class 12

Missing

JEE Advanced

Match the chemical substances in Column I with type of polymers/type of bonds in Column II. Indicate your answer by darkening the appropriate bubbles of the $4×4$ matrix given in the ORS.

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Late $a∈R$and let $f:R$be given by $f(x)=x_{5}−5x+a,$then$f(x)$has three real roots if $a>4$$f(x)$has only one real roots if $a>4$$f(x)$has three real roots if $a<−4$$f(x)$has three real roots if $−4<a<4$

Let $T$be the line passing through the points $P(−2,7)$and $Q(2,−5)$. Let $F_{1}$be the set of all pairs of circles $(S_{1},S_{2})$such that $T$is tangent to $S_{1}$at $P$and tangent to $S_{2}$at $Q$, and also such that $S_{1}$and $S_{2}$touch each other at a point, say, $M$. Let $E_{1}$be the set representing the locus of $M$as the pair $(S_{1},S_{2})$varies in $F_{1}$. Let the set of all straight lines segments joining a pair of distinct points of $E_{1}$and passing through the point $R(1,1)$be $F_{2}$. Let $E_{2}$be the set of the mid-points of the line segments in the set $F_{2}$. Then, which of the following statement(s) is (are) TRUE?The point $(−2,7)$lies in $E_{1}$(b) The point $(54 ,57 )$does NOT lie in $E_{2}$(c) The point $(21 ,1)$lies in $E_{2}$(d) The point $(0,23 )$does NOT lie in $E_{1}$

If $Ik=1∑98 ∫_{k}x(x+1)k+1 dx,then:$$I<5049 $ (b) $I>(g)_{e}99$$I>5049 $ (d) $I<(g)_{e}99$

A box $B_{1}$, contains 1 white ball, 3 red balls and 2 black balls. Another box $B_{2}$, contains 2 white balls, 3 red balls and 4 black balls. A third box $B_{3}$, contains 3 white balls, 4 red balls and 5 black balls.

Let $f(x)=∣1−x∣1−x(1+∣1−x∣) cos(1−x1 )$ for $x=1.$ Then: (A)$(lim)_{n→1_{−}}f(x)$ does not exist (B)$(lim)_{n→1_{+}}f(x)$ does not exist (C)$(lim)_{n→1_{−}}f(x)=0$ (D)$(lim)_{n→1_{+}}f(x)=0$

Let $O$be the origin, and $OXxOY,OZ$be three unit vectors in the direction of the sides $QR$, $RP$, $PQ$, respectively of a triangle PQR.If the triangle PQR varies, then the minimum value of $cos(P+Q)+cos(Q+R)+cos(R+P)$is:$−23 $ (b) $35 $ (c) $23 $ (d) $−35 $

Let $f:(0,∞)R$ be given by $f(x)=∫_{x1}te_{−(t+t1)}dt ,$ then (a)$f(x)$ is monotonically increasing on $[1,∞)$(b)$f(x)$ is monotonically decreasing on $(0,1)$(c)$f(2_{x})$ is an odd function of $x$ on $R$

A vertical line passing through the point $(h,0)$ intersects the ellipse $4x_{2} +3y_{2} =1$ at the points $P$ and $Q$.Let the tangents to the ellipse at P and Q meet at $R$. If $δ(h)$ Area of triangle $δPQR$, and $δ_{1}21 ≤h≤1max δ(h)$ A further $δ_{2}21 ≤h≤1min δ(h)$ Then $5 8 δ_{1}−8δ_{2}$