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The total number of ways of dividing 15 different things into groups of 8,4 and 3 respectively is

Number of functions from a set $A$ containing $6$ elements to a set $B$ containing $3$ elements such that every element in $B$ has atleast one preimage is

Let $A=\{x:x\text{is a prime factor of}30\}$ and $B=\{y:y\in N,-3\le y+3<8\}$. If $R$ is a relation from $A$ to $B$, then $R^{-1}$ can be

$li{m}_{n\to \infty }$ $\frac{n\left(\right(2n+1{)}^2)}{(n+2)(n^2+3n-1)}$ =

Let $\left[k\right]$ denotes the greatest integer less than or equal to $k.$ Then the number of positive integral solutions of the equation $\left[\frac{x}{\left[{\pi }^2\right]}\right]=\left[\frac{x}{\left[11\frac{1}{2}\right]}\right]$ is

If the sum of n terms of an A.P is cn(n - 1), where $c>0$, the sum of the square of these terms is -

The distance, from the origin, of the normal to the curve,$x=2\cos t+2t\sin t,y=2\sin t–2t\cos t,\text{at}t=\frac{\pi }{4}$,is:

If $A=\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& 2\\ 2& 2& 1\end{array}\right]$

and $|(A^2-pA-qI)|=0$, then $p+q=$

What is the condition for a conic $x^2+2xy+2y+kx+3y^2=0$ to represent a pair of straight lines.

If the lengths of the sides of a triangle be $7,4\sqrt{3}and\sqrt{13}cm$, then the smallest angle is

If $(2+\sqrt{3}{)}^n=I+f,n\in N$, where $I$ is integral part and $f$ is fractional part, then $(I+f)(1-f)$ is

Let A,B,C be the feet of perpendiculars drawn from P(3,4,5) on XY,YZ,ZX planes respectively, then Coordinates of A,B and C will be .

Let $A=\{x:x\text{is a prime factor of}240\}$ and $B=\{y:y\text{is the sum of any two prime factors of}240\}$. Then which of the following options is true?

A bag contains 5 white, 6 black and 4 red balls. Three balls are selected from this bag simultaneously. The probability that one of the colour will be missing in the selected balls, is equal to

Three children are selected at random from a group of 6 boys and 4 girls. It is known that in this group exactly one girl and one boy belong to same parent. The probability that the selected group of children have no blood relations, is equal to

In an ellipse, if the lines joining a focus to the extremities of the minor axis make an equilateral triangle with the minor axis, the eccentricity of the ellipse is

In a high school, a committee has to be formed from a group of $6$ boys $M_1,M_2,M_3,M_4,M_5,M_6,$ and $5$ girls $G_1,G_2,G_3,G_4,G_5.$

(i) Let ${\alpha }_1$ be the total number of ways in which the committee can be formed such that the committee has $5$ members, having exactly $3$ boys and $2$ girls.

(ii) Let ${\alpha }_2$ be the total number of ways in which the committee can be formed such that the committee has atleast $2$ members, and having an equal number of boys and girls.

(iii) Let ${\alpha }_3$ be the total number of ways in which the committee can be formed such that the committee has $5$ members, atleast $2$ of them being girls.

(iv) Let ${\alpha }_4$ be the total number of ways in which the committee can be formed such that the committee has $4$ members, atleast $2$ girls and such that both $M_1$ and $G_1$ are NOT in the committee together.

$\begin{array}{cccc}& LIST-I& & LIST-II\\ P.& \text{The value of}{\alpha }_1\text{is}& 1.& 136\\ Q.& \text{The value of}{\alpha }_2\text{is}& 2.& 189\\ R.& \text{The value of}{\alpha }_3\text{is}& 3.& 192\\ P.& \text{The value of}{\alpha }_4\text{is}& 4.& 200\\ & & 5.& 381\\ & & 6.& 461\end{array}$

The correct option is:

If $lo{g}_{0.04}(x-1)\ge lo{g}_{0.2}(x-1)$ then x belongs to the interval

Let ${(-2-\frac{1}{3}i)}^3=\frac{x+iy}{27}(i=\sqrt{-1})$, where $x$ and $y$ are real numbers, then $y-x$ equals:

If the points $A(2,-1,1),B(1,-3,-5)$and$C(3,-4,-4)$ form a triangle, find the circum radius for this triangle.

The auxiliary circle of family of ellipses, passes through origin and makes intercept of $8$ and $6$ units on the $x-$ axis and the $y-$ axis respectively. If eccentricity of all such family of ellipse is $\frac{1}{2}$, then the locus of focus of ellipse will be

Number of real solution(s) of the $|x+2|={\log }_{0.5}x$ is

More than One Answer Type

एक से अधिक उत्तर प्रकार के प्रश्न



Which of the following is/are true?



निम्नलिखित में से कौनसा/कौनसे विकल्प सही है/हैं?

If the focus of the parabola $(y-\beta {)}^2=4(x-\alpha )$ always lies between the lines $x+y=1$ and $x+y=3$ then

The range of the function $f\left(x\right)=\frac{1}{3-\sin 3x},x\in R$ is

If $a,b,c,d$ are distinct positive numbers which are in A.P. with positive common difference, then which of the following is/are correct?

Equations to the sides of a triangle are $x-3y=0$, $4x+3y=5$ and $3x+y=0$. The line $3x-4y=0$ passes through the

Let $\omega =-\frac{1}{2}+i\frac{\sqrt{3}}{2}$ Then the value of the determinant $\left|\begin{array}{ccc}1& 1& 1\\ 1& -1-{\omega }^2& {\omega }^2\\ 1& {\omega }^2& {\omega }^4\end{array}\right|$ is

If $A=\{1,2,3\}$ and $B=\{4,5\},$ then $A\times B=$ ___.

The value of the determinant

$\left|\begin{array}{ccc}lo{g}_a\left(\frac{x}{y}\right)& lo{g}_a\left(\frac{y}{z}\right)& lo{g}_a\left(\frac{z}{x}\right)\\ lo{g}_b\left(\frac{y}{z}\right)& lo{g}_b\left(\frac{z}{x}\right)& lo{g}_b\left(\frac{x}{y}\right)\\ lo{g}_c\left(\frac{z}{x}\right)& lo{g}_c\left(\frac{x}{y}\right)& lo{g}_c\left(\frac{y}{z}\right)\end{array}\right|$ is

If $\frac{|x+2|}{|x-4|}=3$, then the value(s) of $x$ is/are

If $\cos x+\cos y+\cos z=0=\sin x+\sin y+\sin z,$ then

If $\theta +\pi$ is the eccentric angle of a point on the ellipse $16x^2+25y^2=400,$ then the corresponding point on the auxilary circle is

If $x.a=0,x\times b=c\times b$ then x =

The absolute difference between the greatest and the least values of the function $f\left(x\right)=x(\ln x-2)$ on $[1,e^2]$ is

Let A = {1, 2, 3, ...n} and B = {a, b}. Then the number of onto functions from A into B is

A survey shows $40\text{\%}$ of people like only apples, $30\text{\%}$ of people like only mangoes, if every person like atleast one fruit, then the percentage of people who like both apples and mangoes is

If a, b, c, d are in H.P., then ab + bc + cd is equal to

If centroid of the tetrahedron OABC, where A,B,C are given by (a, 2, 3),(1, b, 2) and (2, 1, c) respectively be (1, 2, -1), then distance of P(a,b,c) from origin is equal to

Find number of value of $xϵ[0,\pi ]$ satisfying the relation cos 3x + sin 2x - sin 4x = 0

Maximum value of the expression $\sqrt{{\cos }^{2}x-10\cos x+25}+3$ is

If $\omega$ is the cube root of unity, then $\left|\begin{array}{ccc}1& \omega & {\omega }^2\\ \omega & {\omega }^2& 1\\ {\omega }^2& 1& \omega \end{array}\right|=$

The sum of the series $\frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+\dots \dots$ upto $16$ terms is

If the length of perpendicular from origin to a line is $6$ units and the line makes an angle of ${30}^{\circ }$ with the positive $y-$axis (anti clockwise), then the equation of line is

The sum of two geometric mean's inserted between $3$ and $81$ is

Equation of the circle passing through the focii of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ and having centre at $(0,3)$ is

The number of solutions of the equation $|5\tan 2\theta \tan \theta -12\tan \theta |+|3{\sin }^2\theta -\sin 2\theta |=0$ in the interval $[0,2\pi ]$ is

The value of the expression $\frac{\sin 2x\cos 3x+\sin 3x\cos 8x+\sin 5x\cos 16x}{\sin 2x\sin 3x+\sin 3x\sin 8x+\sin 5x\sin 16x}$ is