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JEE Mathematics / Practice

Question Bank

Showing 401-405 of 408 questions.

IIT-JEE 2004Question 401
$P_1$ and $P_2$ are planes passing through the origin. $L_1$ and $L_2$ are two lines on $P_1$ and $P_2$ respectively such that their intersection is the origin. Show that there exist points $A,B,C$, whose permutation $A',B',C'$ can be chosen such that (i) $A$ is on $L_1$, $B$ on $P_1$ but not on $L_1$ and $C$ not on $P_1$; (ii) $A'$ is on $L_2$, $B'$ on $P_2$ but not on $L_2$ and $C'$ not on $P_2$.
3D Geometry

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IIT-JEE 2004Question 402
A parallelepiped $S$ has base points $A,B,C$ and $D$ and upper face points $A',B',C'$ and $D'$. This parallelepiped is compressed by the upper face $A'B'C'D'$ to form a new parallelepiped $T$ having upper face points $A'',B'',C''$ and $D''$. The volume of parallelepiped $T$ is $90$ percent of the volume of parallelepiped $S$. Prove that the locus of $A''$ is a plane.
Vector Algebra

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IIT-JEE 2004Question 403
If $\vec a,\vec b,\vec c$ and $\vec d$ are distinct vectors such that $\vec a\times\vec c=\vec b\times\vec d$ and $\vec a\times\vec b=\vec c\times\vec d$, prove that $(\vec a-\vec d)\cdot(\vec b-\vec c)\neq0$, i.e. $\vec a\cdot\vec b+\vec d\cdot\vec c\neq\vec d\cdot\vec b+\vec a\cdot\vec c$.
Vector Algebra

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IIT-JEE 2005Question 404
$f(x)$ is a differentiable function and $g(x)$ is a twice differentiable function such that $|f(x)|\le1$ and $f'(x)=g(x)$. If $f^{2}(0)+g^{2}(0)=9$, prove that there exists some $c\in(-3,3)$ such that $g(c)\cdot g''(c)<0$.
Differentiation and its Application

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IIT-JEE 2003Question 405
If $a,b,c$ are in A.P., $a^2,b^2,c^2$ are in H.P., then prove that either $a=b=c$ or $a,b,-\dfrac c2$ form a G.P.
Sequence and Series · Mixed Progressions (AP-GP) · Harmonic Progression

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