A wet, swampy, and marshy region in Northern Plains of India is known as _________
A wet, swampy, and marshy region in Northern Plains of India is known as terai.
Latest Posts
A square matrix is an orthogonal matrix if
AA’ = I In a matrix A of 3 × 3 order. A′ is the transpose matrix of matrix A.... View Article
Complete the following series: 0, 5, 22, 57, ?, 205.
0 = 13 – 1 5 = 23 – 3 22 = 33 – 5 57 = 43 – 7... View Article
The side of a rectangular pentagon is denoted by l. Express the perimeter of the pentagon using the variable l.
A regular pentagon is a polygon where all the sides are equal. Perimeter = l + l + l +... View Article
Write a statement of the Pythagoras theorem and show that the 6, 8 and 10 are Pythagorean triplets.
Statement: The square of the hypotenuse is equal to the sum of the squares of opposite and adjacent sides. For... View Article
A rectangular field is to be fenced on three sides leaving a side of 20 m uncovered. If the area of the field is 680 m2, how many metres of fencing will be required.
The length of one side is 20 m and the area is 680 m2. ⇒ Length of another side =... View Article
Find the missing number 0, 7, 26, 63, ___.
The missing term in the series is \(\begin{array}{l}0,7,26,63, \ldots \\ 1^{3}-1=0\\ 2^{3}-1=7\\ 3^{3}-1=26\\ 4^{3}-1=63\\ 5^{3}-1=124\\ \text { Hence, the answer... View Article
Find the square root of the following number by the prime factorisation method 1936.
The factors of 1936 is 1936 = 2 × 2 × 2 × 2 × 11 × 11 Take square... View Article
If the compound interest on a certain sum for 2 years is Rs 21. What could be the simple interest?
Compound interest at rate r for 2 years becomes: (1 + r)2 = 1.21 ⇒ r = 10% At r... View Article
Prove that cos [(3π / 4) + x] – cos [(3π / 4) – x] = – √2 sinx.
By taking LHS of the given expression \(\begin{array}{l}=\cos \left(\frac{3 \pi}{4}+x\right)-\cos \left(\frac{3 \pi}{4}-\mathrm{x}\right) \\ =-2 \sin \left\{\frac{\left(\frac{3 \pi}{4}+x\right)+\left(\frac{3 \pi}{4}-\mathrm{x}\right)}{2}\right\} \sin \left\{\frac{\left(\frac{3... View Article
How many numbers are there containing 2 digits?
Greatest two digit number − smallest two digit number) + 1 = (99 − 10) + 1 = 89 +... View Article
Find the cube root of the decimal: 19.683.
The cube root of the decimal 19.683 is given by \(\begin{array}{l}\begin{array}{l} \sqrt[3]{19.683}\\=\sqrt[3]{\frac{19683}{1000}} \\ =\frac{\sqrt[3]{19683}}{\sqrt[3]{1000}} \\ =\frac{\sqrt[3]{3 \times 3 \times 3... View Article
Find the prime factors of 128.
Prime factorisation of 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2 Exponential form... View Article
20% of 700 m is
20% of 700 m = (20 / 100) * 700 = 140m
Show that the right-circular cone of the least curved surface and given volume has an altitude equal to √2 times the radius of the base.
Let ABC be right-circular cone having radius r and height h. \(\begin{array}{l}\text { If V and S are its volume... View Article
Show that (sec θ + cos θ) (sec θ – cos θ) = tan2 θ + sin2 θ.
LHS = (sec θ + cos θ) (sec θ – cos θ) = sec2 θ – cos2 θ = (1... View Article
If x sin3 θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ then
x sin3 θ + y cos3 θ = sin θ cos θ \(\begin{array}{l}\Rightarrow(x \sin \theta) \sin ^{2} \theta+(y \cos \theta)... View Article
If (z − 1) / (z + 1) is purely imaginary then what would be the locus of z?
Let z=x+iy \(\begin{array}{l}\frac{\mathrm{z}-1}{\mathrm{z}+1}=\frac{\mathrm{x}+\mathrm{iy}-1}{\mathrm{x}+\mathrm{i} \mathrm{y}+1}\\ =\frac{(\mathrm{x}-1)+\mathrm{i} y}{(\mathrm{x}+1)+\mathrm{i} y} \cdot \frac{(\mathrm{x}+1)-\mathrm{i} \mathrm{y}}{(\mathrm{x}+1)-\mathrm{i} \mathrm{y}}\\ =\frac{(\mathbf{x}-\mathbf{1})(\mathbf{x}+\mathbf{1})-\mathbf{i}^{2} \mathbf{y}^{2}+\mathrm{i} \mathbf{y}[\mathbf{x}+\mathbf{1}-(\mathbf{x}-1)]}{(\mathbf{x}+1)^{2}-\mathbf{i}^{2} \mathbf{y}^{2}} \frac{z-1}{z+1}\\ =\frac{x^{2}-1+y^{2}+i 2 y}{(x+1)^{2}+y^{2}}\\ \frac{\mathrm{z}-1}{\mathrm{z}+1}=\frac{\mathrm{x}^{2}-1+\mathrm{y}^{2}}{(\mathrm{x}+1)^{2}+\mathrm{y}^{2}}+\mathrm{i}... View Article
Father’s age is three times the sum of ages of his two children. After 5 years, his age will be twice the sum of the ages of two children. Find the age of the father.
Assume the age of two children to be x and y. Father’s present age = 3 (x + y) After... View Article
True or False: The arrangement of data in rows and columns is called classification of data.
The given statement is false.
