class 12

Missing

JEE Advanced

Based on the compounds of group 15 elements, the correct statement (s) is (are)

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Let $n_{1},andn_{2}$, be the number of red and black balls, respectively, in box I. Let $n_{3}andn_{4}$,be the number one red and b of red and black balls, respectively, in box II. A ball is drawn at random from box 1 and transferred to box II. If the probability of drawing a red ball from box I, after this transfer, is $31 $ then the correct option(s) with the possible values of $n_{1}andn_{2}$ , is(are)

For $a>b>c>0$, if the distance between $(1,1)$ and the point of intersection of the line $ax+by−c=0$ is less than $22 $ then,

Let $z_{k}=cos(2k10π )+isin(2k10π );k=1,2,34,…,9$ (A) For each $z_{k}$ there exists a $z_{j}$ such that $z_{k}.z_{j}=1$ (ii) there exists a $k∈{1,2,3,…,9}$ such that $z_{1}z=z_{k}$

For every twice differentiable function $f:R→[−2,2]$with $(f(0))_{2}+(f_{prime}(0))_{2}=85$, which of the following statement(s) is (are) TRUE?There exist $r,s∈R$where $r<s$, such that $f$is one-one on the open interval $(r,s)$(b) There exists $x_{0}∈(−4,0)$such that $∣∣ f_{prime}(x_{0})∣∣ ≤1$(c) $(lim)_{x→∞}f(x)=1$(d) There exists $α∈(−4,4)$such that $f(α)+f(α)=0$and $f_{prime}(α)=0$

A cylindrica container is to be made from certain solid material with the following constraints: It has a fixed inner volume of $Vm_{3}$, has a 2 mm thick solid wall and is open at the top. The bottom of the container is a solid circular disc of thickness 2mm and is of radius equal to the outer radius of the container. If the volume the material used to make the container is minimum when the inner radius of the container is $10mm$. then the value of $250πV $ is

Consider two straight lines, each of which is tangent to both the circle $x_{2}+y_{2}=21 $and the parabola $y_{2}=4x$. Let these lines intersect at the point $Q$. Consider the ellipse whose center is at the origin $O(0,0)$and whose semi-major axis is $OQ$. If the length of the minor axis of this ellipse is $2 $, then which of the following statement(s) is (are) TRUE?For the ellipse, the eccentricity is $2 1 $and the length of the latus rectum is 1(b) For the ellipse, the eccentricity is $21 $and the length of the latus rectum is $21 $(c) The area of the region bounded by the ellipse between the lines $x=2 1 $and $x=1$is $42 1 (π−2)$(d) The area of the region bounded by the ellipse between the lines $x=2 1 $and $x=1$is $161 (π−2)$

Let $u^=u_{1}i^+u_{2}j^ +u_{3}k^$ be a unit vector in be a unit vector in $R_{3}andw^=6 1 (i^+j^ +2k^)$.Given that there exists vector $v^$ in $R_{3}$ such that $∣u^×v∣=1andw^.(u^×v)=1$. Which of the following statement(s) is(are) correct?

Let $a,b,c$be three non-zero real numbers such that the equation $3 acosx+2bsinx=c,x∈[−2π ,2π ]$, has two distinct real roots $α$and $β$with $α+β=3π $. Then, the value of $ab $is _______.