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The standard reduction potentials for $Zn_{2+}/Zn,Ni_{2+}/Ni,andFe_{2+}/Fe$ are -0.76, -0.23 and -0.44 V respectively. The reaction $X+y_{2+}→+Y$ will be spontaneous when :

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The set $S={1,2,3,,12)$is to be partitioned into three sets A, B, C of equal size. Thus, $A∪B∪C=S,A∩B=B∩C=A∩C=φ$. The number of ways to partition S is

A motor cycle starts from rest and accelerates along a straight path at $2m/s_{2}$. At the starting point of the motor cycle there is a stationary electric sire. How far has the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was at rest ? (speed of sound $=330ms_{−1}$)

A thin rod of length 'L' is lying along the x-axis with its ends at $x=0andx=L$. Its linear density (mass/length) varies with x as $k(Lx )_{n}$, where n can be zero or any positive number. If the position $x_{CM}$ of the centre of mass of the rod is plotted against 'n', which of the following graph best approximates the dependence of $x_{CM}$ on n ?

The treatment of $CH_{3}MgXwithCH_{3}C≡C−H$ produces

A working transistor with its three legs marked P, Q and R is tested using a multimeter. No conduction is found between P and Q. By connecting the common (negative) terminal of the multimeter to R and the other (positive) terminal to P or Q, some resistance is seen on the multimeter. Which of the following is true for the transistor ?

Consider a uniform sqare plate of side 'a' and mass 'm'. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

The area of the plane region bounded by the curves $x+2y_{2}=0$and $x+3y_{2}=1$is equal to