Here you will learn some sets examples for better understanding of sets concepts. Example 1 : The set A = [x : x \(\in\) R, x^2 = 16 and 2x = 6] equal- Solution : \(x^2\) = 16 \(\implies\) x = \(\pm\)4 2x = 6 \(\implies\) x = 3 There is no value of x …
Here you will learn some sequences and series examples for better understanding of sequences and series concepts. Example 1 : If \({\sum}_{r=1}^{n} T_r\) = \(n\over 8\) (n + 1)(n + 2)(n + 3), then find \({\sum}_{r=1}^{n} \)\(1\over T_r\) Solution : \(\because\) \(T_n\) = \(S_n – S_{n-1}\) = \({\sum}_{r=1}^{n} T_r\) – \({\sum}_{r=1}^{n …
Here you will learn some scalar and vector examples for better understanding of scalar and vector concepts. Example 1 : Find the vector of magnitude 5 which are perpendicular to the vectors \(\vec{a}\) = \(2\hat{i} + \hat{j} – 3\hat{k}\) and \(\vec{b}\) = \(\hat{i} – 2\hat{j} + \hat{k}\). Solution : Unit vectors perpendicular to \(\vec{a}\) & …
Here you will learn some relations examples for better understanding of relation concepts. Example 1 : If A = {2, 4} and B = {3, 4, 5} then (A \(\cap\) B) \(\times\) (A \(\cup\) B) Solution : (A \(\cap\) B) = {4} and (A \(\cup\) B) = {2, 3, 4, 5} \(\therefore\) (A \(\cap\) B) …
Here you will learn some probability examples for better understanding of probability concepts. Example 1 : From a group of 10 persons consisting of 5 lawyers, 3 doctors and 2 engineers,four persons are selected at random. The probability that selection contains one of each category is- Solution : n(S) = \(^{10}C_4\) = 210 n(E)= \(^5C_2 …
Here you will learn some permutation and combination examples for better understanding of permutation and combination concepts. Example 1 : If all the letters of the word ‘RAPID’ are arranged in all possible manner as they are in a dictionary, then find the rank of the word ‘RAPID’. Solution : First of all, arrange all …
Here you will learn some parabola examples for better understanding of parabola concepts. Example 1 : The length of latus rectum of a parabola, whose focus is (2, 3) and directrix is the line x – 4y + 3 = 0 is – Solution : The length of latus rectum = 2 x perp. from …
Here you will learn some logarithm examples for better understanding of logarithm concepts. Example 1 : If \(log_e x\) – \(log_e y\) = a, \(log_e y\) – \(log_e z\) = b & \(log_e z\) – \(log_e x\) = c, then find the value of \(({x\over y})^{b-c}\) \(\times\) \(({y\over z})^{c-a}\) \(\times\) \(({z\over x})^{a-b}\). Solution : \(log_e …
Here you will learn some limits examples for better understanding of limit concepts. Example 1 : If \(\displaystyle{\lim_{x \to \infty}}\)(\({x^3+1\over x^2+1}-(ax+b)\)) = 2, then find the value of a and b. Solution : \(\displaystyle{\lim_{x \to \infty}}\)(\({x^3+1\over x^2+1}-(ax+b)\)) = 2 \(\implies\) \(\displaystyle{\lim_{x \to \infty}}\)\(x^3(1-a)-bx^2-ax+(1-b)\over x^2+1\) = 2 \(\implies\) \(\displaystyle{\lim_{x \to \infty}}\)\(x(1-a)-b-{a\over x}+{(1-b)\over x^2}\over 1+{1\over x^2}\) = …
Here you will learn some inverse trignometric function examples for better understanding of inverse trigonometric function concepts. Example 1 : Find the value of \(sin^{-1}({-\sqrt{3}\over 2})\) + \(cos^{-1}(cos({7\pi\over 6}))\). Solution : \(sin^{-1}({-\sqrt{3}\over 2})\) = – \(sin^{-1}({\sqrt{3}\over 2})\) = \(-\pi\over 3\) \(cos^{-1}(cos({7\pi\over 6}))\) = \(cos^{-1}(cos({2\pi – {5\pi\over 6}}))\) = \(cos^{-1}(cos({5\pi\over 6}))\) = \(5\pi\over 6\) Hence \(sin^{-1}({-\sqrt{3}\over …
