Solved papers for JEE Main & Advanced JEE Main Paper (Held On 22 April 2013)
done JEE Main Paper (Held On 22 April 2013) Total Questions - 30
question_answer1) The number of ways in which an examiner can assign 30 marks to 8 question, giving not less than 2 marks to any question, is:
JEE Main Online Paper (Held On 22 April 2013)
question_answer2) If the system of linear equations \[{{x}_{1}}+2{{x}_{2}}+3{{x}_{3}}=6\] \[{{x}_{1}}+3{{x}_{2}}+5{{x}_{3}}=9\] \[2{{x}_{1}}+5{{x}_{2}}+a{{x}_{3}}=b\] is consistent and has infinite number of solutions, then:
JEE Main Online Paper (Held On 22 April 2013)
A)
\[a=8,b\] can be any real number
doneclear
B)
\[b=15,\]a cab be any real number
doneclear
C)
\[a=R-\{8\}\] and \[\operatorname{b}\in \operatorname{R}-[15]\]
question_answer3) Given sum of the first n terms of an A.P. is \[2n+3{{n}^{2}}\]. Anther A.P. is formed with the same first term and double of the common difference, the sum of n terms of the new A.P. is :
JEE Main Online Paper (Held On 22 April 2013)
question_answer4) Statement 1: The function \[{{x}^{2}}({{\operatorname{e}}^{x}}+{{\operatorname{e}}^{-x}})\]is increasing for all \[x>0.\] Statement 2: The functions \[{{x}^{2}}{{e}^{x}}\] and \[{{x}^{2}}{{e}^{-x}}\] are increasing for all \[x>0\] and the sum of two increasing functions in any interval (a, b) is an increasing function in (a, b).
JEE Main Online Paper (Held On 22 April 2013)
A)
Statement 1 is false; Statement 2 is true.
doneclear
B)
Statement 1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.
doneclear
C)
Statement 1 is true; Statement 2 is false.
doneclear
D)
Statement 1 is true; Statement 2 is true; Statement 2 is a correct explanation for Statement 1.
question_answer5) Mean of 5 observations is 7. If four of these observations are 6, 7, 8, 10 and one is missing then the variance of all the five observations is :
JEE Main Online Paper (Held On 22 April 2013)
question_answer6) The area of the region (in sq. units), in the first quadrant, bounded by the parabola \[y=9{{x}^{2}}\] and the lines \[x=0,\] \[y=1\] and \[y=4\] is:
JEE Main Online Paper (Held On 22 April 2013)
question_answer7) If the \[x-\] intercept of some line L is double as that of the line, \[3x+4y=12\] and the \[y-\]intercept of L is half as that of the same line. Then the slope of L is :
jEE Main Online Paper (Held On 22 April 2013)
question_answer8) The sum \[\frac{3}{{{1}^{2}}}+\frac{5}{{{1}^{2}}+{{2}^{2}}}+\frac{7}{{{1}^{2}}+{{2}^{2}}+{{3}^{2}}}+...\] upto 11 ?terms is:
JEE Main Online Paper (Held On 22 April 2013)
question_answer9) The integral \[\int\limits_{7\pi /4}^{7\pi /3}{\sqrt{{{\tan }^{2}}}x\operatorname{d}x}\] is equal to :
JEE Main Online Paper (Held On 22 April 2013)
question_answer10) Let \[\operatorname{R}=\{(3,3),(5,5),(9,9)(12,12),\] \[(5,12),(3,9),(3,12)(3,5),\}\] be a relation on the set A = {3, 5, 9, 12} . Then, R is :
JEE Main Online Paper (Held On 22 April 2013)
question_answer11) If a complex number z satisfies the equation \[z+\sqrt{2}\left| z+1 \right|+i=0,\operatorname{then}\left| z \right|\] is equal to :
JEE Main Online Paper (Held On 22 April 2013)
question_answer12) If the 7th term in binomial expansion of \[{{\left( \frac{3}{^{3}\sqrt{84}}+\sqrt{3}\operatorname{In}x \right)}^{9}},x>0,\] equal to 729, then \[x\]cab be :
JEE Main Online Paper (Held On 22 April 2013)
question_answer13) Statement 1: The line \[x-2y=2\] meets the parabola, \[{{y}^{2}}+2x=0\] only at the point \[(-2,-2):\] Statement 2: The line \[y=mx-\frac{1}{2m}(\operatorname{m}\#0)\]is tangent to the parabola, \[{{y}^{2}}=-2x\] at the point \[\left( -\frac{1}{2{{\operatorname{m}}^{2}}},\frac{1}{\operatorname{m}} \right).\]
JEE Main Online Paper (Held On 22 April 2013)
A)
Statement 1 is true; Statement 2 is false.
doneclear
B)
Statement 1 is true; Statement 2 is true; Statement 2 is a correct explanation for Statement 1.
doneclear
C)
Statement 1 is false; Statement 2 is true.
doneclear
D)
Statement 1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.
question_answer14) If a circle C passing though (4, 0) touches the circle \[{{x}^{2}}+{{y}^{2}}+4x-6y-12=0\] externally at point (1, -1), then the radius of the circle C is:
JEE Main Online Paper (Held On 22 April 2013)
question_answer15) Let Q be the foot of perpendicular from the origin to the plane \[4x-3y+z+13=0\] and R be point (-1, 1, -6) on the plane Then length QR is :
JEE Main Online Paper (Held On 22 April 2013)
question_answer16) Given two independent events, if the probability that exactly one of them occurs is \[\frac{26}{49}\] and the probability that nine of them occurs is \[\frac{15}{49},\] then the probability of more probable of the two events is :
JEE Main Online Paper (Held On 22 April 2013)
question_answer19) If \[\int{\frac{{{x}^{2}}-x+1}{{{x}^{2}}+1}e{{\cot }^{-1}}}x\operatorname{d}x=\operatorname{A}(x){{\operatorname{e}}^{{{\cot }^{-1}}}}x+C,\] then A\[\left( x \right)\] is equal to :
JEE Main Online Paper (Held On 22 April 2013)
question_answer20) If two vertices of an equilateral triangle are \[\operatorname{A}(-a,0)\] and \[B(a,\,0),\,a>0\], the third vertex C lies above \[x-\]axis then the equation of the circumcircle of \[\Delta \operatorname{ABC}\] is :
JEE Main Online Paper (Held On 22 April 2013)
question_answer21) The acute angle between two lines such that the direction cosines I, m, n of each of them satisfy the equations I + m + n = 0 and \[{{\operatorname{I}}^{2}}+{{\operatorname{m}}^{2}}-{{\operatorname{n}}^{2}}=0\] is:
JEE Main Online Paper (Held On 22 April 2013)
question_answer22) Consider the differential equation \[\frac{dy}{dx}=\frac{{{y}^{3}}}{2(x{{y}^{2}}-{{x}^{2}})}:\] Statement 1: The substitution \[z={{y}^{2}}\] transforms the above equation into a first order homogenous differential equation. Statement 2: The solution of this differential equation is \[{{y}^{2}}e\frac{-{{y}^{2}}}{x}=C.\]
question_answer23) The number of solution of the equation, \[{{\sin }^{-1}}\] \[x=2\] \[{{\tan }^{-1}}\] \[x\] (in principal values is :)
JEE Main Online Paper (Held On 22 April 2013)
question_answer24) For \[>0,\operatorname{t}\in \left( 0,\frac{\pi }{2} \right),\] let \[x=\sqrt{{{a}^{\sin -1}}t}\] and \[y=\sqrt{a{{\cos }^{-1}}\operatorname{t}}.\] Then , \[1+{{\left( \frac{\operatorname{dy}}{dx} \right)}^{2}}\]equals:
JEE Main Online Paper (Held On 22 April 2013)
question_answer25) If p, q, r are 3 real numbers satisfying the matrix equation, \[[p\,q\,r]\left[ \begin{matrix} 3 & 4 & 1 \\ 3 & 2 & 3 \\ 2 & 0 & 2 \\ \end{matrix} \right]=[3\,\,0\,\,1]\] then \[2\operatorname{p}+\operatorname{q}-\operatorname{r}\] equals:
JEE Main Online Paper (Held On 22 April 2013)
question_answer26) If \[\hat{a},\hat{b}\] and \[\hat{c}\] are unit vectors satisfying \[\hat{a}-\sqrt{3}\] \[\hat{b}+\hat{c}=\overset{\to }{\mathop{0}}\,\] then the angle between the vectors \[\hat{a}\] and \[\hat{c}\] is :
JEE Main Online Paper (Held On 22 April 2013)
question_answer27) Let the equations of two ellipses be \[{{\operatorname{E}}_{1}}:\frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{2}=1\] and \[{{\operatorname{E}}_{2}}:\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{{{\operatorname{b}}^{2}}}=1\]. If the product of their eccentricities is \[\frac{1}{2},\] then the length of the minor axis of ellipse \[{{\operatorname{E}}_{2}}\] is:
JEE Main Online Paper (Held On 22 April 2013)
question_answer28) If \[\alpha \] and \[\beta \] are roots of the equation \[{{x}^{2}}+\operatorname{p}x+\frac{3\operatorname{p}}{4}=0,\] such that \[\left| \alpha -\beta \right|\]=\[\sqrt{10},\]then p belongs to the set:
JEE Main Online Paper (Held On 22 April 2013)
question_answer29) Statement 1: The number of common solution of the trigonometric equations \[2{{\sin }^{2}}\theta -\cos 2\theta =0\] and 2\[{{\cos }^{2}}\theta -3\] \[\sin \theta =0\]in the interval [0, 2\[\pi \]] is two : Statement 2: The number of solutions of the equation, \[2{{\cos }^{2}}\theta -3\]\[\sin \theta =0\] in the interval \[\left[ 0,\pi \right]\] is two
JEE Main Online Paper (Held On 22 April 2013)
A)
Statement 1 is true; Statement 2 is true; Statement 2 is a correct explanation for Statement 1.
doneclear
B)
Statement 1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.
question_answer30) Let \[f(x)=-1+\left| x-2 \right|,\]and g\[\left( x \right)=1-\left| x \right|;\] then the set of all points where \[fog\] us discontinuous is :