class 12

Missing

JEE Advanced

STATEMENT-1: p-Hydroxybenzoic acid has a lower boiling point than o-hydroxybenzoic acid. because STATEMENT-2: o-Hydroxybenzoic acid has intramolecular hydrogen bonding.

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

PARAGRAPH AThere are five students $S_{1},S_{2},S_{3},S_{4}$and $S_{5}$in a music class and for them there are five seats $R_{1},R_{2},R_{3},R_{4}$and $R_{5}$arranged in a row, where initially the seat $R_{i}$is allotted to the student $S_{i},i=1,2,3,4,5$. But, on the examination day, the five students are randomly allotted five seats. For $i=1,2,3,4,$let $T_{i}$denote the event that the students $S_{i}$and $S_{i+1}$do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event $T_{1}∩T_{2}∩T_{3}∩T_{4}$is$151 $(b) $101 $(c) $607 $(d) $51 $

A farmer $F_{1}$has a land in the shape of a triangle with vertices at $P(0,0),Q(1,1)$and $R(2,0)$. From this land, a neighbouring farmer $F_{2}$takes away the region which lies between the side $PQ$and a curve of the form $y=x_{n}(n>1)$. If the area of the region taken away by the farmer $F_{2}$is exactly 30% of the area of $PQR$, then the value of $n$is _______.

Let $S$be the set of all column matrices $[b_{1}b_{2}b_{3}]$such that $b_{1},b_{2},b_{3}∈R$and the system of equations (in real variable)$−x+2y+5z=b_{1}$$2x−4y+3z=b_{2}$$x−2y+2z=b_{3}$has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each $[b_{1}b_{2}b_{3}]∈S$?(a) $x+2y+3z=b_{1},4y+5z=b_{2}$and $x+2y+6z=b_{3}$(b) $x+y+3z=b_{1},5x+2y+6z=b_{2}$and $−2x−y−3z=b_{3}$(c) $−x+2y−5z=b_{1},2x−4y+10z=b_{2}$and $x−2y+5z=b_{3}$(d) $x+2y+5z=b_{1},2x+3z=b_{2}$and $x+4y−5z=b_{3}$

Let $f(x)=xsinπx$, $x>0$ Then for all natural numbers n, f\displaystyle{\left({x}\right)}{v}{a}{n}{i}{s}{h}{e}{s}{a}{t}

Let $f:R→Randg:R→R$ be respectively given by $f(x)=∣x∣+1andg(x)=x_{2}+1$. Define $h:R→R$ by $h(x)={max{f(x),g(x)},ifx≤0andmin{f(x),g(x)},ifx>0$.The number of points at which $h(x)$ is not differentiable is

In a triangle PQR, P is the largest angle and $cosP=31 $. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)

Let $O$be the origin, and $OX,OY,OZ$be three unit vectors in the direction of the sides $QR$, $RP$, $PQ$, respectively of a triangle PQR.$∣OX×OY∣=$$s∈(P+R)$ (b) $sin2R$$(c)sin(Q+R)$(d) $sin(P+Q)˙$

The following integral $∫_{4π}(2cosecx)_{17}dx$is equal to$(a)∫_{0}2(e_{u}+e_{−u})_{16}du$$(b)∫_{0}2(e_{u}+e_{−u})_{17}du$$(c)∫_{0}2(e_{u}−e_{−u})_{17}du$$(d)∫_{0}2(e_{u}−e_{−u})_{16}du$