class 12

Missing

JEE Advanced

The correct statement(s) about $O_{3}$ is (are)

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Let $[x]$ be the greatest integer less than or equal to $x˙$ Then, at which of the following point (s) function $f(x)=xcos(π(x+[x]))$ is discontinuous? (a)$x=1$ (b) $x=−1$ (c) $x=0$ (d) $x=2$

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 $f_{prime}(α)=0$

The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least 0.96 is :

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

Let $M$be a $2×2$symmetric matrix with integer entries. Then $M$is invertible ifThe first column of $M$is the transpose of the second row of $M$The second row of $M$is the transpose of the first column of $M$$M$is a diagonal matrix with non-zero entries in the main diagonalThe product of entries in the main diagonal of $M$is not the square of an integer

Let $f:(0,π)→R$be a twice differentiable function such that $(lim)_{t→x}t−xf(x)sint−f(x)sinx =sin_{2}x$for all $x∈(0,π)$. If $f(6π )=−12π $, then which of the following statement(s) is (are) TRUE?$f(4π )=42 π $(b) $f(x)<6x_{4} −x_{2}$for all $x∈(0,π)$(c) There exists $α∈(0,π)$such that $f_{prime}(α)=0$(d) $f(2π )+f(2π )=0$

Let $f:(−2π ,2π )R$be given by $f(x)=(g(secx+tanx))_{3}$then$f(x)$is an odd function$f(x)$is a one-one function$f(x)$is an onto function$f(x)$is an even function

Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover cards numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done isa.$264$ b. $265$ c. $53$ d. $67$