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Which of the following complexes is/are square planar in shape ?
(I) [Ni(CN)4]2− (II) [MnCl4]2− (III) [ZnCl4]2− (IV) [Ni(NH3)4]2+

By using properties of definite integrals, evaluate the integrals
Show that
${\int }_0^{a}f\left(x\right)g\left(x\right)dx=2{\int }_0^{a}f\left(x\right)dx,$ $\text{if f and g are defined}$ $asf\left(x\right)=f(a-x)\text{and}g\left(x\right)+g(a-x)=4$

If a variable line in two adjacent positions has direction cosines l,m,n and $l+\delta l,m+\delta m,n+\delta n$, then show that the small angle $\delta \theta$ between the two positions is given by $\delta {\theta }^2=\delta l^2+\delta m^2+\delta n^2.$

Show that the function $f:R\to \{x\in R:-1<x<1\}$ defined by $f\left(x\right)=\frac{x}{x+|x{|}^{\prime }}x\in R$ is one-one and onto function.

If $z$ and $w$ be two complex numbers such that $|z|\le 1,|w|\le 1$ and $|z+iw|=|z-i\overline{w}|=2,$then

If $\frac{5-2x}{3}\le \frac{x}{6}-5$, then $x$ lies in

$\left|\begin{array}{ccc}{a}^2+1& ab& ac\\ ab& b^2+1& bc\\ ca& cb& c^2+1\end{array}\right|=1+a^2+b^2+c^2$

Find the equation of tangent at $x=0$ on the curve $y=x{e}^x$

The coordinates of the centre of a circle, whose radius is $2$ units and which touches the line pair $x^2-y^2-2x+1=0,$ are

If $\tan x-\tan y=m$ and $\cot y-\cot x=n,$ then $(\frac{1}{m}+\frac{1}{n})$ is equal to

If the function $f\left(x\right)=x^5+e^{\frac{x}{5}}$ and $g\left(x\right)=f^{-1}\left(x\right)$, then the value of $\frac{1}{g^{{}^{\prime }}(1+e^{\frac{1}{5}})}$ 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.
$4x^2+9y^2=36$

Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.

1. if a,b,c,d are in ap then log a to base x, log b to base x, log c to base x are in ?

2.the value of (1/sq root27)^2-(log16 base5/ 2log9 base5)

Sham can take any one of three routes from school (S) to the town center (T), and can then take four possible routes from the town center to his home (H). He doesn't retrace his steps.
How many different possible ways can Sham walk home from school?

Vector A has a magnitude of 2 units and makes an angle of $0^{\circ }$ with the positive x- axis, Vector B has a magnitude of 6 units and makes an angle of ${30}^{\circ }$
(clock-wise) with the positive y- axis. Find the magnitude of the resultant of Vector A& B and also the angle that it makes with Vector A.

Sum to n terms of the series $\frac{1}{(1+x)(1+2x)}$ + $\frac{1}{(1+2x)(1+3x)}$ + $\frac{1}{(1+3x)(1+4x)}$ + ..............is

Match $\text{List I}$ with the $\text{List II}$ and select the correct answer using the code given below the lists :

$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{In an A.P., the series containing 99 terms, the sum of all}& \text{(P)}& 5010\\ & \text{the odd numbered terms is}2550.\text{The sum of all the}99\text{terms}& & \\ & \text{of the A.P. is}& & \\ \text{(B)}& f\text{is a function for which}f\left(1\right)=1\text{and}f\left(n\right)=n+f(n-1)& \text{(Q)}& 5049\\ & \text{for each natural number}n\ge 2\text{. The value of}f\left(100\right)\text{is}& & \\ \text{(C)}& \text{Suppose}f\left(n\right)={\log }_2\left(3\right)\cdot {\log }_3\left(4\right)\cdot {\log }_4\left(5\right)\dots {\log }_{n-1}\left(n\right).& \text{(R)}& 5050\\ & \text{Then the sum}\sum _{k=2}^{100}f\left(2^k\right)\text{equals}& & \\ \text{(D)}& \text{Concentric circles of radii}1,2,3,\dots ,100\text{cms}\text{are drawn. The}& \text{(S)}& 5100\\ & \text{interior of the smallest circle is coloured red and the annular}& & \\ & \text{regions are coloured alternately green and red, so that no}& & \\ & \text{two adjacent regions are of the same colour. The total area}& & \\ & \text{of the green regions in sq. cm is}k\pi .\text{Then}k\text{equals}& & \\ & & \text{(T)}& 5030\end{array}$

Which of the following is the only CORRECT combination?

There are two die $A$ and $B$ both having six faces. Die $A$ has three faces marked with $1$, two faces marked with $2$, and one face marked with $3$. Die $B$ has one face marked with $1$, two faces marked with $2$, and three faces marked with $3$. Both dices are thrown randomly once. If $E$ be the event of getting sum of the numbers appearing on top faces equal to $x$, let $P\left(E\right)$ be the probability of event $E$, then
When $x=4$, then $P\left(E\right)$ is equal to

If x+y=4 & xy=45 then find the value of x³-y³?

Solve this fast📝

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How many words can be formed with the letters of the word "ORDINATE" so that vowels occupy odd places?

And) sir/mam can this be done like this:

No. Of words that can be formed=4!*3!*2!

If $(1+x+x^2{)}^n=a_0+a_{1}x+a_2{x}^2+....+a^{2n}{x}^{2n},then{a}_0+a_3+a_6+.....=$

The number of solutions of the equation
$\sin \left(9x\right)+\sin \left(3x\right)=0$
in the closed interval $[0,2\pi ]$ is

Refer to question 6 above, state true or false (give reason for your answer)
(i) A and B are mutually exclusive
(ii) A and B are mutually exclusive and exhaustive
(iii) A = B'
(iv) A and C are mutually exclusive
(v) A and B' are mutually exclusive
(vi) A' B', C are mutually exclusive and exhaustive.

Integrate the function.
$\int e^x(\frac{1}{x}-\frac{1}{x^2})dx.$

Which of the following can best represent the graph of $f\left(x\right)=e^{\left\{x\right\}}$?
[Note: $\left\{x\right\}$ denotes the fractional part of $x$]

If x + y = k is normal to the curve y² = 12x, then k is equal to

From 50 students taking examinations in Mathematics, Physics and Chemistry, each of the student has passed in atleast one of the subjects, 37 passed in Mathematics, 24 in Physics and 43 in Chemistry. At most 29 passed in Mathematics and Chemistry, at most 19 passed in Mathematics and Physics and at most 20 in Physics and Chemistry. Find the largest possible number of students that could have passed in all three examinations.

$\int e^{tan-1}x\left(\frac{1+x+x^2}{1+x^2}\right)dx=$

Find the radian measures corresponding to the following degree measures:

(i) ${25}^0$

(ii) $-{47}^0{30}^{\prime }$

(iii) ${240}^0$

(iv) ${520}^0$

The function f is defined by
$f\left(x\right)=\{\begin{array}{c}{x}^2,0\le x\le 3\\ 3x,3\le x\le 10\end{array}$
The relation g is defined by
$g\left(x\right)=\{\begin{array}{c}{x}^2,0\le x\le 2\\ 3x,2\le x\le 10\end{array}$
Show that f is a function and g is not a function.

Matrices of order $3\times 3$ are formed using the elements of set $A=\{-3,-2,-1,0,1,2,3\}.$ Then the probability that matrices are either symmetric or skew-symmetric, is

Rearrange the following sentences (A), (B), (C), (D), (E) and (F) to make a meaningful paragraph and answer the questions which follow:

For what value of x, the given algebraic expression 8x³ - 7x² + 12x - 13 becomes 0

Match the following:

$\begin{array}{cc}\left(A\right)i^{1947}& \left(1\right)i\\ \left(B\right)i^{2000}& \left(2\right)-i\\ \left(C\right)i^{2014}& \left(3\right)1\\ \left(D\right)i^{589}& \left(4\right)-1\end{array}$

In an experiment with 15 observations on $x$, the following results were available: $\sum x^2=2830,\sum x=170$ One observation that was $20$ was found to be wrong and was replaced by the correct value $30$. The corrected variance is:

If $x+y-2=0,$ $2x-y+1=0$ and $px+qy-r=0$ are concurrent lines, then the slope of the member in the family of lines $2px+3qy+4r=0$ which is farthest from the origin is

The number of ordered triplets of positive integers which are solutions of the equation x+y+z=100 is

$\underset{x\to 0}{lim}\frac{\sqrt{1-cos2x}}{\sqrt{2}x}$ is

(JEE 2002)

If z = 3+5i, then $z^3$ + $\overline{z}$ + 198 =

5 students of a class have an average height $150\text{cm}$ and variance $18{\text{cm}}^2$. A new student, whose height is $156\text{cm}$, joined them. The variance $\left(\text{in}{\text{cm}}^2\right)$ of the height of these six students is:

A pair of linear equations which has a unique solution $x=2,y=-3$ is

The value of ${lim}_{n\to \infty }{\sum }_{r=n^2}^{(n+1{)}^2}\left(\frac{1}{\sqrt{r}}\right)$ is___.

1. 2

   
   

For positive numbers x, y and z the numerical value of the determinant $\left|\begin{array}{ccc}1& lo{g}_{x}y& lo{g}_{x}z\\ lo{g}_{y}x& 1& lo{g}_{y}z\\ lo{g}_{z}x& lo{g}_{z}y& 1\end{array}\right|$ is