class 12

Missing

JEE Advanced

If at angle $θ$the light takes maximum time to travel in optical fiber. Then the maximum time is $x×10_{−8}$, calculate x.

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

The function $y=f(x)$ is the solution of the differential equation $dxdy +x_{2}−1xy =1−x_{2} x_{4}+2x $ in $(−1,1)$ satisfying $f(0)=0.$ Then $∫_{23}f(x)dx$ is

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 _______.

A circle S passes through the point (0, 1) and is orthogonal to the circles $(x−1)_{2}+y_{2}=16$ and $x_{2}+y_{2}=1$. Then (A) radius of S is 8 (B) radius of S is 7 (C) center of S is (-7,1) (D) center of S is (-8,1)

Let $f:RR$be a differentiable function such that $f(0),f(2π )=3andf_{prime}(0)=1.$If $g(x)=∫_{x}[f_{prime}(t)cosect−cottcosectf(t)]dtforx(0,2π ],$then $(lim)_{x0}g(x)=$

Let $a,b,andc$ be three non coplanar unit vectors such that the angle between every pair of them is $3π $. If $a×b+b×x=pa+qb+rc$ where p,q,r are scalars then the value of $q_{2}p_{2}+2q_{2}+r_{2} $ is

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 $f_{prime}(α)=0$

Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively.Column I, Column 2, Column 3I, $x_{2}+y_{2}=a$, (i), $my=m_{2}x+a$, (P), $(m_{2}a ,m2a )$II, $x_{2}+a_{2}y_{2}=a$, (ii), $y=mx+am_{2}+1 $, (Q), $(m_{2}+1 −ma ,m_{2}+1 a )$III, $y_{2}=4ax$, (iii), $y=mx+a_{2}m_{2}−1 $, (R), $(a_{2}m_{2}+1 −a_{2}m ,a_{2}m_{2}+1 1 )$IV, $x_{2}−a_{2}y_{2}=a_{2}$, (iv), $y=mx+a_{2}m_{2}+1 $, (S), $(a_{2}m_{2}+1 −a_{2}m ,a_{2}m_{2}+1 −1 )$The tangent to a suitable conic (Column 1) at $(3 ,21 )$is found to be $3 x+2y=4,$then which of the following options is the only CORRECT combination?(IV) (iii) (S) (b) (II) (iii) (R)(II) (iv) (R) (d) (IV) (iv) (S)

Let $a$ and $b$ be two unit vectors such that $a.b=0$ For some $x,y∈R$, let $c=xa+yb+(a×b$ If $(∣c∣=2$ and the vector $c$ is inclined at same angle $α$ to both $a$ and $b$ then the value of $8cos_{2}α$ is