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What is the effect on the interference fringes in a Young’s double-slit experiment if the separation between the two slits is increased?
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What is the effect on the interference fringes in a Young’s double-slit experiment if the separation between the two slits is increased?
Answer
In case if we increase the separation between two slits, both the actual separation of fringes and the angular separation of the fringes decreases.
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A point moves such that the sum of the squares of its distances from the two sides of length \( a\) of a rectangle is twice the sum of the squares of its distances form the other two sides of length \( b\). The locus of the point can be （ ）
A. A circle
B. An ellipse
C. A hyperbola
D. A pair of lines
A slip of paper is given to a person \(A\) who marks it either with a plus sign or a minus sign. The probability of his writing a plus sign is \(1/3\) . \(A\) passes the slip to \(B\) , who may either leave it alone or change the sign before passing it to \(C\) . Next \(C\) passes the slip to \(D\) after perhaps changing the sign. Finally, \(D\) passes it to a referee after perhaps changing the sign. \(B,C,D\) each change the sign with probability \(2/3\) .
If the referee observes a plus sign on the slip then the probability that \(A\) originally wrote a plus sign is
（ ）
If the referee observes a plus sign on the slip then the probability that \(A\) originally wrote a plus sign is
（ ）
A. \(13\text /41\)
B. \(19\text /27\)
C. \(17\text /25\)
D. \(21\text /37\)
If \(x^{y}+y^{x}+x^{x}=m^{n}\), then find the value of \(\frac {dy}{dx}\).
What is the effect on the interference fringes in a Young’s double-slit experiment if the source slit is moved closer to the double-slit plane?
Let \( A\) be a \( 3\times\;3\) matrix given by \( A=({a}_{ij}{)}_{3\times\;3}\). If for every column vector \( X\) satisfies \( {X'}AX=0\) and \( {a}_{12}=2008,{a}_{13}=1010\) and \( {a}_{23}=-2012\). Then the value of \( {a}_{21}+{a}_{31}+{a}_{32}=\)
（ ）
（ ）
A. \( -6\)
B. \( 2006\)
C. \( -2006\)
D. \( 0\)
The Edison storage cell is represented as: \(Fe(s)/FeO(s)/KOH(aq)/Ni_{2}O_{3}(s)/Ni(s)\)
The half-cell reactions are :
\(Ni_{2}O_{3}(s)+H_{2}O(l)+2e^{-}\rightleftharpoons 2NiO(s)+2OH^{-}\)\(E^{\circ }=+0.40V\)
\(FeO(s)+H_{2}O(l)+2e^{-}\rightleftharpoons Fe(s)+2OH^{-}\) \(E^{\circ }=-0.87V\). What is the cell reaction?
The half-cell reactions are :
\(Ni_{2}O_{3}(s)+H_{2}O(l)+2e^{-}\rightleftharpoons 2NiO(s)+2OH^{-}\)\(E^{\circ }=+0.40V\)
\(FeO(s)+H_{2}O(l)+2e^{-}\rightleftharpoons Fe(s)+2OH^{-}\) \(E^{\circ }=-0.87V\). What is the cell reaction?
\(^{23}Na\) is the more stable isotope of \(Na\). Find out the process by which \(^{24}_{11}Na\)can undergo radioactive decay.（ ）
A. \(\beta^{-}-emission\)
B. \(\alpha-emission\)
C. \(\beta^{+}-emission\)
D. \(K-electron capture\)
The length of a rectangle is increasing at the rate of \(3.5\) cm/sec. and its breadth is decreasing at the rate of 3 cm/sec. Find the rate of change of the area of the rectangle when length is 12 cm and breadth is 8 cm.
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At a point \( P\) on the ellipse \( \frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1\) tangent \( PQ\) is drawn. If the point \( Q\) be at a distance \( \frac{1}{P}\) from the point \( P\), where '\( P'\) is distance of the tangent from the origin, then the locus of the point \( Q \)is
（ ）
（ ）
A. \( \frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1+\frac{1}{{a}^{2}{b}^{2}}\)
B. \( \frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1-\frac{1}{{a}^{2}{b}^{2}}\)
C. \( \frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=\frac{1}{{a}^{2}{b}^{2}}\)
D. \( \frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=\frac{1}{{a}^{2}{b}^{2}}\)
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