It is given that logb a = loga b.\(\begin{array}{l}\Rightarrow \frac{\log \mathrm{a}}{\log \mathrm{b}}=\frac{\log \mathrm{b}}{\log \mathrm{a}}\\ \Rightarrow(\log \mathrm{a})^{2}=(\log \mathrm{b})^{2}\\ \Rightarrow(\log \mathrm{a})^{2}-(\log \mathrm{b})^{2}=0\\... View Article
The given equations are 3x + 4y = 10 and 2x – 2y = 2. \(\begin{array}{l}\begin{bmatrix}3x+4y=10\\ 2x-2y=2\end{bmatrix}\\ 3x+4y=10\\ 3x+4y-4y=10-4y\\ 3x=10-4y\\... View Article
The given equation is x2 – 2x + 4 = 0.\(\begin{array}{l}x^2-2x+4=0\\ x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ a=1,\:b=-2,\:c=4\\ x_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:1\cdot \:4}}{2\cdot \:1}\\ \sqrt{\left(-2\right)^2-4\cdot... View Article
Odds in favour of the event = [number of fair events] / [number of unfair events]The odds in favour of... View Article
Let – 33 / 8 be divided by x to get – 11 / 2.\(\begin{array}{l}\frac{-33}{8} \div \mathbf{x}=\frac{-11}{2} \\ \Rightarrow \mathbf{x}=\frac{-33}{8}... View Article
The angle of elevation and angle of depression is measured with the line of sight that is always horizontal.
The largest four-digit number is 9999. The smallest five-digit number is 10000. 9999 + 10000 = 19999
Cost price of football = Rs. 120Selling price of football = Rs. 105Selling price < Cost price, a loss is... View Article
The side of a square board is 50 cm.Perimeter of square board = 4 x side = 4 x 50... View Article
It can be expressed in the usual form as follows.\(\begin{array}{l}3.02 \times 10^{-6} \\ =\frac{302}{100} \times 10^{-6} \\ =\frac{302}{10^{2}} \times 10^{-6}... View Article
The length of a class can be obtained by the difference between the upper and lower limits of the class... View Article
The number of red flags = 4 The number of white flags = 2 The number of green flags =... View Article
(i) Average = [48 + 23 + 13 + 54 + 7] / 5= 145 / 5= 29 (ii) Average... View Article
The number of ways of choosing 2 station from 15 different stations = 15C2 = [15 * 14] / 2=... View Article
The time between 8.30 a.m. and 9.05 a.m. = 35 minutesArea swept in one 60 minutes = π . 82... View Article
23 × 2 + 2 = 48,48 × 2 + 3 = 99,99 × 2 + 5 = 203,203 ×... View Article
The value of r can be found as follows.\(\begin{array}{l}{ }^{\mathrm{n}} \mathrm{P}_{\mathrm{r}}={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}} \times \mathrm{r} ! \\ { }^{6} \mathrm{P}_{\mathrm{r}}=15... View Article
The net of a rectangular prism has six rectangles.
Let the three digits be a, ar and ar2.\(\begin{array}{l}100 a+10 a r+a r^{2} \ldots(\mathrm{i}) \\ a+a r^{2}=2 a r+1 or... View Article
Let the number be x.(4 / 7) x = 84x = [84 * 7] / 4x = 21 * 7x... View Article
