question_answer2) The system of linear equations \[x+\lambda y-z=0\] \[\lambda x-y-z=0\] \[x+y-\lambda z=0\] has a non-trivial solution for :
[JEE Main Solved Paper-2016 ]
question_answer3) A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then :
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question_answer4) A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is \[30{}^\circ \]. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is \[60{}^\circ \]. Then the time taken (in minutes) by him, form B to reach the pillar, is :
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question_answer5) Let two fair six-faced dice A and B be thrown simultaneously. If \[{{E}_{1}}\] is the event that die A shows up four, \[{{E}_{2}}\]is the event that die B shows up two and \[{{E}_{3}}\] is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true ?
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question_answer8) The distance of the point (1, -5, 9) from the plane x - y + z = 5 measured along the line x = y = z is :
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question_answer9) The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is :
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question_answer10) Let P be the point on the parabola, y2 = 8x which is at a minimum distance from the center C of the circle, \[{{x}^{2}}+{{(y+6)}^{2}}=1\]. Then the equation of the circle, passing through C and having its centre at P is :
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question_answer12) Consider \[f(x)={{\tan }^{-1}}\left( \sqrt{\frac{1+\sin x}{1-\sin x}} \right),x\in \left( 0,\frac{\pi }{2} \right).\] A normal to \[y=f(x)at\,x=\frac{\pi }{6}\]also passes through the point :
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question_answer13) Two sides of a rhombus are along the lines, \[x-v+1=0\]and \[\text{7x}\text{y}\text{5}=0.\] If its diagonals intersect at (-1, -2), then which one of the following is a vertex of this rhombus ?
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question_answer14) If a curve y = f(x) passes through the point (1, -1) and satisfies the differential equation, \[y(1+xy)dx=xdy,\]then \[f\left( -\frac{1}{2} \right)\] is equal to :
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question_answer15) If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is :
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question_answer16) If the 2nd, 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is :-
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question_answer17) If the number of terms in the expansion of \[{{\left( 1-\frac{2}{x}+\frac{4}{{{x}^{2}}} \right)}^{n}},x\ne 0,\] , is 28, then the sum of the coefficients of all the terms in this expansion, is :-
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question_answer18) If the sum of the first ten terms of the series \[{{\left( 1\frac{3}{5} \right)}^{2}}+{{\left( 2\frac{2}{5} \right)}^{2}}+{{\left( 3\frac{1}{5} \right)}^{2}}+....,\]is\[\frac{16}{5}m,\]then m is equal to :-
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question_answer19) If the line,\[\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}\]lies in the plane, \[1x+my-z=9,\]then\[{{1}^{2}}{{+}^{2}}\] is equal to :-
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question_answer22) If one of the diameters of the circle, given by the equation, \[\text{x2}+\text{y2}\text{4x}+\text{6y}\text{12}=0,\]is a chord of a circle S, whose centre is at (-3, 2), then the radius of S is :-
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question_answer24) The centres of those circles which touch the circle, \[{{\text{x}}^{\text{2}}}+{{\text{y}}^{\text{2}}}\text{8x}\text{8y}\text{4}=0,\]externally and also touch the x-axis, lie on :-
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question_answer25) Let\[\overrightarrow{a},\overrightarrow{b}\]\[\overrightarrow{c}\]be three unit vectors such that\[\overrightarrow{a}\times \left( \overrightarrow{b}\times \overrightarrow{c} \right)=\frac{\sqrt{3}}{2}\left( \overrightarrow{b}+\overrightarrow{c} \right).\]If \[\overrightarrow{b}\]is not parallel to \[\overrightarrow{c}\], then the angle between \[\overrightarrow{a}\]and\[\overrightarrow{b}\]is :-
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question_answer26) Let\[p=\underset{x\to 0+}{\mathop{\lim }}\,{{\left( 1+{{\tan }^{2}}\sqrt{x} \right)}^{\frac{1}{2x}}}\] then log p is equal to :-
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question_answer27) If \[0\le x<2\pi ,\]then the number of real values of x, which satisfy the equation \[\cos x+\cos 2x+\cos 3x+\cos 4x=0,\]is :-
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question_answer28) The sum of all real values of x satisfying the equation \[{{\left( {{x}^{2}}-5x+5 \right)}^{{{x}^{2}}+4x-60}}=1\]is :-
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question_answer29) The area (in sq. units) of the region \[\{(x,y):{{y}^{2}}\ge 2x\]and\[{{x}^{2}}+{{y}^{2}}\le 4x,x\ge 0,y\ge 0\]\[\}\] is :-
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