How Do You Determine The Molar Mass Of Helium
The molar mass of an element is its atomic weight in grams/mole (g/mol). The atomic weight for helium on the... View Article
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Explain Theoretically The Lewis Structure Diagram Of Covalent Compound Al2cl6
AlCl3 has 6 covalent bonds and 2 coordinate bonds. Chlorine has 17 electrons. 10 electrons are occupied in these orbitals... View Article
25 Nov 2020: The Hindu Analysis
UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 25th November 2020. Important news and... View Article
Gist of EPW November Week 3, 2020
The Economic and Political Weekly (EPW) is an important source of study material for IAS, especially for the current affairs segment.... View Article
How is cosine calculated?
Trigonometry is an important branch of mathematics that deals with finding the missing sides and angles of a right angled... View Article
How do You Solve Linear Equations by Graphical Method?
In Algebra, the linear equation is defined as an algebraic equation, in which each term has an exponent value of... View Article
What is a solid triangle called
In geometry, a solid that is made up of four triangular faces is called tetrahedron. Also, a pyramid that has... View Article
What is tan cos and sin?
Tan, cos and sin are three primary trigonometric functions or trigonometric ratios. Tan, cos and sin are abbreviations of tangent,... View Article
How is sin calculated
In trigonometry, sine is one of three primary functions. Sine function is abbreviated as sin. To calculate the sine of... View Article
Is circle a solid shape?
A circle is not a solid shape. A circle is a closed, two-dimensional figure or a flat figure. Therefore, it... View Article
What are the six trig identities
The six trigonometric identities or the trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant and Cotangent. They are abbreviated as... View Article
If a_n = i ^(n+1)2, where i =√-1 and n = 1,2,3… Then , the value of a1 + a3 +a5+…+a25 is (1) 13 (2) 13 + i (3) 13 – i (4) 12 (5) 12 – i
Solution: Given an = i (n+1)2 a1 + a3 +a5+…+a25 =\(\begin{array}{l}i^{(1+1)^{2}}+i^{(3+1)^{2}}+i^{(5+1)^{2}}+..i^{(25+1)^{2}}\end{array} \) There are 13 odd numbers from 1 to... View Article
The equation z bar z + a bar z+b=0 , b∈R represents a circle if (1) |a|^2 = b (2) |a|^2 > b (3) |a|^2 < b(4) None of these
Solution: \(\begin{array}{l}z\bar{z}+a\bar{z}+\bar{a}z+b = 0\end{array} \) \(\begin{array}{l}a\bar{a}+z\bar{z}+a\bar{z}+b = 0\end{array} \) \(\begin{array}{l}(z+a)(\bar{z}+\bar{a})= a\bar{a}-b\end{array} \) |z+a|2 = |a|2-b This will represent a circle... View Article
If |z- bar z| + |z+ bar z| = 2, then z lies on (1) a circle (2) a square (3) an ellipse (4) a line
Solution: Given \(\begin{array}{l}\left | z-\bar{z} \right |+\left | z+\bar{z} \right |=2\end{array} \) Consider z = x+iy \(\begin{array}{l}\bar{z}=x-iy\end{array} \) \(\begin{array}{l}z+\bar{z}= 2x\end{array}... View Article
If (3+ i) ( z-bar z )- (2+ i) ( z-bar z) + 14i = 0, then z bar z is equal to (1) 5 (2) 8 (3) 10 (4) 40
Solution: Given \(\begin{array}{l}(3+i)(z+\bar{z})-(2+i)(z-\bar{z})+14i = 0\end{array} \) ..(1) Let z = x+iy \(\begin{array}{l}\bar{z}\end{array} \) = x-iy \(\begin{array}{l}z+\bar{z}\end{array} \) = 2x \(\begin{array}{l}z-\bar{z}\end{array}... View Article
If Z and ω are two complex numbers such that |Z| ≤ 1, |ω|≤ 1 and |Z – iω| = [latex]\left| Z-i\bar{\omega }\right|[/latex] = 2. Then, z is equal to (1) 1 or i (2) i or – i (3) 1 or – 1 (4) i or -1
Solution: Given |Z| ≤ 1, |ω|≤ 1. |Z – iω| = \(\begin{array}{l}\left| Z-i\bar{\omega }\right|\end{array} \) = 2. squaring |Z –... View Article
If -π
Solution: If arg (z) = -π+θ Then arg \(\begin{array}{l}\bar{z}\end{array} \) = π-θ So arg \(\begin{array}{l}\bar{z}\end{array} \) – arg \(\begin{array}{l}-\bar{z}\end{array} \)... View Article
If Z = 4/(1-i) then bar z is equal to (where, bar z is complex conjugate of z) (1) 2(1+i) (2) 1+i (3) 2/(1-i) (4) 4/(1+i)
Solution: If Z = x+iy, then conjugate of Z is (x-iy) Z = 4/(1-i) = 4(1+i)/(1-i)(1+i) = 4(1+i)/2 = 2(1+i)... View Article
If |z1 + z2|^2 = |z1|^2 + |z2|^2 , then z1/z2 is (1) purely real (2) purely imaginary(3) zero of purely imaginary (4) Neither real nor imaginary
Solution: Given |z1 + z2|2 = |z1|2 + |z2|2 ⇒ \(\begin{array}{l}(z_{1}+z_{2})+(\bar{z_{1}}+\bar{z_{2}})=\left | z_{1} \right |^{2}+\left | z_{2} \right |^{2}\end{array} \)... View Article
What is the modulus of elasticity of steel?
Modulus of elasticity is a property that measures the resistance of materials towards deformation under load. Modulus of elasticity, also... View Article
