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JEE Advanced

Upon treatment with ammonical $H_{2}s$, the metal ion that precipitates as a sulfide is

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The option(s) with the values of a and L that satisfy the following equation is (are) $∫_{0}e_{t}(sin_{6}at+cos_{4}at)dt∫_{0}e_{t}(sin_{6}at+cos_{4}at)dt =L$

Let $S_{n}=k=1∑4n (−1)2k(k+1) k_{2}˙$Then $S_{n}$can take value (s)$1056$b. $1088$c. $1120$d. $1332$

A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the tune, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?

Let $f:[−21 ,2]→R$ and $g:[−21 ,2]→R$ be functions defined by $f(x)=[x_{2}−3]$ and $g(x)=∣x∣f(x)+∣4x−7∣f(x)$, where [y] denotes the greatest integer less than or equal to y for $y∈R$. Then,

Let $P$be a point in the first octant, whose image $Q$in the plane $x+y=3$(that is, the line segment $PQ$is perpendicular to the plane $x+y=3$and the mid-point of $PQ$lies in the plane $x+y=3)$lies on the z-axis. Let the distance of $P$from the x-axis be 5. If $R$is the image of $P$in the xy-plane, then the length of $PR$is _______.

The slope of the tangent to the curve $(y−x_{5})_{2}=x(1+x_{2})_{2}$at the point $(1,3)$is.

If $2x−y+1=0$ is a tangent to the hyperbola $a_{2}x_{2} −16y_{2} =1$ then which of the following CANNOT be sides of a right angled triangle? (a)$a,4,2$ (b) $a,4,1$(c)$2a,4,1$ (d) $2a,8,1$

A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation $3 x+y−6=0$ and the point D is (3 sqrt3/2, 3/2). Further, it is given that the origin and the centre of C are on the same side of the line PQ. (1)The equation of circle C is (2)Points E and F are given by (3)Equation of the sides QR, RP are