The lines which aren’t on the same plane and they neither intersect each other are called:
Skew lines are the lines that are neither on the same plane and they do not intersect each other.
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A person writes letters to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that (a) At least two of them are in the wrong envelopes? (b) All the letters are in the wrong envelopes?
A person writes letters to six friends and addresses the corresponding envelopes. \(\begin{array}{l}(a) \text { The number of ways in... View Article
Find three rational numbers between 0. 1 and 0.11.
0.101, 0.102, 0.103 are the 3 rational numbers between 0.1 and 0.11.
Find the cost price, if: (i) S.P. = Rs. 1,680 and profit = 12% (ii) S.P. = Rs. 1,128 and loss = 6%
To find the cost price \(\begin{array}{l}\begin{array}{l} \text { (i) S.P. = Rs. } 1680 \text { and Profit }=12 \%... View Article
4, 9, 25, 49, ….
The given sequence is the square on prime number 2, 3, 5, 7, 11 etc. The next number is 121.
Express the given number as a product of its prime factors: 32760.
32760 can be expressed as \(\begin{array}{l}\begin{array}{l|l} 2 & 32760 \\ \hline 2 & 16380 \\ \hline 2 & 8190 \\... View Article
The number of lines of symmetry for a line segment is _____.
There is one line of symmetry.
√10 * √15 =
The given expression is \(\begin{array}{l}\sqrt{10} \times \sqrt{15}\\=\sqrt{5 \times 2} \times \sqrt{5 \times 3}\\=\sqrt{5 \times 5 \times 2 \times 3}\\=5 \sqrt{6}\end{array}... View Article
Find the number of integers from 0 to 999999 that have no two equal neighbouring digits in their decimal representation –
Total number of digits from 0-9 having no neighbour common = 10 \(\begin{array}{l} \text { Total number of digits from... View Article
Find the continued product: (x – 3) (x + 3) (x2 + 9).
Consider the given expression. \(\begin{array}{l}\begin{array}{l} (\mathbf{x}-3)(\mathbf{x}+3)\left(\mathbf{x}^{2}+9\right) \\ (\mathbf{a}+\mathbf{b})(\mathbf{a}-\mathbf{b})=\mathbf{a}^{2}-\mathbf{b}^{2} \\ =\left(\mathbf{x}^{2}-9\right)\left(\mathbf{x}^{2}+9\right) \\ =\mathbf{x}^{4}-\mathbf{8 1} \end{array}\end{array} \)
5, 11, 23, 47, 95, ____
The logic is + 6, + 12, + 24, + 48, + 96, …. The next term is 95 +... View Article
The principal value of sin-1 (- √3 / 2) is
The principal value of \(\begin{array}{l} \sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)=\sin ^{-1}\left(\sin \left(-\frac{\pi}{3}\right)\right)=-\frac{\pi}{3}\end{array} \)
If a + b = 5 and ab = 6, then find a2 + b2.
To find a2 + b2. \(\begin{array}{l}(\mathbf{a}+\mathbf{b})^{2}=\mathbf{a}^{2}+\mathbf{b}^{2}+\mathbf{2 a b} \\ =>\mathbf{a}^{2}+\mathbf{b}^{2}=(\mathbf{a}+\mathbf{b})^{2}-2 \mathrm{ab} \\ \mathbf{a}+\mathbf{b}=5 \text { and } \mathrm{ab}=6 \\ \mathbf{a}^{2}+\mathbf{b}^{2}=(\mathbf{a}+\mathbf{b})^{2}-2... View Article
Write the following integers in ascending order (smallest to biggest) – 4, – 3, – 5, 2.
The following integers in ascending order is – 5, – 4, – 3, 2.
The multiplicative inverse of 1010 is
The multiplicative inverse of 1010 = 1 / 1010 = 10-10.
How do you find the square root of 6561?
√6561 = √3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 = √6561 =... View Article
In the library, 136 copies of a certain book require a shelf length of 3.4 metres. How many copies of the same book would occupy a shelf length of 5.1 meters?
Let the number of copies be ‘x’. 3.4 / 136 = 5.1 / x By cross-multiplying 3.4x = 5.1 (136) ... View Article
The solution of the differential equation y dx + (x + x2y) dy = 0 is
The given equation can be written as \(\begin{array}{l}\begin{array}{l} \Rightarrow \mathrm{ydx}+\mathrm{xdy}=-\mathrm{x}^{2} \mathbf{y d} \mathrm{y}\\ \Rightarrow \frac{\mathbf{y d x}+\mathbf{x d y}}{\mathbf{x}^{2} \mathbf{y}^{2}}=-\frac{1}{\mathbf{y}}... View Article
The age of the mother is twice the square of the age of her son. Eight years hence, the age of the mother will be 4 years more than three times the age of her son. Find their present age.
Assume the age of the son to be x years. The age of the mother is twice the square of... View Article
Convert 0.05 kg into grams.
1 kg = 1000 g 0.05 kg = 0.05 × 1000 = 50 grams
