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Which of the following is a row matrix?

If $\alpha and\beta$ ($\alpha <\beta$ ) are the roots of equation $x^2+2x-5=0$, then the value of $\frac{1}{\alpha }-\frac{1}{\beta }$ is:

Rohan attends a test with multiple choice questions with no negative marking. There were fifty questions and each question had four marks for answering right. What is the sample space of marks that Rohan could score?

Let $f:(4,6)\to (6,8)$ be a function defined by $f\left(x\right)=x+\left[\frac{x}{2}\right]$ (where [.] denotes the greatest integer function),

then $f^{-1}\left(x\right)$ is equal to

The image of a point $(3t+1,1-4t),\forall t\in R-\left\{0\right\}$ in a line, lies on $3x-4y+1=0.$ Then the slope of line(s) is (are)

A hyperbola has its centre at the origin, passes through the point $(4,2)$ and has transverse axis of length $4$ unit along the $x-$axis. Then the eccentricity of the hyperbola is

If $C_0,C_1,\cdots C_n$ are the coefficient of $x$ in expansion of $(1+x{)}^n$, then $C_0-C_2+C_4-C_6+\cdots +(-1{)}^n{C}_n=$

If ${}^9{P}_5+5{}^9{P}_4={}^{10}{P}_r,$ then value of $r$ is

The set of all $x$ satisfying $4^{x^2+2}-9\times 2^{x^2+2}+8=0$ consists of

If $A=\{y:|y|=3x,x\le 2,x\in N\},$

$B=\{x:x\text{is a positive even number},x<14\}$ and $C=\{1,4,8\},$ then $n\left(\right(A\times B)\cap (A\times C\left)\right)$ is

The shortest distance between the line $x-y=1$ and the curve $x^2=2y$ is :

A circle passes through the origin O and cuts the axis at A(a, 0) and B(0, b). The reflection of O in the line AB is the point

A group of students comprises of $5$ boys and $n$ girls. If the number of ways in which a team of $3$ students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is $1750$, then $n$ is equal to :

If $(x,y)$ represents the Cartesian coordinates for the polar coordinates $(4,\theta )$, then the correct relationship between $x$ and $y$ is

Box I contain three cards bearing numbers 1,2,3; box II contains five cards bearing numbers 1,2,3,4,5; and box III contains seven cards bearing numbers 1,2,3,4,5,6,7. A card is drawn from each of the boxes. Let $x_i$ be the number on the card drawn from the $i^{th}$ box $i=1,2,3.$



The probability that $x_1+x_2+x_3$ is odd, is ?

If the roots of a quadratic equation are $-6$ and $7$, then the quadratic equation is

If A is a diagonal matrix of order 3 $\times$ 3 is commutative with every square matrix of order 3 $\times$ 3 under multiplication and trace (A) = 12, then

If the angle between two lines is $\frac{\pi }{3}$ and the slope of one of the lines is $\frac{1}{2}$,

then the slope of the other line is/are:

The sides of a rhombus $ABCD$ are parallel to the lines, $x-y+2=0$ and $7x-y+3=0$. If the diagonals of the rhombus intersect at $P(1,2)$ and the vertex $A$ (different from the origin) is on the $y-$axis, then the ordinate of $A$ is

If $A(7,9),B(3,-7)$ and $C(-3,3)$ represent the vertices of a triangle, then orthocentre of the triangle is

If $\frac{sinx}{siny}=\frac{1}{2},\frac{cosx}{cosy}=\frac{3}{2},xyϵ(0,\frac{\pi }{2})$, then tan (x+y)=___

If $a{x}^2+(1-\lambda )x+(a-1-\lambda )=0$ where $a\ne 0,$ has real roots for all $\lambda \in R,$ then

If $A=\{y:y={\log }_2|x-2|,x<5,x\text{is a whole number}\},B=\{y:y=|x-2|,x\in [0,1],y\in N\},C=\{1,3,5\}$

, then $n\left(\right(A\times B)\cap (B\times C\left)\right)$ is

In a shelf there are $2$ different physics books and $3$ different chemistry books. The number of ways in which a student can select a physics book and chemistry book is:

Let $\alpha$ and $\beta$ be the roots of equation $p{x}^2+qx+r=0,\ne 0.$ If p,q,r are in A.P. and $\frac{1}{\alpha }+\frac{1}{\beta }=4,$ then the value of $|\alpha -\beta |$is :

Plot the graph of $|y|=ln\left(x\right)$

$\frac{1}{1.2}$ +

$\frac{1}{2.3}$ +

$\frac{1}{3.4}$ +.......+ .........

$\frac{1}{n.(n+1)}$ equals

A and B having equal skill, are playing a game of best of 5 points. After A has won two points and B has won one point, the probability that A will win the game is:

$I_{m,n}={\int }_0^1{x}^m(\log x{)}^{n}dx$, then $I_{m,n}$ is equal to

The solution set of $x^2-4x+1<0$ is

Consider the integral $I=\underset{0}{\overset{10}{\int }}\frac{\left[x\right]e^{\left[x\right]}}{e^{x-1}}dx,$ where $\left[x\right]$ denotes the greatest integer less than or equal to $x.$ Then the value of $I$ is equal to :

If A(4, -3), B(3, -2) and C(2, 8) are the vertices of a triangle, then its centroid will be

The function f(x) is continuous in the interval (a, b) then which among the following is true?

If $a,b,c$ are non zero real numbers, then minimum value of the expression$\left(\frac{(a^4+a^2+1)(b^4+7b^2+1)(c^4+11c^2+1)}{\left(a^2{b}^2{c}^2\right)}\right)$ is

For all real number $x$, $2^x+3^x-4^x+6^x-9^x$ is always less than

The function $f\left(x\right)=\frac{2x^2-1}{x^4},x>0$, decreases in the interval

Let the line $y=mx$ and the ellipse $2x^2+y^2=1$ intersect at point $P$ in the first quadrant. If the normal to this ellipse at $P$ meets the co-ordinate axes at $(-\frac{1}{3\sqrt{2}},0)$ and $(0,\beta )$, then $\beta$ is equal to:

The plane which bisects the line segment joining the points $(-3,-3,4)$ and $(3,7,6)$ at right angles, passes through which one of the following points?

The quadratic equation $(\cos p-1)x^2+\left(\cos p\right)x+\sin p=0$

(where $x\in R$) has real roots if $p$ lies in

The set of values of $x$ for which ${\log }_2(-{\log }_{1/2}(1+\frac{1}{x^4})-1)$ is defined is

Let $F_1(x_1,0)$ and $F_2(x_2,0),$ for $x_1<0$ and $x_2>0,$ be the foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{8}=1.$ Suppose a parabola having vertex at the origin and focus at $F_2$ intersects the ellipse at point $M$ in the first quadrant and at point $N$ in the fourth quadrant.



If the tangents to the ellipse at $M$ and $N$ meet at $R$ and the normal to tha parabola at $M$ meets the $x-$axis at $Q$, then the ratio of area of the triangle $MQR$ to area of the quadrilateral $M{F}_{1}N{F}_2$ is

The length of transverse common tangent to two circles is $5\text{units}$ and a direct common tangent is $15\text{units}$, then the product of the radii of two circles is

If $\frac{(1+i)x-2i}{3+i}+\frac{(2-3i)y+i}{3-i}=i$, then values of $x$ and $y$ are

If A and B are two square matrices such that $B=-A^{-1}$ BA, then $(A+B{)}^2=$

What is the range of lengths of chord of contact of a circle with radius R.

If $B_0=\left[\begin{array}{ccc}-4& -3& -3\\ 1& 0& 1\\ 4& 4& 3\end{array}\right],B_n=\text{adj}\left(B_{n-1}\right),\forall n\in N$ and $I$ is identity matrix of order $3.$ Then $B_1+B_3+B_5+B_7+B_9$ is equal to