The height of the rectangular piece after being bent is 5 in.The new length of the rectangular piece is 50... View Article
The given expression is cos x + √sin x = 0.\(\begin{array}{l}\cos x=\sqrt{\sin x}\\ \text { Squaring on both sides}\\ \cos... View Article
⇒ f (1) + 2 f (2) + 3 f (3) . . . . + n f (n) =... View Article
The distance between the points x and y that is – 9 and 0 is given by |x – y|=... View Article
Total number of ways of selecting a card = 52 waysThere exist 8 honours on the 26 red cards.A red... View Article
log (100 / 90)\(\begin{array}{l}=\log _{10}\left(\frac{10\cdot \:10}{90}\right)\\ =\log _{10}\left(\frac{10\cdot \:10}{10\cdot \:9}\right)\\ =\log _{10}\left(\frac{10}{9}\right)\\ \log _a\left(\frac{x}{y}\right)=\log _a\left(x\right)\:-\:\log _a\left(y\right)\\ \log _{10}\left(\frac{10}{9}\right)=\log _{10}\left(10\right)-\log _{10}\left(9\right)\\... View Article
The given series is 1, 4, 16, 64, . . .a = 1r = 4 / 1 = 4The nth... View Article
The given expression is 175o 45’.\(\begin{array}{l}175^{0} 45^{\prime} =\left(175+\frac{45}{60}\right)^{0} \\ =\left(175+\frac{3}{4}\right)^{0} \\ =\left(\frac{703}{4}\right)^{0}\\ 1^{0}=\frac{\pi}{180} radian\\ \Rightarrow\left(\frac{703}{4}\right)^{0} \\=\frac{\pi}{180} \times \frac{703}{4} \\ =\frac{703}{720}... View Article
P = Rs. 1500, R = 12% p.a. and Time = 3 years 3 months.3 years 3 months = (39... View Article
The given expression is sin 7θ = sin 4θ – sin θ.\(\begin{array}{l}\Rightarrow \sin 7 \theta+\sin \theta=\sin 4 \theta\\ \Rightarrow 2... View Article
3, 7, 9, 21, 27, 66, 81, 189, 243.There exist two alternate series.Series I: 3, 9, 27, 81, 243Series II:... View Article
The diameter of a tennis ball is 6.58 cm; the radius of the sphere is:\(\begin{array}{l}\mathrm{r} =\frac{1}{2} 6.58 \mathrm{~cm} \\ \mathrm{r}... View Article
The three numbers are in the ratio 2 : 3 : 5 and the sum of them is 800. Sum... View Article
30 less than 12 times the number y equals 6.
As the x-coordinate of every point in the yz-plane is zero. Let P (0, y, z) be a point on... View Article
Let the percentage be x.(150 / 30) × (100 / 100) = [(150 × 100) / (30)] × (1 /... View Article
The midpoints need to be found by taking the average of the upper and lower limits of each class interval... View Article
The cost of 2 (1 / 3) meters of cloth is Rs. 75 (1 / 4).The cost of 1 meter... View Article
i. (13)1/5 ii. (9)1/6 iii. (256)1/2 iv. (17)1/3 v. (100)1/8 vi. (30)1/7
The given expression is 2x4 – 32.\(\begin{array}{l}2 \mathrm{x}^{4}-32=2\left(\mathrm{x}^{2}-16\right)\\ 2 \mathrm{x}^{4}-32=2\left[\left(\mathrm{x}^{2}\right)^{2}-4^{2}\right]\\ 2\mathrm{x}^{4}-32=2\left[\left(\mathrm{x}^{2}+4\right)\left(\mathrm{x}^{2}-4\right)\right]\\ 2\mathrm{x}^{4}-32=2\left[\left(\mathrm{x}^{2}-2^{2}\right)\left(\mathrm{x}^{2}+4\right)\right]\\ 2 x^{4}-32=2\left[(x+2)(x-2)\left(x^{2}+4\right)\right]\\ 2 x^{4}-32=2(x+2)(x-2)\left(x^{2}+4\right)\end{array} \)
