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Find the equation of the straight line which passes through (1, - 2) and cuts off equal intercepts on the axes

The ionic radii of $x^{+}and{y}^{-}$ ions are 146 and 216 pm. The probable type of structure is

If $Z$ is a non zero complex number such that $Re\left(Z\right)=0,$ then

The logically equivalent proposition of $p\iff q$ is

Let $\text{sgn}\left(y\right)$ denote the signum function of $y.$ If $f\left(x\right)=\int (\cot \frac{x}{2}-\tan \frac{x}{2})dx$ and $f\left(\frac{\pi }{2}\right)=0,$ then which of the following statements is CORRECT?

If $f\left(x\right)=2\sqrt{x+1}{\sin }^{-1}\left(x\right)+4\sqrt{1-x},$ then $f^{\prime }\left(x\right)$ is equal to

If the normal of the plane makes angles $\frac{\pi }{4},\frac{\pi }{4}\text{and}\frac{\pi }{2}$ with positive $X$-axis and $Y$-axis and $Z$-axis respectively and the length of the perpendicular line segment from origin to the plane is $\sqrt{2}$, then the equation of the plane is:

Following is the Receipts and Payments Account of Queen's Club, Kolkata for the year ended 31st March, 2014 :

$\begin{array}{cccc}\text{Receipts}& \text{Rs}& \text{Payments}& \text{Rs}\\ \text{Balance b/d (1-4-2013)}& & \text{Rent, Rates}\&\text{Taxes}& 15,000\\ \text{Cash}& 3,600& \text{Advertisement}& 2,700\\ \text{Current A/c with Bank}& 7,570& \text{Salaries}& 27,400\\ \text{Subscriptions}& 42,200& \text{Insurance Premium}& 1,200\\ \text{Entrance fees}& 3,800& \text{Electric Charges}& 2,500\\ \text{Life Membership Fees}& 6,000& \text{Telephone Expenses}& 2,400\\ \text{Interest on Investments}& 200& \text{Furniture (Purchased on}& \\ & & \text{1st October, 2013)}& 8,000\\ & & \text{Balance c/d (31-3-2014): -}& \\ & & \text{Cash}& 2,400\\ & & \text{Current A/c with Bank}& 1,770\\ & \underset{–}{\overline{63,370}}& & \underset{–}{\overline{63,370}}\end{array}$

Prepare Income and Expenditure A/c of the club for the year ended 31st March, 2014 and a Balance Sheet as at that date having due regard for the following information:

Rs

(1) Subscriptions Outstanding on 31st March 2013 4,000

Subscriptions Outstanding on 31st March, 2014 5,400

Subscriptions Received in advance on 31st March, 2013 1,500

Subscriptions Received in advance on 31st March, 2014 2,100

(2) Two months rent Rs 2,500 was due both at the beginning and end of the year.

(3) As on 31st March, 2013, Premises stood in the books at Rs 55,000 and Investments at Rs 20,000. Depreciate furniture by 10% p.a.

Let $\alpha$ and $\beta$ be the roots of the equation, $5x^2+6x-2=0.$

If $S_n={\alpha }^n+{\beta }^n,n=1,2,3,.........,$ then:

If the point $(\lambda ,\lambda +1)$ lies inside the region bounded by the curve $x=\sqrt{25-y^2}$ and y-axis, then $\lambda$ belongs to the interval

The fundamental period of the function $f\left(x\right)=2cos\frac{1}{3}(x-\pi )$ is

Question 1: Use the figure to name :

(a)Five points

If in a class of $100$ students, $60$ like mathematics, $72$ like physics, $68$ like chemistry and no student likes all three subjects, then the number of students who didn't like mathematics and chemistry is ?

Let any circle $S$ passes through the point of intersection of lines $\sqrt{3}(y-1)=x-1$ and $y-1=\sqrt{3}(x-1)$ and having its centre on the acute angle bisector of the given lines. If the common chord of $S$ and the circle $x^2+y^2+4x-6y+5=0$ passes through a fixed point, then the fixed point is

If $\overrightarrow{A}\cdot (\overrightarrow{B}+\overrightarrow{C})=\overrightarrow{B}\cdot (\overrightarrow{C}+\overrightarrow{A})=\overrightarrow{C}\cdot (\overrightarrow{A}+\overrightarrow{B})=0$ and $|\overrightarrow{A}|=3,|\overrightarrow{B}|=4$ and $|\overrightarrow{C}|=5,$ then $|\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}|=$

If -0.25x + 1.3 = -0.55x - 0.2 , then x.

If a unit vector $\overrightarrow{a}$ makes an angle $\frac{\pi }{3}$ with $\hat{i}$, $\frac{\pi }{4}$ with $\hat{j}$ and $\theta \in (0,\pi )$ with $\hat{k}$, then a value of $\theta$ is :

For the
matrix,
find the numbers a and b such that A²
+ aA + bI = O.

If $\sqrt{{\log }_2\left(\frac{2x-3}{x-1}\right)}<1,$ then $x\in$

The value of the integral $\int \frac{e^{2{\tan }^{-1}x}(1+x{)}^2}{1+x^2}dx$ is equal to

What is the remainder when $7^{103}$ is divided by 50?

The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.

If $co{s}^{-1}p+co{s}^{-1}q+co{s}^{-1}r=\pi$ then $p^2+q^2+r^2=$

If $n_1,n_2$ and $n_3$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by:
If $n_1$ origin

Let $z\in C$ be such that $|z|<1$. If $\omega =\frac{5+3z}{5(1-z)}$, then :