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JEE Advanced
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Mathematics
List of top Mathematics Questions asked in JEE Advanced
Let AB be a chord of the circle
$x^2 + y^2 = r^2$
subtending a right angle at the centre. Then, the locus of the centroid of the
$\Delta PAB$
as P moves on the circle, is
JEE Advanced - 2001
JEE Advanced
Mathematics
Conic sections
Let
$ \alpha, \beta$
be the roots of
$x^2 - x + p = 0$
and
$y, \delta$
be the roots of
$x^2 - 4x + q = 0$
if
$ \alpha, \beta, y \delta$
are in GP, then the integer values of p and q respectively are
JEE Advanced - 2001
JEE Advanced
Mathematics
Sequence and series
Let
$f(x) = (1 + b^2)x^2 + 2bx + 1$
and let m(b) be the minimum value of f(x). As b varies, the range of m(b) is
JEE Advanced - 2001
JEE Advanced
Mathematics
Application of derivatives
Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the second term is 3/4 then
JEE Advanced - 2000
JEE Advanced
Mathematics
Sequence and series
If
$\alpha$
and
$\beta$
are
$(\alpha < \beta)$
the roots of the equation
$x^2+bx+c=0,$
where
$c < 0 < b$
,the
JEE Advanced - 2000
JEE Advanced
Mathematics
Complex Numbers and Quadratic Equations
If
$ x^2 + y^2 = 1$
, then
JEE Advanced - 2000
JEE Advanced
Mathematics
Differentiability
A straight line through the origin O meets the parallel lines
$4x + 2y = 9 $
and
$2x + y + 6 = 0$
at points P and Q respectively. Then, the point O divides the segment PQ in the ratio
JEE Advanced - 2000
JEE Advanced
Mathematics
Straight lines
Let f : R
$\to$
R be any function. Define g : R
$\to$
R by g(x) = |f(x)| for all x. Then g is
JEE Advanced - 2000
JEE Advanced
Mathematics
Relations and functions
For the equation
$3x^2+px+3=0,p>0,$
if one of the root is square of the other, then p is equal to
JEE Advanced - 2000
JEE Advanced
Mathematics
Complex Numbers and Quadratic Equations
If
$\overrightarrow{a}, \overrightarrow{b}$
and
$\overrightarrow{c}$
are unit coplanar vectors, then the scalar triple product
$[2\overrightarrow{a}-\overrightarrow{b}2\overrightarrow{b}-\overrightarrow{c}2\overrightarrow{c}-\overrightarrow{a}]$
is
JEE Advanced - 2000
JEE Advanced
Mathematics
Vector Algebra
In a $\triangle ABC, $ 2 ac sin $ \bigg [ \frac{1}{2} (A - B + C ) \bigg ] $ is equal to
JEE Advanced - 2000
JEE Advanced
Mathematics
Three Dimensional Geometry
The incentre of the triangle with vertices
$(1, \sqrt{3}), (0,0)$
and
$ (2,0) is $
JEE Advanced - 2000
JEE Advanced
Mathematics
coordinates of a point in space
Let $f(x) = \begin{cases} |x|, & \quad \text{for}\, 0 < | x | \le 2 \\ 1, & \quad \text{for} \, x = 0 \end{cases}$ then at x = 0, f has
JEE Advanced - 2000
JEE Advanced
Mathematics
Application of derivatives
For all
$x\,\in\,(0,1)$
JEE Advanced - 2000
JEE Advanced
Mathematics
Application of derivatives
If
$a, b, c, d$
are positive real numbers such that
$a + b +c + d = 2,$
then
$M =(a + b) (c+d) $
satisfies the relation.
JEE Advanced - 2000
JEE Advanced
Mathematics
Sequence and series
For
$2 \le \, r \, \le \, n,\binom{n}{r}+2 \binom{n}{r-1}+\binom{n+2}{r}$
is equal to
JEE Advanced - 2000
JEE Advanced
Mathematics
Binomial theorem
if
$\ f ( x )$
$=\bigg \{ \begin {array} \ e^{\cos x}\sin \ x \\ 2 \\ \end {array} \begin {array} \ for |x|\le 2 \\ \text{otherwise} \\ \end {array}
$ then $
\int^{3}_{-2} f ( x ) \ dx$ is equal to
JEE Advanced - 2000
JEE Advanced
Mathematics
Integrals of Some Particular Functions
The value of the integral
$ \int^{e^2}_{e^{-1}} \bigg | \frac{ \log_e \, x }{ x } \bigg | \, dx $
is
JEE Advanced - 2000
JEE Advanced
Mathematics
Integrals of Some Particular Functions
If
$ i = \sqrt -1$
then
$ 4 + 5 \bigg(-\frac{1}{2}+\frac{i\sqrt 3}{2}\bigg)^{334}+3\bigg(-\frac{1}{2}+\frac{i\sqrt 3}{2}\bigg)^{365}$
is equal to
JEE Advanced - 1999
JEE Advanced
Mathematics
Complex Numbers and Quadratic Equations
In a
$\triangle PQR, \angle R = \frac{\pi}{2} , \, if \, tan \, \bigg( \frac{ P}{2}\bigg) $
and \, tan
$ \bigg( \frac{ Q}{2}\bigg)$
are the roots of the equation
$ ax^2 + bx + c = 0 \, (a \ne 0 )$
, then
JEE Advanced - 1999
JEE Advanced
Mathematics
Quadratic Equations
The function f (x) =
$ [ x]^2 - [ x]^2 $
(where, [x] is the greatest integer less than or equal to x), is discontinuous at
JEE Advanced - 1999
JEE Advanced
Mathematics
Functions
Let
$PQR$
be a right angled isosceles triangle, right angled at
$P (2,1)$
. If the equation of the line
$QR$
is
$2x + y = 3$
, then the equation representing the pair of lines PQ and PR is
JEE Advanced - 1999
JEE Advanced
Mathematics
Straight lines
For a positive integer n, let
$f_n(\theta)=\Bigg(tan\frac{\theta}{2}\Bigg)(1+sec \theta)(1+sec 2\theta)(1+ sec 2^2 \theta)... (1+sec 2^n \theta), then$
JEE Advanced - 1999
JEE Advanced
Mathematics
Sum of First n Terms of an AP
For a positive integer n let
$a (n) = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + ...+ \frac{1}{(2^n)-1},$
then
JEE Advanced - 1999
JEE Advanced
Mathematics
Sequence and series
The harmonic mean of the roots of the equation
$ (5+\sqrt 2)\, x^2 - (4+\sqrt 5)\, x + 8 + 2\sqrt5 = 0 $
is
JEE Advanced - 1999
JEE Advanced
Mathematics
Sequence and series
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