0/52
0
0
Save Progress
Show Timer
Qn #1999
00:00
$\text{Which of the following are greater than } x \text{ when } x=\frac{9}{11}?$
$(I)\ \frac{1}{x}$
$(II)\ \frac{x+1}{x}$
$(III)\ \frac{x+1}{x-1}$
Qn #1969
If $a,b,c$ are the roots of the equation
$x^3-3px^2+3qx-1=0$,
then the centroid of the triangle with vertices
$\left(a,\frac1a\right),\left(b,\frac1b\right),\left(c,\frac1c\right)$
is the point
Qn #1959
If $a,b$ are the roots of $x^2+px+1=0$ and $c,d$ are the roots of $x^2+qx+1=0$, the value of
$E=(a-c)(b-c)(a+d)(b+d)$ is
Qn #1945
If $f(x)$ is a polynomial satisfying
$f(x)f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right)$
and $f(3)=28$, then $f(4)$ is
Qn #1853
Qn #1844
Qn #1835
Qn #1733
Qn #1732
Qn #1621
Qn #1607
If $sin x + a cos x = b$, then what is the expression for $|a sin x – cos x|$ in terms of $a$ and $b$?
Qn #1598
Qn #1556
Qn #1538
If x and y are positive real numbers satisfying the system of equations $x^{2}+y\sqrt{xy}=336$ and $y^{2}+x\sqrt{xy}=112$, then x + y is:
Qn #1532
If $\alpha$ and $\beta$ are the roots of the equation $2x^{2}+ 2px + p^{2} = 0$, where $p$ is a non-zero real number, and $\alpha^{4}$ and $\beta^{4}$ are the roots of $x^{2} - rx + s = 0$, then the roots of $2x^{2} - 4p^{2}x + 4p^{4} - 2r = 0$ are:
Qn #1451
Qn #1432
$a, b, c$ are positive integers such that $a^{2}+2b^{2}-2bc=100$ and $2ab-c^{2}=100$. Then the value of $\frac{a+b}{c}$ is
Qn #1423
The value of k for which the equation $(k-2)x^{2}+8x+k+4=0$
has both real, distinct and
negative roots is
Qn #1421
Qn #1419
The value of the sum $\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{25\sqrt{24}+24\sqrt{25}}$ is
Qn #1147
Some friends planned to contribute equally to jointly buy a CD player. However, two of them decided to withdraw at the last minute. As a result, each of the others had to shell out one rupee more than what they had planned for. If the price (in Rs.) of the CD player is an integer between 1000 and 1100, find the number of friends who actually contributed?
Qn #1088
If $x, y, z$ are distinct real numbers, then
$$
\begin{vmatrix}
x & x^{2} & 2 + x^{3} \\
y & y^{2} & 2 + y^{3} \\
z & z^{2} & 2 + z^{3}
\end{vmatrix} = 0
$$
Then find $xyz$.
Qn #1078
Qn #1075
, then a possible value of n is among the following is Qn #1030
Qn #1012
Qn #1006
Roots of equation are $ax^2-2bx+c=0$ are n and m ,
then the value of $\frac{b}{an^2+c}+\frac{b}{am^2+c}$ is
Qn #872
If $a\, \cos \theta+b\, \sin \, \theta=2$ and $a\, \sin \, \theta-b\, \cos \, \theta=3$ , then ${a}^{2^{}}+{b}^2=$
Qn #864
If α≠β and $\alpha^2=5\alpha-3,\beta^2=5\beta-3$, then the equation whose roots are $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ is
Qn #847
In a triangle, if the sum of two sides is x and their product is y such that (x+z)(x-z)=y, where z is the third side of the triangle , then triangle is
Qn #835
If $\frac{n!}{2!(n-2)!}$ and $\frac{n!}{4!(n-4)!}$ are in the ratio 2:1, then the value of n is
Qn #833
Qn #775
Coefficients a, b, c of $ax^2 + bx + c = 0$ are chosen by tossing 3 fair coins.
Head means 1, Tail means 2.
Find the probability that the roots are imaginary
Qn #763
The number of values of $k$ for which the system of equations
$(k+1)x + 8y = 4k$ and $kx + (k+3)y = 3k-1$ has infinitely many solutions, is
Qn #665
Qn #662
Let a, b, c, d be no zero numbers. If the point of intersection of the line 4ax + 2ay + c = 0 & 5bx + 2by + d=0 lies in the fourth quadrant and is equidistance from the two are then
Qn #653
Qn #647
Qn #603
If one AM (Arithmetic mean) 'a' and two GM's (Geometric means) p and q be inserted between any two positive numbers, the value of p^3+q^3 is
Qn #589
Qn #561
At how many points the following curves intersect $\frac{{y}^2}{9}-\frac{{x}^2}{16}=1$ and $\frac{{x}^2}{4}+\frac{{(y-4)}^2}{16}=1$
Qn #551
The system of equations $x+2y+2z=5$, $x+2y+3z=6$, $x+2y+\lambda z=\mu$ has
infinitely many solutions if
Qn #549
The number of solutions of ${5}^{1+|\sin x|+|\sin x{|}^2+\ldots}=25$ for $x\in(-\mathrm{\pi},\mathrm{\pi})$ is
Qn #547
If $x=1+\sqrt[{6}]{2}+\sqrt[{6}]{4}+\sqrt[{6}]{8}+\sqrt[{6}]{16}+\sqrt[{6}]{32}$ then ${\Bigg{(}1+\frac{1}{x}\Bigg{)}}^{24}$ =
Qn #545
Let C denote the set of all tuples (x,y) which satisfy $x^2 -2^y=0$ where x and y are natural numbers. What is the cardinality of C?
Qn #543
If the perpendicular bisector of the line segment joining p(1,4) and q(k,3) has yintercept -4, then the possible values of k are
Qn #471
Given the equation $x+y =1$, $x^2+y^2 =2$, $x^5 +y^5 =A$. Let N be the number
of solution pairs (x,y) to this system of equations. Then AN is equal to
Qn #464
If $\alpha$ and $\beta$ are the two roots of the quadratic equation $x^2 + ax + b
= 0, (ab \ne 0)$ then the quadratic roots whose roots $\frac{1}{\alpha^3+\alpha}$ and
$\frac{1}{\beta^3+\beta}$ is
Qn #449
If x, y and z are three cube roots of 27, then the determinant of the
matrix $\begin{bmatrix}{x} & {y} & {z} \\ {y} & {z} & {x} \\ {z} & {x}
& {y}\end{bmatrix}$ is
Qn #442
Let A and B be two square matrices of same order satisfying $A^2+5A+5I =0$ and
$B^2+3B+I=0$ repectively. Where I is the identity matrix. Then the inverse of the matrix $C=
BA+2B+2A+4I$ is
Qn #437
If $8^{x-1}=(1/4)^{x}$, then the value of
$\frac{1}{\log_{x+1}4-\log_{x+1}5}+\frac{1}{\log_{1-x}4-\log_{1-x}5}$ is
Qn #403
A group of 630 children is arranged in rows for a group photograph. Each row contains
three fewer children than the row in front of it. What number of rows is not possible?