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Which of the following elements is ninth to the right of the fifteenth from the left end of the above arrangement?

Which term of the following sequences :

(a) $2,2\sqrt{2},4.....\text{is}128?$

(b) $\sqrt{3},3,3\sqrt{3},.....\text{is}729?$

c) $\frac{1}{3},\frac{1}{9},\frac{1}{27},.....\text{is}\frac{1}{19683}?$

The total number of integral solution(s) of $|4x-5|+|6x-12|=|2x-7|$ is/are

The value of $\sum _{r=1}^{n}log\left(\frac{a^r}{b^{r-1}}\right)$ is

Simplest form of $\frac{2}{\sqrt{2+\sqrt{2+\sqrt{2+2cos4x}}}}$ is

Find the equation of the ellipse whose foci are at $(0,\pm 4)$ and $e=\frac{4}{5}.$

Intersecting the x-axis at a distance of 3 units to the left of origin with slope -2.

Solve the following inequalities graphically in two dimensional plane:

x > -3

Find the lengths of the axes; the coordinates of the vertices and the foci the eccentricity and length of the latus rectum of the hyperbola $y^2-16x^2=16.$

In a right-angled triangle, $a$ and $b$ are the lengths of the two sides and $c$ is the length of the hypotenuse. If $c+b$ and $c-b$ are numbers other than $1$, then ${\log }_{c+b}a+{\log }_{c-b}a=$

$If\left(x\right)=x^{n}andif{f}^1\left(1\right)=10thenn=$

Which of the following are equivalent statements to the implication $p\to q$.

If $cosA=\frac{4}{5}$ and $cosB=\frac{12}{13},\frac{3\pi }{2}<A,B<2\pi$, find the value of the following

$\left(i\right)cos(A+b)$

$\left(ii\right)sin(A-B)$

The mean and variance of seven observations are 8 and 16 respectively. If five of these are 2, 4, 10, 12, 14,find the remaining two observations.

Write down all the subsets of the following sets.

(i) {a} (ii) {a, b} (iii) {1, 2, 3} (iv) $\varphi$.

If A = {5, 7, 9, 11}, B = {9, 10} let a R b means a < b. a $\in$ A, (a, b) $\in$ R, b $\in$ B. Then

If the number of terms in the expansion of $(x+1+\frac{1}{x}{)}^n$ is 501, then n =

The value of $\sum _{k=1}^{10}$$(sin\frac{2k\pi }{11}-icos\frac{2k\pi }{11})$ is

The equation of circle concentric with circle $x^2+y^2-6x+12y+15$ = 0 and double its area is

If $f\left(x\right)=\frac{1}{(x-1)(x-2)}andg\left(x\right)=\frac{1}{x^2}$, then points of discontinuity of f(g(x)) are

The sum of 1 + $\frac{2}{5}$ + $\frac{3}{\left(5^2\right)}$ + $\frac{4}{\left(5^3\right)}$ + .........upto n terms is

$\sim (\sim p\wedge q)$ is logically equivalent to

Three statements p,q,r are given below

p: 4 is an even prime number
q: 6 is a divisor of 12
r: the HCF of 4 and 6 is 12

Which of the following are true?

$a^n-b^n$ is always divisible by

What are the conditions for $a{x}^2+bx+c$> $0\forall$ x $ϵ$ R

The normal at an end of a latus rectum of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ passes through an end of the minor axis if

Function Domain Range

(i)sinx (P) R (L) [-1, 1]

(ii) cosx (Q) R - {n $\pi$} (M) R

(iii) tanx (R) R- {(2n + 1})$\frac{\pi }{2}$} (N) $(-\infty$, -1] u [1, $\infty$)

(iv) cosecx

(v) secx

(vi) cotx

How many of the following are matched correct?

(i) -P-L, (ii) -P-L, (iii)-R-M, (iv) -Q-N, (v) -R-N, (vi) -Q-M

$\text{The value of}{lim}_{h\to 0}\frac{In(1+2h)-2In(1+h)}{h^2}is$

The ratio of the sum of m and n terms of an AP is $m^2:n^2.$ Show that the ratio of the mth and nth terms is (2m - 1) : (2n - 1).

Find the value of n, so that $\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ is the geometric mean between a and b

Or

If f is a function satisfying $f(x+y)=f\left(x\right)f\left(y\right)$ for all $x,y\in N$ such that f(1)=3 and ${\sum }_{x=1}^{n}f\left(x\right)=120$ find the value of n.

Find the coefficients of $x^{32}$ and $\frac{1}{x^{17}}$ in the expansion of ${(x^4-\frac{1}{x^3})}^{15}$

The negation of the compound statement $p\wedge (\sim p\vee q)$ is ___.

If $x=a{t}^4,y=b{t}^3,then\frac{dy}{dx}=?$

There are 16 points in a plane out of which 6 are collinear, then how many lines can be drawn by joining these points?

Team of four students is to be selected from a total of 12 students for a quiz competition. In how many ways it can be selected if two particular students wish to be included together only.

Find the value of ${\log }_2.{\log }_{3}9$

When x is so small that its square and higher powers may be neglected, find the value of
$\frac{{(1+\frac{2}{3}x)}^{-5}+\sqrt{4+2x}}{\sqrt{(4+x{)}^3}}$.

$\sum _{r=1}^n$( $a^r$ + br), a, b ∈ $R^{+}$, a ≠ 1 is equal to:

Find the value of i.$i^i$ is _______.

Find the value of 'k' if the expression $(4-k)x^2+2(k+2)x+5k+1$ is a perfect square

Sum of the common roots of $z^{2006}+z^{100}+1=0$
and $z^3+2z^2+2z+1=0$ is

If $|z|=1$, then ${\left(\frac{1+z}{1+\overline{z}}\right)}^n+{\left(\frac{1+\overline{z}}{1+z}\right)}^n$ is equal to

$(cos\alpha +cos\beta {)}^2+(sin\alpha +sin\beta {)}^2$ =

If $\frac{1}{b-c}$, $\frac{1}{c-a}$, $\frac{1}{a-b}$ be consecutive terms of an A.P., then $(b-c{)}^2,(c-a{)}^2,(a-b{)}^2$ will be in ___.

Let one root of $a{x}^2+bx+c=0$ where $a,b,c$ are integers be $3+\sqrt{5}$, then the other root is

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
$\frac{x^2}{100}+\frac{y^2}{400}=1.$