. If at least one root of the quadratic equation $a{x}^2+bx+c=0$ with integral coefficients is same as one of the roots of the quadratic equation $x^2+kx+2=0$ where $k\in N,k>12$ , then $\tan \left(\frac{C+A}{2}\right)\cot \left(\frac{C-A}{2}\right)$ is equal to

In a $△ABC,$ $E$ is the midpoint of side $BC$ and $D$ is a point on side $AC.$ If length of side $AC$ is $1$ unit and $\angle BAC={60}^{\circ },$ $\angle ACB={20}^{\circ },$ $\angle DEC={80}^{\circ },$ then the value of $Area\left(△ABC\right)+2Area\left(△CDE\right)$ is

If roots of equation of $x^2+x+1=0$ are $a,b$ and roots of $x^2+px+q=0$ are $\frac{a}{b},\frac{b}{a}$ then value of $p+q$ is

Column 1

1.$Lo{g}_{a}x,a>1$

2.$Lo{g}_{a}x,0<a<1$

3.$a^x,a>1$

4.$a^x,0<a<1$

Column 2

Graph of P :

Graph of Q :

Graph of R :

Graph of S :

Match $\text{List I}$ with the $\text{List II}$ and select the correct answer using the code given below the lists :



$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{If}m\text{and}n\text{are positive integers satisfying}& \text{(P)}& 9\\ & 1+\cos 2\theta +\cos 4\theta +\cos 6\theta +\cos 8\theta +\cos 10\theta =\frac{\cos m\theta \cdot \sin n\theta }{\sin \theta },& & \\ & \text{then}(m+n)\text{is equal to}& & \\ \text{(B)}& \text{The minimum value of the expression}\frac{9x^2{\sin }^{2}x+4}{x\sin x}\text{for}x\in (0,\pi )\text{is}& \text{(Q)}& 10\\ \text{(C)}& \text{Let}f\left(x\right)=11-8\sin x-2{\cos }^{2}x.\text{If the maximum and minimum values of}f\left(x\right)& \text{(R)}& 11\\ & \text{are denoted by}M\text{and}m\text{respectively, then}\frac{M+8}{m}\text{has the value equal to}& & \\ \text{(D)}& \text{If}\tan 9\theta =\frac{3}{4}(\text{where}0<\theta <\frac{\pi }{18}),\text{then the value of}(\text{3 cosec 3}\theta -4\sec 3\theta )& \text{(S)}& 12\\ & \text{is equal to}& & \\ & & \text{(T)}& 13\end{array}$



Which of the following is a CORRECT combination ?

In a mathematics class, 20 children forgot their rulers and 17 forgot their pencils. Teacher said "Go and borrow them from someone at once”. 24 children left the room, then how many children forgot both:

In which city is the number of couples having more than four children and less than seven children is the least?

If $\left|\begin{array}{ccc}{\lambda }^2+3\lambda & \lambda -1& \lambda +3\\ \lambda +1& 2-\lambda & \lambda -4\\ \lambda -3& \lambda +4& 3\lambda \end{array}\right|=p{\lambda }^4+q{\lambda }^3+r{\lambda }^2+s\lambda +t,$ then $t$ equals to

If the $m^{th}$ term of a H.P. be n and $n^{th}$ be m, then the $r^{th}$ term will be

In any triangle, the minimum value of $\frac{r_1{r}_2{r}_3}{r^3}$ is equal to $k$, then the number of positive integral solutions of the equation $x_1+x_2+x_3=k$ is :

Find the equation of the line which passes though and is inclined with the x-axis at an angle of 75°.

${lim}_{x\to 0}(cosecx-cotx)$