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Recent questions tagged 1991
Questions
$\int \large\frac{3 \cos x +2 \sin x}{4 \sin x+ 5 \cos x}$$dx$=.............. .
jeemain
eamcet
math
1991
fitb
q30
asked
Sep 13, 2013
by
meena.p
0
answers
Given $x$ is positive, the values of $f(x)=-3 \cos \sqrt {3+x+x^2}$ lie in the interval .............. .
jeemain
eamcet
math
1991
fitb
q29
asked
Sep 13, 2013
by
meena.p
0
answers
If $u=\log \tan \bigg(\large\frac{\pi}{4}+\frac{\theta}{2}\bigg), $ then $cos\; u$=............... .
jeemain
eamcet
math
1991
fitb
q28
asked
Sep 13, 2013
by
meena.p
0
answers
Two die thrown simultaneously. The probability of getting even numbers on both the die is ...............
jeemain
eamcet
math
1991
fitb
q27
asked
Sep 13, 2013
by
meena.p
0
answers
The greatest negative integer satisfying $x^2-4x-77=0$ and $x^2 >4$ is ................... .
jeemain
eamcet
math
1991
fitb
q26
asked
Sep 13, 2013
by
meena.p
0
answers
The condition for $ax^2+2cxy+by^2+2bx+2ay+c$ is resolvable into two linear factors, is ................
jeemain
eamcet
math
1991
fitb
q25
asked
Sep 13, 2013
by
meena.p
1
answer
$\lim \limits _{x \to 0} \large\frac{x-\sin x}{x+ \cos ^2 x}$=............... .
jeemain
eamcet
math
1991
fitb
q24
asked
Sep 13, 2013
by
meena.p
0
answers
In $\Delta ABC,a= \sqrt 3+1, \angle B=30^{\circ},\; \angle C=45^{\circ};$ then $c=$................ .
jeemain
eamcet
math
1991
fitb
q23
asked
Sep 13, 2013
by
meena.p
0
answers
The locus of the point of intersection of the perpendicular tangents to the ellipse $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1$ is ................
jeemain
eamcet
math
1991
fitb
q22
asked
Sep 13, 2013
by
meena.p
1
answer
If $C_0,C_1,C_2,$................... are the binomial coefficient in the expansion of $(1+x)^n$, then $C_0+\large\frac{C_1}{2}$$x+\large\frac{C_2}{3}$$x^2+........+ \large\frac{C_n}{n+1}$$x^n$= ...................
jeemain
eamcet
math
1991
fitb
q21
asked
Sep 13, 2013
by
meena.p
0
answers
The vector equation to the plane through the points $(1,-2,-3)$ and parallel to the vectors $(2,3,-6)$ is .............. .
jeemain
eamcet
math
1991
fitb
q20
asked
Sep 13, 2013
by
meena.p
0
answers
$^{14}C_4+ \sum \limits_ {j=1}^4\; ^{18-j}C_3$=................ .
jeemain
eamcet
math
1991
fitb
q19
asked
Sep 13, 2013
by
meena.p
0
answers
The locus of the middle points of chord of the circle $x^2+y^2-2x=0$ passing through the orgin is ................. .
jeemain
eamcet
math
1991
fitb
q18
asked
Sep 13, 2013
by
meena.p
0
answers
If $\overrightarrow {a}, \overrightarrow {b}, \overrightarrow {c}$ are mutually perpendicular unit vectors, then $ |\overrightarrow {a}+ \overrightarrow {b}+ \overrightarrow {c}|$=.................. .
jeemain
eamcet
math
1991
fitb
q17
asked
Sep 13, 2013
by
meena.p
0
answers
The maximum value of $\large\frac{\log x}{x}$ in $0 < x < \infty $ is .................. .
jeemain
eamcet
math
1991
fitb
q16
asked
Sep 13, 2013
by
meena.p
0
answers
The length of portion of tangent at any point on the curve $x^{\Large\frac{2}{3}}$$+y^{\Large\frac{2}{3}}$$=a^{\Large\frac{2}{3}}$ intercepted between the axes is ................ .
jeemain
eamcet
math
1991
fitb
q15
asked
Sep 13, 2013
by
meena.p
0
answers
The remainder obtained when the polynomial $1+x+x^3+x^9+x^{27}+x^{81}+x^{243}$ is divided by $x-1$, is .................. .
jeemain
eamcet
math
1991
fitb
q14
asked
Sep 13, 2013
by
meena.p
1
answer
The orthocentre of triangle whose sides are $2y-x=9,x+y=9,2x-y=9$ is .............
jeemain
eamcet
math
1991
fitb
q13
asked
Sep 13, 2013
by
meena.p
0
answers
$\int \limits_1^3 \large\frac{dx}{2x-1},$ using simpson's rule with 4 equal intervals, The approximate value of $\int \limits_1^3 \large\frac{dx}{2x-1}$=.................. .
jeemain
eamcet
math
1991
fitb
q12
asked
Sep 13, 2013
by
meena.p
0
answers
When 2 balls are drawn from bag containing 2 white,4 red and 6 black balls, the chance for both of them to be red is ............... .
jeemain
eamcet
math
1991
fitb
q11
asked
Sep 13, 2013
by
meena.p
1
answer
Equation to the common tangent to the circle $x^2+y^2=2a^2$ and the parabola $y^2=8ax$ is ................ .
jeemain
eamcet
math
1991
fitb
q10
asked
Sep 13, 2013
by
meena.p
0
answers
$\sum \limits_{n=0}^{\infty} (-1)^n x^{n+1}$=............
jeemain
eamcet
math
1991
fitb
q9
asked
Sep 13, 2013
by
meena.p
0
answers
$(i)^{243}$=.................. .
jeemain
eamcet
math
1991
fitb
q8
asked
Sep 13, 2013
by
meena.p
0
answers
$2 \begin {bmatrix} 1 & 1 & 1 \\ a & b & c \\ a^2-bc & b^2-ca & c^2-ab \end {bmatrix}$= ................. .
jeemain
eamcet
math
1991
fitb
q7
asked
Sep 13, 2013
by
meena.p
0
answers
$x= \cos \theta+ \theta \sin \theta, y=\sin \theta-\theta \cos \theta,$ then $\large\frac{d^2y}{dx^2}$ = ................... .
jeemain
eamcet
math
1991
fitb
q6
asked
Sep 13, 2013
by
meena.p
0
answers
If $u= \large\frac{x+y}{x-y},$ then $\large\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}$ = .................. .
jeemain
eamcet
math
1991
fitb
q5
asked
Sep 13, 2013
by
meena.p
0
answers
$\sqrt { \sqrt 3-\sqrt {4+\sqrt 5+\sqrt {17-4 \sqrt {15}}}}$= ..................... .
jeemain
eamcet
math
1991
fitb
q4
asked
Sep 13, 2013
by
meena.p
0
answers
The area between the curve $y=1-|x| $ and the x-axis is ............... .
jeemain
eamcet
math
1991
fitb
q3
asked
Sep 13, 2013
by
meena.p
0
answers
When two dies are thrown. The probability of getting equal number is ................... .
jeemain
eamcet
math
1991
fitb
q2
asked
Sep 13, 2013
by
meena.p
0
answers
If the relation between sub-normal and sub-tangent at any point on the curve $by^2=(x+a)^3$ is $p(SN)=q(ST)^2,$ then $\large\frac{p}{q}$=..................... .
jeemain
eamcet
math
1991
fitb
q1
asked
Sep 13, 2013
by
meena.p
0
answers
$X=\begin {bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$;$X^n$ is equal to :
jeemain
eamcet
math
1991
q20
asked
Sep 13, 2013
by
meena.p
1
answer
The vector area of triangle whose two sides are given by $2 \hat {i}-7 \hat {j}+\hat {k} $ and $ 4 \hat j -3 \hat k$ is :
jeemain
eamcet
math
1991
q19
asked
Sep 13, 2013
by
meena.p
1
answer
Derive $\sec^{-1}\bigg(\large\frac{1}{2x^2-1}\bigg)$ with respect to $\sqrt {1+3x}$ at $x=-\large\frac{1}{3}$:
jeemain
eamcet
math
1991
q18
asked
Sep 13, 2013
by
meena.p
1
answer
The inverse element of $\omega ^2$ in the multiplicative catine group $\{1, \omega,\omega ^2\}$ where $\omega$ is the cube roots of unity, is :
jeemain
eamcet
math
1991
q17
asked
Sep 13, 2013
by
meena.p
1
answer
The circles $x^2+y^2-4x+6y+8=0$ and $x^2+y^2-10x -6y+14=0,$ touch:
jeemain
eamcet
math
1991
q16
asked
Sep 13, 2013
by
meena.p
1
answer
Tha smallest value of $x^2-3x+3$ in the interval $(-3,\large\frac{3}{2})$ is equal to :
jeemain
eamcet
math
1991
q15
asked
Sep 13, 2013
by
meena.p
1
answer
The value of the integral $\int \sqrt x e^{\sqrt x} dx$ is :
jeemain
eamcet
math
1991
q14
asked
Sep 13, 2013
by
meena.p
1
answer
The students while solving a quadratic equation in $x$, one copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of $x^2 $ as $-6$ and $1$ respectively. The correct roots are:
jeemain
eamcet
math
1991
q13
asked
Sep 13, 2013
by
meena.p
1
answer
The equation of the circle passing through (2,1) and touching the co-ordinate axes, is :
jeemain
eamcet
math
1991
q12
asked
Sep 13, 2013
by
meena.p
1
answer
The locus represented by $|z-1|=|z+i|$ is :
jeemain
eamcet
math
1991
q11
asked
Sep 13, 2013
by
meena.p
1
answer
If the mean and variance of a binomial distribution are $\large\frac{15}{4}$ and $\large\frac{15}{16}$. The number of trials are:
jeemain
eamcet
math
1991
q10
asked
Sep 13, 2013
by
meena.p
1
answer
The length of the latus rectum of an ellipse is $\large\frac{1}{3}$ of the major axis. It's $e$ is :
jeemain
eamcet
math
1991
q9
asked
Sep 13, 2013
by
meena.p
1
answer
The probabilities of problem being solved by two students are $\large\frac{1}{2}$ and $\large\frac{1}{3}$. Find the probability of the problem being solved.
jeemain
eamcet
math
1991
q8
asked
Sep 12, 2013
by
meena.p
1
answer
The unit vector perpendicular to each of $2 \hat {i}-\hat {j}+\hat {k}$ and $ 3 \hat {i}+4 \hat j-\hat k$ is :
jeemain
eamcet
math
1991
q7
asked
Sep 12, 2013
by
meena.p
1
answer
The number of non-zero terms in the expansion of $(1+ 3 \sqrt {2}x)^9+(1-3 \sqrt {2} x)^9$ is equal to :
jeemain
eamcet
math
1991
q6
asked
Sep 12, 2013
by
meena.p
1
answer
$\tan x-\tan 3x-\tan 2x $ is equal to :
jeemain
eamcet
math
1991
q5
asked
Sep 12, 2013
by
meena.p
1
answer
$y= \sin ^{-1} \bigg[\large\frac{1-x^2}{1+x^2}\bigg],$ find $\large\frac{dy}{dx}$:
jeemain
eamcet
math
1991
q4
asked
Sep 12, 2013
by
meena.p
1
answer
The orthocentre of a triangle whose vertices are $(0,0),(8,0),(4,6), $ is :
jeemain
eamcet
math
1991
q3
asked
Sep 12, 2013
by
meena.p
1
answer
In how many ways can 5 red and 4 white balls be drawn from a bag containing 10 red and 8 white balls?
jeemain
eamcet
math
1991
q2
asked
Sep 12, 2013
by
meena.p
1
answer
If the function $f(x)=\large\frac{3x+4 \tan x}{x}$ is continuous, then what is the value of $f(x)$ at $x=0$?
jeemain
eamcet
math
1991
q1
asked
Sep 12, 2013
by
meena.p
1
answer
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