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Recent questions tagged set-11
Questions
The proposition $\;\sim (p \vee \sim q) \vee \sim (p \vee q)\;$ is logically equivalent to :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be $\;\alpha\;$ . After moving a distance 2 meters from P towards the foot of the tower , the angle of elevation changes to $\;\beta\;$. Then the height (in meters) of the tower is :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
If $\;2 cos \theta + sin \theta =1 \;(\theta \neq \large\frac{\pi}{2})\;$ , then $\;7 cos \theta + 6 sin \theta\;$ is equal to :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
If X has a binomial distribution , B(n , p) with parameters n and p such that P(X=2)=P(X=3) , then E(x) , the mean of variable X , is
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
A set contains 7 elements . A non - empty subset A of S and an element x of S are chosen at random . Then the probability that $\; x \in A\;$ is :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
If $\;|\overrightarrow{a}|^{2} =60 \;$ and $\;\overrightarrow{c} \times (\hat{i} + 2 \hat{j} +5 \hat{k}) = \overrightarrow{0}\;$ , then the value of $\;\overrightarrow{c}\;.(-7 \hat{i} + 2 \hat{j} +3 \hat{k}) \;$ is :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
The plane containing the line $\;\large\frac{x-1}{1}=\large\frac{y-2}{2}=\large\frac{z-3}{3} \;$ and parallel to the line $\;\large\frac{x}{1}=\large\frac{y}{1}=\large\frac{z}{4}\;$ passes through the point :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
Let $\;A (2 , 3 , 5)\;,B(-1 ,3 , 2)\;$ and $\;C(\lambda , 5 , \mu)\;$ be the vertices of a $\;\bigtriangleup ABC\;$ . If the median through A is equally inclined to the coordinate axes , then :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
Let $\;P(3 sec \theta , 2 tan \theta)\;$ and $\;Q( 3sec \phi ,2 tan \phi)\;$ where $\;\theta + \phi = \large\frac{\pi}{2}\;$ , be two distinct points on the hyperbola $\;\large\frac{x^{2}}{9} - \large\frac{y^{2}}{16}= 1\;$ . Then the ordinate of the point of intersection of the normals at P and Q is :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
Let $\;L_{1}\;$ be the length of the common chord of the curves $\;x^{2}+y^{2}=9\;$ and $\;y^{2}=8x\;$ , and $\;L_{2}\;$ be the length of the latus rectum of $\;y^{2}=8x\;$, then :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
The set of all real values of $\;\lambda\;$ for which exactly two common tangents can be drawn to the circles $\;x^{2}+y^{2}-4x-4y+6=0\;$ and $\;x^{2}+y^{2}-10x-10y+\lambda=0\;$ is the interval :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
The base of an equilateral triangle is along the line given by $\;3x+4y=9\;$. If a vertex of the triangle is (1,2) , then the length of a side of the triangle is :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
A stair - case of length l rests against a vertical wall and a floor of a room , let P be a point on the stair - case , nearer to its end on the wall , that divides its length in the ratio 1:2 . If the stair - case begins to slide on the floor , then the locus of P is :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
If the general solution of the differential equation $\;y^{'}=\large\frac{y}{x} +\Phi (\large\frac{x}{y})\;$, for some function $\;\Phi\;$ , is given by $\;y ln |cx| = x\;$ , where c is an arbitrary constants , $\;\Phi(2)\;$ is equal to :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
If for $\; n \geq 1\;,P_{n} = \int_{1}^{e} (log x)^{n} dx\;$ , then $\;P_{10} - 90 P_{8}\;$ is equal to :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
The integral $\; \int x cos^{-1}(\large\frac{1-x^{2}}{1+x^{2}}) dx\;(x > 0)\;$ is equal to :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius = $\;\sqrt{3}\;$ is :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
1
answer
Two ships A and B are sailing straight away from a fixed point O along routes such that $\;\angle{AOB}\;$ is always $\;120^{0}\;$ . At a certain distance , OA=8 km ,OB=6 km and the ship A is sailing at the rate of 20 km/hr while the ship B sailing at the rate of 30 km/hr . Then the distance between A and B is changing at the rate ( in km/hr ) :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
1
answer
For the curve $\;y=3 sin \theta cos \theta \;,x=e^{\theta} sin \theta\;, 0 \leq \theta \leq \pi ,\;$ the tangent is parallel to x - axis when $\;\theta\;$ is :
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
Let $\;f(x)=x|x|\;,g(x)=sinx\;$ and $\;h(x) =(gof)(x)\;$.Then
jeemain
mathematics
2014
set-11
asked
May 10, 2014
by
yamini.v
0
answers
If $\;\lim_{x\to2} \large\frac{tan(x-2) \{ x^{2}+(k-2)x-2k\}}{x^{2}-4x+4}=5\;$ ,then k is equal to :
jeemain
mathematics
2014
set-11
asked
May 8, 2014
by
yamini.v
0
answers
The sum of the first 20 terms common between the series $\;3+7+11+15+----\;$ and $\;1+6+11+16+---\;$, is :
jeemain
mathematics
2014
set-11
asked
May 8, 2014
by
yamini.v
0
answers
In a geometric progression , if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49 , and the sum of the first and the third term is 35 .Then the first term of this geometric progression is :
jeemain
mathematics
2014
set-11
asked
May 8, 2014
by
yamini.v
0
answers
The coefficient of $\;x^{50}\;$ in the binomial expansion of $\;(1+x)^{1000} +x (1+x)^{999}+x^{2}(1+x)^{998}+----+x^{1000}\;$ is :
jeemain
mathematics
2014
set-11
asked
May 8, 2014
by
yamini.v
0
answers
An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits . The number of ways in which this can be done is :
jeemain
mathematics
2014
set-11
asked
May 8, 2014
by
yamini.v
0
answers
Let for $\;i=1,2,3,p_{i}x\;$ be a polynomial of degree 2 in $\;x,p_{i}^{'}x,p_{i}^{''}x\;$ be the first and second order derivatives of $\;p_{i}x\;$ respectively . Let , $\;A(x) = \begin{bmatrix} p_{1}(x)&p_{1}^{'}(x)&p_{1}^{''}(x) \\[0.3em] p_{2}(x)&p_{2}^{'}(x)&p_{2}^{''}(x) \\[0.3em] p_{3}(x)&p_{}^{'}(x)&p_{3}^{''}(x) \end{bmatrix}\;$ and $\;B(x) =[A(x)]^{T}A(x) \;$.Then determinant of $\;B(x)\;$ :
jeemain
mathematics
2014
set-11
asked
May 8, 2014
by
yamini.v
0
answers
Let A be a $\;3 \times 3\;$ matrix such that $\;A \begin{bmatrix} 1&2&3\\[0.3em] 0&2&3 \\[0.3em] 0&1&1 \end{bmatrix}= \begin{bmatrix} 0&0&1\\[0.3em] 1&0&0 \\[0.3em] 0&1&0 \end{bmatrix}\;$ then $\;A^{-1}\;$ is
jeemain
mathematics
2014
set-11
asked
May 8, 2014
by
yamini.v
0
answers
If $\;\alpha\;$ and $\;\beta\;$ are roots of the equation , $\;x^{2} - 4 \sqrt{2}k x +2e^{4 ln k}-1=0\;$ for some k , and $\;\alpha^{2} + \beta^{2} =66\;$ , then $\;\alpha^{3} + \beta^{3}\;$ is equal to :
jeemain
mathematics
2014
set-11
asked
May 8, 2014
by
yamini.v
0
answers
If $\;z_{1} ,z_{2}\;$ and $\;z_{3} ,z_{4}\;$ are 2 pairs of conjugate numbers , then $\;arg(\large\frac{z_{1}}{z_{4}}) + arg(\large\frac{z_{2}}{z_{3}})\;$ equals :
jeemain
mathematics
2014
set-11
asked
May 8, 2014
by
yamini.v
0
answers
Let f be an odd function defined on the set of real numbers such that for $\;x \geq 0\;$ ,$\;f(x)=3 sinx + 4 cos x$ .Then $\;f(x)\;$ at $\;x=-\large\frac{11 \pi}{6}\;$ is equal to :
jeemain
mathematics
2014
set-11
asked
May 8, 2014
by
yamini.v
0
answers
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