question_answer 1) Let \[(x)={{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)+{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right),x\in [-1,0]\] Then the number of points where g(x) is non-differentiable in [-1,0] is
A) 0 done
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B) 1 done
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C) 2 done
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D) 3 done
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question_answer 2) If \[{{\cos }^{-1}}x={{\sin }^{-1}}3x,\]then sum of all possible values of x equals
A) 0 done
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B) \[\frac{1}{\sqrt{10}}\] done
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C) \[\frac{2}{\sqrt{10}}\] done
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D) \[\frac{-2}{\sqrt{10}}\] done
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question_answer 3) If the three lines x - 3y = p, ax + 2y = q and ax + y = r form a right-angled triangle, then
A) \[{{a}^{2}}-9a+18=0\] done
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B) \[{{a}^{2}}-6a-18=0\] done
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C) \[{{a}^{2}}-9a+12=0\] done
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D) \[{{a}^{2}}-6a-12=0\] done
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question_answer 4) The value of definite integral \[\int\limits_{\frac{7\pi }{4}}^{\frac{7\pi }{3}}{\sqrt{{{\tan }^{2}}x}}\] dx is equal to
A) \[\ell n\,2\] done
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B) \[\ell n\,4\] done
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C) \[\frac{1}{2}\ell n\,2\] done
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D) \[\frac{3}{2}\ell n\,2\] done
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question_answer 5) The locus of the middle points of the focal chords of parabola, \[{{y}^{2}}=8x\]is another parabola whose length of latus rectum is
A) 1 done
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B) 2 done
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C) 3 done
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D) 4 done
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question_answer 6) If the lines \[\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}\]and \[\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}\]are coplanar, then the sum of all possible values of k is
A) \[-3\] done
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B) 3 done
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C) \[-4\] done
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D) 4 done
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question_answer 7) The minimum value of \[f(x)={{x}^{\frac{2}{3}}}+{{x}^{\frac{1}{3}}},x\in R\]is
A) \[\frac{-1}{2}\] done
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B) \[\frac{-1}{4}\] done
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C) \[\frac{-1}{8}\] done
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D) \[\frac{-1}{16}\] done
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question_answer 8) If \[\frac{dy}{dx}=\frac{{{y}^{3}}}{{{e}^{2x}}+{{y}^{2}}}\], and \[y\left( 0 \right)=1,\]then
A) \[{{y}^{2}}=4{{e}^{2x}}-2{{e}^{2x}}\,\,\ell ny\] done
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B) \[{{y}^{2}}={{e}^{2x}}+2{{e}^{2x}}\,\,\ell ny\] done
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C) \[{{y}^{2}}={{e}^{2x}}-\frac{1}{2}{{e}^{2x}}\,\,\ell ny\] done
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D) \[{{y}^{2}}={{e}^{2x}}+\frac{1}{2}{{e}^{2x}}\,\,\ell ny\] done
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question_answer 9) Suppose that co and z are complex numbers such that both (1 + 2i) \[\omega \] and (1 + 2i)z are different real numbers. The slope of the line connecting \[\omega \] and z in the complex plane is
A) \[-2\] done
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B) \[-1/2\] done
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C) 2 done
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D) cannot be determined done
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question_answer 10) A test is made up of 5 questions, for each question there are 4 possible answers and only one is correct. For every right choice you gain 1 mark while for each wrong choice there is a penalty of 1 mark. The probability of getting at least 2 marks answering to every question in a random way is
A) \[\frac{1}{16}\] done
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B) \[\frac{1}{64}\] done
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C) \[\frac{15}{64}\] done
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D) \[\frac{1}{1024}\] done
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question_answer 11) Four students from University \[{{U}_{1}}\], one of them is Mr. A, and five students from University \[{{U}_{2}}\], one of them is Mr. B, are going to see an Inter University Cricket tournament. However, they found, that only 5 ticket remaining, so 4 of them must go back. Suppose that at least one student from each University must go to see the game, and at least one of Mr. A and Mr. B must go to see the game. Number of ways of selecting 5 students satisfying the above constraint, is equal to
A) 126 done
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B) 140 done
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C) 104 done
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D) 116 done
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question_answer 12) A ray with the starting point at the origin in the complex plane passes through the point\[\left( 2+2i \right)\]. Another ray with the same starting point passes through the point \[(2-2\sqrt{3}i).\]The angle formed by these two
A) \[105{}^\circ \] done
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B) \[90{}^\circ \] done
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C) \[75{}^\circ \] done
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D) \[45{}^\circ \] done
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question_answer 13) \[=2\hat{i}-\hat{j}+\hat{k},\overrightarrow{q}=\hat{i}+2\hat{j}-\hat{k}\]and \[=\hat{i}+\hat{j}-2\hat{k}.\]. If \[=\overrightarrow{p}+\lambda \overrightarrow{q}\] and projection of \[\]on \[\overrightarrow{r}\] is \[\frac{4}{\sqrt{6}},\] then \[\lambda \] equals
A) \[1\] done
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B) \[\frac{1}{5}\] done
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C) \[\frac{3}{5}\] done
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D) \[\frac{2}{5}\] done
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question_answer 14) Suppose that \[f\left( 0 \right)=-3\] and \[f\left( x \right)\le 5\] for all real values of x. Then the largest value which f(2) can attain is
A) \[7\] done
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B) \[-7\] done
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C) \[13\] done
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D) \[8\] done
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question_answer 15) Angles A, B and C of a triangle ABC are in A.P. If \[\frac{b}{c}=\sqrt{\frac{3}{2}}\]- then \[\angle A\] is equal to
A) \[\pi /6\] done
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B) \[\pi /4\] done
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C) \[5\pi /12\] done
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D) \[\pi /2\] done
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question_answer 16) If a curve passes through the point \[M\left( -1,\text{ }1 \right)\]and has slope \[\left( 2x-\frac{1}{{{x}^{2}}} \right)\] at any point P(x, y) on it, then the ordinate of the point on the curve whose abscissa is \[-2\], is
A) \[\frac{5}{2}\] done
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B) \[\frac{7}{2}\] done
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C) \[\frac{9}{2}\] done
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D) \[\frac{11}{2}\] done
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question_answer 17) The area bounded by the curves \[f(x)=9{{x}^{2}}-9x+2,\,\,g(x)=9{{x}^{2}}-18x+8\]and \[x=1\] is
A) \[\frac{1}{3}\] done
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B) \[\frac{1}{2}\] done
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C) \[\frac{2}{3}\] done
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D) \[\frac{3}{4}\] done
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question_answer 18) Consider the conic \[=\frac{{{(x+1)}^{2}}}{\pi }+\frac{{{y}^{2}}}{3}=1.\] Suppose P is any point on the conic and \[{{S}_{1}},{{S}_{2}}\] are the foci of the conic, then the maximum value of \[(P{{S}_{1}}+P{{S}_{2}})\] is
A) \[2\pi \] done
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B) \[3\sqrt{\pi }\] done
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C) \[2\sqrt{\pi }\] done
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D) \[\pi \sqrt{3}\] done
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question_answer 19) If tangents drawn to circle \[\left| z \right|=4\] at points \[A({{z}_{1}})\] and \[B({{z}_{2}})\] intersect at P such that arg \[\left( \frac{{{z}_{2}}}{{{z}_{1}}} \right)=\frac{\pi }{2},\], then locus of P is
A) \[\left| z \right|=2\] done
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B) \[\left| z \right|=4\sqrt{2}\] done
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C) \[\left| z \right|=2\sqrt{2}\] done
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D) \[\left| z \right|=8\] done
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question_answer 20) If the perpendicular distance of the point (2, 3, 1) from the line \[3x+2y+z=0=x+2y\]is \[\frac{N}{\sqrt{2}}\] . Then N equals
A) 1 done
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B) 2 done
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C) 4 done
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D) 5 done
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question_answer 21) If one root of the quadratic equation \[(a-b){{x}^{2}}+ax+1=0\] is double the other root where \[a\in R\], then the greatest value of b is
A) \[\frac{7}{6}\] done
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B) \[\frac{8}{7}\] done
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C) \[\frac{9}{8}\] done
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D) \[\frac{10}{9}\] done
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question_answer 22) Let S be the sum of the first n terms of the arithmetic sequence 8, 12, 16,....., and T be the sum of first n terms of arithmetic sequence 17,19,21......... If S-T=0, then n is equal to
A) 8 done
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B) 10 done
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C) 18 done
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D) 22 done
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question_answer 23) Let \[y'(x)+\frac{g'(x)}{g(x)}y(x)=\frac{g'(x)}{1+{{g}^{2}}(x)}\]where f(x) denotes \[\frac{df(x)}{dx}\]and g(x) is a given non-constant differentiable function an R If \[g\left( 1 \right)=y\left( 1 \right)=1\]and \[g(e)=\sqrt{(2e-1)}\] then y(e) equals (Here e denotes napier's constant)
A) \[\frac{3}{2g(e)}\] done
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B) \[\frac{1}{2g(e)}\] done
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C) \[\frac{2}{3g(e)}\] done
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D) \[\frac{1}{3g(e)}\] done
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question_answer 24) Let P be arbitrary point on the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}-1=0,a>b>0.\]Suppose \[{{F}_{1}}\] and \[{{F}_{2}}\] are the foci of the ellipse. The locus of the centroid of the triangle \[P{{F}_{1}}{{F}_{2}}\] as P moves on the 1 ellipse, is
A) a circle done
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B) a parabola done
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C) an ellipse done
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D) a hyperbola done
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question_answer 25) The area bounded by the curve \[y=\frac{\cos x-\sin x}{1+\sin 2x}\]and the x-axis on the interval \[\left[ 0,\frac{\pi }{6} \right]\] , is
A) \[\sqrt{3}-2\] done
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B) \[2-\sqrt{3}\] done
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C) \[\sqrt{3}-1\] done
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D) \[2+\sqrt{3}\] done
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question_answer 26) A common tangent to the conies \[{{x}^{2}}=6y\] and \[2{{x}^{2}}-4{{y}^{2}}=9,\],is
A) \[x+y=1\] done
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B) \[x-y=1\] done
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C) \[x+y=\frac{9}{2}\] done
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D) \[x-y=\frac{3}{2}\] done
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question_answer 27) Distance from origin to the image of the point \[2\hat{i}-3\hat{j}+3\hat{k}\] in the plane \[\overrightarrow{r}.(\hat{i}-2\hat{j}-\hat{k})+1=0\]is
A) \[4\] done
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B) \[\sqrt{17}\] done
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C) \[\sqrt{18}\] done
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D) \[\sqrt{26}\] done
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question_answer 28) The relation P defined from R to R as \[a\,\,p\,\,b\,\,\Leftrightarrow 1+ab>0,\], for alia, be R is
A) reflexive only done
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B) reflexive and symmetric only done
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C) transitive only done
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D) equivalence done
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question_answer 29) The mean weight of 9 items is 15. If one more item is added to the series, the mean becomes 16. The value of 10th item is
A) 35 done
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B) 30 done
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C) 25 done
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D) 20 done
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question_answer 30) Let p and q be any two logical statements and \[r:p\to \left( \sim \text{ }p\vee \text{ }q \right)\]. If r has a truth value F, then the truth values of p and q are respectively
A) F, F done
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B) T, T done
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C) F, T done
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D) T, F done
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question_answer 31) A flag is hoisted on a car which is moving towards east with velocity 60 km/h and wind is blowing with 60 km/h south to north .The direction of flutter of the flag is:
A) north east done
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B) north west done
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C) south east done
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D) south west done
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question_answer 32) A particle is projected at an angle \[{{\tan }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]At a height, velocity of the particle is \[9\hat{i}+3\hat{j}\] (m/s). Find the height \[\left( g=10m/{{s}^{2}} \right)\]
A) 1.8 cm done
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B) 0.9 cm done
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C) 0.7m done
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D) 0.11m done
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question_answer 33) A block of mass 0.1 kg is held against a wall applying a horizontal force of 5N on the block. If the coefficient of friction between the block and the wall is 0.50, the magnitude of frictional force acting on the block is:
A) 2.5 N done
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B) 4.9N done
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C) 0.49 N done
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D) 0.98 N done
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question_answer 34) A hemispherical vessel of radius R moving with a constant velocity \[{{v}_{0}}\] and containing a ball, is suddenly halted. Find the height by which ball will rise in the vessel. The surface is smooth.
A) \[\frac{v_{0}^{2}}{2g}\] done
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B) \[\frac{2v_{0}^{2}}{g}\] done
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C) \[\frac{v_{0}^{2}}{g}\] done
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D) none done
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question_answer 35) Four particles A, B, C and D of equal masses are placed at the comers of a square. They move with equal uniform speed V towards the intersection of the diagonals. After collision A comes to rest, B traces its path back with same speed and C and D move with equal velocities. What is the velocity of C after collision.
A) \[\frac{2V}{3}\] done
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B) \[2V\] done
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C) \[\frac{V}{2}\] done
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D) \[V\] done
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question_answer 36) A equilateral triangle ABC formed from a uniform wire has two small indentical beads initially located at A. The triangle is set rotating about the vertical axis AO. Then the beads are released from rest simultaneously and allowed to slide down one along AB and the other along AC, as shown, neglect friction. The quantities that are conserved as beads slies down are:
A) angular velocity and total energy. done
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B) angular velocity and moment of inertia about axis of rotation done
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C) total angular momentum and moment of inertia about axis of rotation. done
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D) total angular momentum and total energy. done
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question_answer 37) A particle is executing SHM. At a point x = A/3, kinetic energy of the particle is K, where A is the amplitude. At a point x = 2A/3, kinetic energy of the particle will be :
A) \[2K\] done
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B) \[\sqrt{2}K\] done
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C) \[\frac{5}{8}K\] done
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D) \[\frac{5}{3}K\] done
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question_answer 38) The orbital velocity of a satellite at point B with radius \[{{r}_{B}}\] is v. The radius of point A is \[{{r}_{A}}.{{r}_{A}}\]and \[{{r}_{B}}\] are semi major and semi minor axis respectively. If the orbit is increased in radial direction so that \[{{r}_{A}}\] becomes 1\[1.2{{r}_{A}}\]. find the orbital velocity at \[(1.2{{r}_{A}})\]
A) \[\frac{v{{r}_{B}}}{{{r}_{A}}\sqrt{1.2}}\] done
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B) \[\frac{v{{r}_{A}}}{1.2{{r}_{B}}}\] done
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C) \[\frac{v{{r}_{B}}}{1.2{{r}_{A}}}\] done
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D) \[\frac{v{{r}_{B}}}{{{r}_{B}}\sqrt{1.2}}\] done
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question_answer 39) Wire A and B are connected with blocks P are as shown. The ratio of lengths, radii and Young?s modulus of wires A and B are r, 2r and 3r respectively (r is a constant). Find the mass of block P if ratio of increase in their corresponding lengths is \[1/6{{r}^{2}}\]. The mass of block Q is 3M.
A) M done
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B) 3M done
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C) 6M done
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D) 9M done
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question_answer 40) Earth's receives \[1400W/{{m}^{2}}\] of solar power. If all the solar energy falling on a lens of area \[0.2{{m}^{2}}\]is focused onto a block of ice of mass 280 g, the time taken to melt the ice will be (in min.)
A) 10.2 done
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B) 7.8 done
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C) 5.5 done
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D) 4.8 done
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question_answer 41) A bubble rises from bed of a lake to its surface. The depth of lake is 103 times the value by which bubble increases in size. If the atmospheric pressure is equal to pressure due to a column of water of 10 m, find the value by which bubble increases in size (approximately)
A) 100 done
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B) 10 done
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C) \[10\sqrt{2}\] done
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D) \[10\sqrt{3}\] done
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question_answer 42) The snapshot of a wave is shown at \[t=0\]. Find x-coordinate of point P in \[\lambda \], while the wave speed is 300 m/sec.
A) \[\frac{27\lambda }{12}\] done
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B) \[\frac{29\lambda }{12}\] done
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C) \[\frac{25\lambda }{12}\] done
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D) \[\frac{31\lambda }{12}\] done
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question_answer 43) What should be the angle of incidence at A of the spherical glass placed in air so that total internal reflection takes place at B?
A) \[30{}^\circ \] done
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B) \[45{}^\circ \] done
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C) \[60{}^\circ \] done
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D) \[90{}^\circ \] done
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question_answer 44) In compound microscope, the intermediate image is:
A) virtual, erect and magnified done
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B) real, erect and magnified done
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C) real, inverted and magnified done
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D) virtual, erect and reduced done
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question_answer 45) Three charges \[+Q,+q\] and \[+q\] are placed at the vertices of a right angle triangle (isosceles triangle) as shown. The net electrostatic energy of the configuration is zero, if Q is equal to:
A) \[\frac{q}{1+\sqrt{2}}\] done
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B) \[\frac{-2q}{2+\sqrt{2}}\] done
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C) \[-2q\] done
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D) \[+q\] done
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question_answer 46) A parallel place capacitor of capacitance C is connected to a battery and is charged to a potential difference V. Another capacitor of capacitance 2C is similarly charged to a potential difference 2V. The charging battery is now disconnected and the capacitor are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is:
A) zero done
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B) \[\frac{3}{2}C{{V}^{2}}\] done
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C) \[\frac{25}{6}C{{V}^{2}}\] done
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D) \[\frac{9}{2}C{{V}^{2}}\] done
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question_answer 47) A battery of internal resistance 4Q-is connected to the network of resistances as shown. In order that the maximum power can be delivered to the network, the value of R in \[\Omega \] should be
A) 4/9 done
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B) 2 done
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C) 8/3 done
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D) 18 done
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question_answer 48) The current is uniformly distributed over the cross-section of a straight cylindrical conductor of radius r. The variation of magnetic field B along a distance x from axis of conductor is shown in the curves. Find the correct option:
A) done
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B) done
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C) done
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D) done
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question_answer 49) A small square loop of wire of side \[l\] is placed inside a large square loop of wire of side L \[\left( L>>l \right)\]. The loops are coplanar and their centre coincides. The mutual inductance of the system is proportional to:
A) \[l/L\] done
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B) \[{{l}^{2}}/L\] done
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C) \[L/l\] done
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D) \[{{L}^{2}}/l\] done
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question_answer 50) LCR circuit is connected to a 200 V, AC source L= 10 H, \[C=160\mu F\] and \[R=80\Omega \] at resonance. Let \[{{i}_{1}},{{i}_{2}}\] and \[{{i}_{3}}\] be rms current through L, C and R respectively then:
A) \[{{i}_{1}}={{i}_{2}}\] and \[{{i}_{1}}>{{i}_{3}}\] done
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B) \[{{i}_{1}}={{i}_{2}}\] and \[{{i}_{1}}<{{i}_{3}}\] done
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C) \[{{i}_{1}}={{i}_{2}}\]and \[{{i}_{2}}={{i}_{3}}\] done
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D) \[{{i}_{1}}={{i}_{2}}\]and \[{{i}_{3}}=0\] done
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question_answer 51) After 280 days, the activity of a radioactive sample is 600 dps. The activity reduces to 300 dps after another 140 days. The initial activity of the sample in dps is:
A) 6000 done
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B) 9000 done
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C) 3000 done
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D) 24000 done
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question_answer 52) \[{{K}_{\alpha }}\]wavelength emitted by an atom of atomic number \[Z=11\]is \[\lambda \]. Find the atomic number for an atom that emits \[{{K}_{\alpha }}\]radiation with wavelength \[4\lambda \].
A) \[Z=6\] done
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B) \[Z=4\] done
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C) \[Z=11\] done
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D) \[Z=44\] done
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question_answer 53) A proton colloids with a stationary hydrogen atom in ground state elastically. Energy of colliding photon is 10.2eV. After a time interval of the order microsecond another photon collides with same hydrogen atom in elastically with an energy of 15 eV. What will be observed by the detector:
A) 2 photon of energy 10.2 eV done
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B) 2 photon of energy 1.4 eV done
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C) One photon of energy 10.2 eV and an electron of energy 1.4 Ev done
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D) One photon of energy 10.2 eV and another photon of energy 1.4 eV done
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question_answer 54) How much energy an electron in the hydrogen atom in ground state should absorb so that its angular momentum changes by \[\left( h/\pi \right)\]
A) 12.1eV done
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B) 10.2eV done
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C) 12.75 eV done
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D) 13.05 eV done
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question_answer 55) The circuit sown in figure contains two diodes each with a forward resistance of 500 and with infinite backward resistance. If the battery voltage is 6V, the current through 100W resistance (in amperes) is:
A) zero done
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B) 0.02 done
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C) 0.03 done
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D) 0.036 done
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question_answer 56) Height of the antena use to transmit wave of wavelength \[\lambda \]is H choose correct option?
A) \[H<\frac{\lambda }{8}\] done
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B) \[H<\frac{\lambda }{4}\] done
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C) \[H>\frac{\lambda }{4}\] done
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D) \[H<\frac{\lambda }{10}\] done
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question_answer 57) A radar has power of 1kW and is operating at a frequency 10 GHz. It is located on a steep mountain of height 600 m. The maximum distance up to which it can detect an object on the surrounding earth surface is :
A) 87.6 km done
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B) 26.4 km done
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C) 43.5 km done
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D) 15.2 km done
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question_answer 58) In any reversible isothermal expansion the Entropy of gas will :
A) decrease done
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B) increase done
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C) stable done
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D) uncertain done
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question_answer 59) The time period of a simple pendulum is 2 sec. Initial amplitude is 10 degree becomes 5degree in 100 oscillations .The quality factor of the weakly damped oscillation will be:
A) \[\pi 200/In\,2\] done
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B) \[\pi 100/In\,2\] done
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C) \[\pi 300/In\,2\] done
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D) None done
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question_answer 60) Two simple harmonic motions are represented by the equations \[{{y}_{1}}=0.1\,\sin \,(100\pi t+\pi /3)\] and \[\,(100\pi t+\pi /3)\]. The phase difference of the velocity of particle 1 with respect to the velocity of particle 2is:
A) \[-\pi /3\] done
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B) \[\pi /6\] done
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C) \[-\pi /6\] done
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D) \[\pi /3\] done
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question_answer 61) \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}.5{{H}_{2}}O\] Sodium thiosulphate is used in photography to
A) remove reduced silver done
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B) remove unrecompensed \[AgBr\]as soluble silver thiosulphate complex done
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C) convert the metallic silver to silver salt done
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D) reduce the silver bromide grains to metallic silver done
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question_answer 62) How many elements would be in the IInd period of the Period Table if the spin quantum numbers could have the value \[+\frac{1}{2},0,-\frac{1}{2}?\]
A) 18 done
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B) 12 done
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C) 10 done
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D) 8 done
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question_answer 63) 1 mol \[C{{H}_{3}}OOH\] is added in 250 g benzene. Acetic acid diereses in benzene due to hydrogen bond K of benzene is \[2\text{ }K\text{ }kgmo{{l}^{-1}}\]. The boiling point has increased by 6.4K. % dimerisation of acetic acid is:
A) 150 done
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B) 40 done
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C) 30 done
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D) 20 done
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question_answer 64) Time taken to produce 1 mol of photon by a \[100\text{ }W\text{ }\left( J{{s}^{-1}} \right)\]yellow lamp is (Given \[\lambda \] of light is 500 nm):
A) 340min done
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B) 12min done
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C) 36 min done
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D) 40min done
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question_answer 65) Given is the graph between \[{{\left( a-x \right)}^{-1}}\]and time. Hence, rate at the start of the reaction is
A) \[1.25\text{ }mol\text{ }{{L}^{-1}}\text{ }mi{{n}^{-1}}\] done
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B) \[0.125\text{ }mol\text{ }{{L}^{-1\text{ }}}mi{{n}^{-1}}\] done
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C) \[0.5\text{ }mol\text{ }{{L}^{-1}}\text{ }mi{{n}^{-1}}\] done
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D) \[1.25\text{ }mol\text{ }mi{{n}^{-1}}\] done
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question_answer 66) The substance, P, Q and R have coagulation values 3, 0.6, 0.08 for a metal sol respectively. Their flocculating powers are in the ratio:
A) \[0.0267:5:1\] done
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B) \[1:5;\text{ }37.5\] done
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C) \[0.08:0.6:3\] done
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D) \[1:0.2:0.0267\] done
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question_answer 67) \[{{H}_{2}}S\]reacts with lead acetate forming a black compound which reacts with \[{{H}_{2}}{{O}_{2}}\] to form another compound. The colour of the compound is:
A) pink done
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B) black done
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C) yellow done
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D) white done
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question_answer 68) 1 mole of an ideal gas is subject to a reversible process as shown in the figure. Calculate the work done (in joule) in the process. [In 2 =0.7]
A) 0.6 Joule done
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B) 6 Joule done
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C) 8 Joule done
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D) 0.8 Joule done
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question_answer 69)
(I) \[{{\{MnC{{l}_{6}}\}}^{3-}},{{[Fe{{F}_{6}}]}^{3-}}\], and \[{{[Co{{F}_{6}}]}^{3-}}\]are paramagnetic having four, five and four unpaired electrons respectively. (II) Valence bond theory gives a quantitative interpretation of the thermodynamic stabilities of coordination compounds. (III) The crystal field spliting \[{{\Delta }_{o}}\], depends upon the field produced by the ligand and charge on the metal ion.
Amongst the following correct statements are:
A) I, III done
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B) I, II done
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C) I, II, III done
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D) II, III done
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question_answer 70) In which of the following reaction \[C{{H}_{4}}\] will be obtained?
(i) \[C{{H}_{3}}-Mg\,Br+C{{H}_{3}}-C\equiv CH\] (ii) (iii) \[C{{H}_{3}}-MgBr+C{{H}_{3}}OH\] (iv)
A) (i),(ii) & (iii) done
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B) (i), (ii),(iii) & (iv) done
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C) (iii) & (iv) done
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D) (iii) & (i),(iv) done
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question_answer 71) The following carbohydrate is:
A) a ketohexose done
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B) an aldohexose done
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C) an a-furanose done
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D) a ketopentose done
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question_answer 72) In the given reaction sequence B is
A) done
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B) done
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C) done
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D) done
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question_answer 73) \[Ph-\underset{o}{\mathop{\underset{||}{\mathop{C}}\,}}\,-\overset{Et}{\mathop{\overset{|}{\mathop{\underset{Me}{\mathop{\underset{|}{\mathop{C}}\,}}\,}}\,}}\,-\underset{O}{\mathop{\underset{||}{\mathop{C}}\,}}\,-C{{H}_{3}}\xrightarrow[\underset{(3)\Delta }{\mathop{(2){{H}^{\oplus }}}}\,]{(1){{\text{l}}_{2}}/O{{H}^{\oplus }}}\] product is:
A) \[Ph-\underset{o}{\mathop{\underset{||}{\mathop{C}}\,}}\,-\overset{Me}{\mathop{\overset{|}{\mathop{\underset{Et}{\mathop{\underset{|}{\mathop{C}}\,}}\,}}\,}}\,-COOH\] done
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B) \[Ph-\underset{o}{\mathop{\underset{||}{\mathop{C}}\,}}\,-\underset{Et}{\mathop{\underset{|}{\mathop{C}}\,}}\,-Me\] done
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C) \[Ph-\underset{o}{\mathop{\underset{||}{\mathop{C}}\,}}\,-O-\underset{Et}{\mathop{\underset{|}{\mathop{CH}}\,}}\,-Et\] done
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D) \[Ph-\underset{o}{\mathop{\underset{||}{\mathop{C}}\,}}\,-\underset{Me}{\mathop{\underset{|}{\mathop{CH}}\,}}\,-OEt\] done
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question_answer 74) Arrange the following compound in decreasing order of rate of electrophilic substitution reaction:
A) \[\left( I \right)>\left( III \right)>\left( II \right)>\left( IV \right)\] done
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B) \[\left( III \right)>\left( I \right)>\left( II \right)>(IV)\] done
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C) \[\left( I \right)>\left( II \right)>\left( III \right)>\left( IV \right)\] done
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D) \[\left( I \right)>\left( IV \right)>\left( II \right)>\left( III \right)\] done
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question_answer 75) The structure of product (P) is
A) done
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B) done
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C) done
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D) done
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question_answer 76) Among the following select the correct the statements:
(I) \[P{{H}_{5}}\] do not exist. (II) \[p\pi -d\pi \] bond is present in \[S{{O}_{2}}\]. (III) \[Se{{F}_{4}}\] and \[C{{H}_{4}}\] have the same shape. (IV) \[\text{l}_{3}^{+}\]has a bent shape.
A) II, III done
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B) I, II done
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C) I, IV done
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D) I, II, IV done
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question_answer 77) In the process of extraction of silver, Identify the complexes [P] and [Q]
A) \[P={{[Ag{{(CN)}_{4}}]}^{-}},Q,={{[Zn{{(CN)}_{4}}]}^{2-}}\] done
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B) \[P={{[Ag{{(CN)}_{4}}]}^{-}},Q,={{[Zn{{(CN)}_{6}}]}^{4-}}\] done
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C) \[P={{[Ag{{(CN)}_{4}}]}^{3-}},Q,={{[Zn{{(CN)}_{4}}]}^{2-}}\] done
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D) \[P={{[Ag{{(CN)}_{2}}]}^{-}},Q,={{[Zn{{(CN)}_{4}}]}^{2-}}\] done
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question_answer 78) If \[{{r}_{0}}\] be the radius of first Bohr's orbit of H-atom, the de-Broglie's wavelength of an electron revolving q in third Bohr's orbit will be:
A) \[2\pi {{r}_{0}}\] done
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B) \[4\pi {{r}_{0}}\] done
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C) \[6\pi {{r}_{0}}\] done
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D) \[\pi {{r}_{0}}\] done
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question_answer 79) A \[5.0\text{ }c{{m}^{3}}\] solution of \[{{H}_{2}}{{O}_{2}}\] liberates 0.508 g of \[{{1}_{2}}\], from an acidified KI solution. The strength of \[{{H}_{2}}{{O}_{2}}\], solution in terms of volume strength at STP is:
A) 2.24V done
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B) 1.12V done
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C) 4.48V done
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D) 8.96V done
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question_answer 80) For the equilibrium, \[CuS{{O}_{4}}.5{{H}_{2}}O(s)\rightleftharpoons CuS{{O}_{4}}.3{{H}_{2}}O(s)+2{{H}_{2}}O(g),{{K}_{p}}=1.086\times {{10}^{-4}}\] at \[{{25}^{o}}C\]. The efflorescent nature of \[CuS{{O}_{4}}.5{{H}_{2}}O(s)\] can be noticed when the vapour pressure of water in the atmosphere is (in mm Hg):
A) \[10.92\] done
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B) \[7.90\] done
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C) \[<7.90\] done
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D) \[>7.90\] done
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question_answer 81) The reaction of \[Xe{{F}_{6}}\], with silica \[(Si{{O}_{2}})\] gives:
A) \[Xe{{O}_{3}}\] and \[Si{{F}_{4}}\], done
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B) \[Xe{{F}_{4}}\],and \[Si{{F}_{4}}\], done
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C) \[XeO{{F}_{2}}\],and \[Si{{F}_{4}}\], done
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D) \[XeO{{F}_{4}}\].and \[Si{{F}_{4}}\], done
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question_answer 82) In FCC lattice A, B, C, D atoms are arranged at corners, face centres, octahedral voids and tetrahedral voids respectively then the body diagonal contains:
A) 2A, 2D done
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B) 2A, C, 2D done
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C) 2A, 2B, D done
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D) 2A, 2B, 2C done
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question_answer 83)
(I) \[{{\left[ Co\left( EDTA \right) \right]}^{-}}\]has two optical isomers. (II) \[{{\left[ Co{{\left( N{{H}_{3}} \right)}_{4}},{{\left( N{{O}_{2}} \right)}_{2}} \right]}^{+}}\]show linkage isomers. (Ill) For \[[Pt(py)(N{{H}_{3}})(N{{O}_{2}})ClBrl]\]Theoretically fifteen different geometrical isomers are possible. (IV) \[[Cr{{({{H}_{2}}O)}_{4}}C{{l}_{2}}]\,\,C{{l}_{2}}.2{{H}_{2}}O\]can show hydrate as well as ionisation isomerism.
Amongst the following correct statements are:
A) II, III done
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B) III done
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C) I, III done
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D) I, III & III done
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question_answer 84) The vander Waals' constant 'a' for the gases\[C{{H}_{4}},{{N}_{2}},N{{H}_{2}}\], and \[{{O}_{2}}\] are \[2.25,1.39,4.17\]and at \[1.3\text{ }{{L}^{2}}\] atai- \[mo{{l}^{-2}}\] respectively. The gas which shows highest critical temperature is:
A) \[C{{H}_{4}}\] done
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B) \[{{N}_{2}}\] done
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C) \[N{{H}_{3}}\] done
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D) \[{{O}_{2}}\] done
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question_answer 85) In the formation of \[HBr\] from \[{{H}_{2}}\] & \[B{{r}_{2}}\], following mechanism is observed.
[1] \[B{{r}_{2}}2Br\centerdot \]Equilibrium step [2] \[{{H}_{2}}+Br\centerdot \xrightarrow{{}}HBr+H\centerdot \]Slow step [3]\[H\centerdot +B{{r}_{2}}\xrightarrow{{}}HBr+Br\centerdot \] Fast step
Calculate the rate of reaction, if concentration of hydrogen is twice that of bromine and the rate constant is equal to \[I{{M}^{-1/2}}Se{{c}^{-1}}\]. Concentration of bromine is 1M.
A) \[2M\,Se{{c}^{-1}}\] done
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B) \[3M\,Se{{c}^{-1}}\] done
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C) \[4M\,Se{{c}^{-1}}\] done
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D) \[5M\,Se{{c}^{-1}}\] done
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question_answer 86) \[Zn\] Amalgam is prepared by electrolysis of aqueous \[ZnC{{l}_{2}}\] using Hg cathode (9gm). How much current is to be passed through \[ZnC{{l}_{2}}\] solution for 1000 seconds to prepare a Zn Amalgam with 25% Zn by wt.(Zn=65.4)
A) 5.6 amp done
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B) 7.2 amp done
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C) 8.85 any done
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D) 11.2 amp done
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question_answer 87) A certain acid-base indicator is red in acid solution and blue in basic solution. At pH = 5.75% of the indicator is present in the solution in its blue form. Calculate the pH at which the indicator shows 90% red form? \[\left( Given\text{ }{{10}^{-4.523}}=3\times {{10}^{-5}} \right)\]
A) 3.56 done
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B) 5.47 done
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C) 2.5 done
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D) 7.4 done
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question_answer 88) Which of the following is used in relieving pain?
A) Acetyl salicylic acid done
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B) Methyl salicylate done
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C) Methyl acetate done
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D) Phenylacrylate done
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question_answer 89) The major produce is:
A) done
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B) done
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C) done
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D) done
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question_answer 90) D-Glucose and D-Mannose are
A) Anomers done
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B) Enantiomers done
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C) Geometrical isomers done
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D) Epimers done
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