class 12

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JEE Advanced

In the reaction the structure of the product T is

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If $α=3sin_{−1}(116 )$and $β=3cos_{−1}(94 )$, where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are)

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

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 $R$

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 :

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), $(a_{2}m_{2}+1 −a_{2}m ,a_{2}m_{2}+1 −1 )$If a tangent to a suitable conic (Column 1) is found to be $y=x+8$and its point of contact is (8,16), then which of the followingoptions is the only CORRECT combination?(III) (ii) (Q) (b) (II) (iv) (R)(I) (ii) (Q) (d) (III) (i) (P)

Perpendiculars are drawn from points on the line $2x+2 =−1y+1 =3z $ to the plane $x+y+z=3$ The feet of perpendiculars lie on the line (a) $5x =8y−1 =−13z−2 $ (b) $2x =3y−1 =−5z−2 $ (c) $4x =3y−1 =−7z−2 $ (d) $2x =−7y−1 =5z−2 $

Let $P$be a matrix of order $3×3$such that all the entries in $P$are from the set ${−1,0,1}$. Then, the maximum possible value of the determinant of $P$is ______.

A solution curve of the differential equation $(x_{2}+xy+4x+2y+4)(dxdy )−y_{2}=0$ passes through the point $(1,3)$ Then the solution curve is