The Central Board of Secondary education is responsible for conducting an examination of the schools affiliated to the Central Board. Students usually find maths as one of the most difficult paper. The major reason is due to lack of confidence and less of practice. It is suggested that practicing maths on daily basis will help students to develop to their full potential and also help them to solve the question with high accuracy.
We at BYJU’S provide the student with 4 marks maths important questions for class 11th. Students can practice 4 marks wise question to be aware of the questions that can be framed in their final examination.
Question 1- In triangle ABC, prove that
\(\frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} = \frac{a^{2}+ b^{2}+ c^{2}}{2abc}\)Question 2- How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letter out of word DAUGHTER?
Question 3- Find the coordinates of the orthocentre of the triangle whose vertices are (-1,3), (2,-1) and (0,0).
Question 4- Find the domain and range of the function \(f(x) = \frac{1}{\sqrt{x – \left | x \right |}}\).
Question 5- Find the variance for the following data-
Classes |
0-30 |
30-60 |
60-90 |
90-120 |
120-150 |
150-180 |
180-210 |
Frequencies |
2 |
3 |
5 |
10 |
3 |
5 |
2 |
Question 6- Using principle of mathematical induction, prove that
\(\frac{1}{3.5} + \frac{1}{5.7} + \frac{1}{7.9} + …….. + \frac{1}{(2n+1)(2n+3)} = \frac{n}{3(2n+3)}, \forall n \in N\).
Question 7- Express in the form of a+ib,
\(\left ( \frac{(3 + i\sqrt{5})(3 – i\sqrt{5})}{(\sqrt{3} + i\sqrt{2})(\sqrt{3} – i\sqrt{2})} \right )\)Question 8- Prove that: \(\cot (15/2)^{\circ} = \sqrt{2} + \sqrt{3} + \sqrt{4} + \sqrt{6}\)
Question 9- Four cards are drawn at random from a pack of 52 playing cards. Find the probability of getting one card from each suit.
Question 10- If a is A.M. and b and c be two G.M.s between any two positive numbers, then prove that \(b^{3} + c^{3} = 2abc\).
Question 11- In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee?
Question 12- Represent the complex number \(1 + \sqrt{3}i\) in polar form.
Question 13- On an evening a man planned a party of their friends on his 25th marriage anniversary. When all of his friends have arrived, he introduced all to each other and everybody shakes hand with everybody else. Find the total person in a room, if total shake hands are 66.
Question 14- A committee of two members is selected from two men and two women. What is the probability that the committee will have one man.
Question 15- A teacher teaches their students with such a spirit that they must know what he knows? After teaching with same spirit, he decided to check the ability of the students through a test. He has given a question, if a,b are roots of \(x^{2} – 3x + p = 0\), c and d are roots of \(x^{2} – 12x + 1 = 0\), where a,b,c,d are in G.P. Evaluate the ratio q+p to q-p.
Question 16- Find the equation of set of points ‘P’ such that its distance from the points (3,4,-5) and (-2,1,4) are equal.
Question 17- A horse is tied to a pole by a rope. If the horse moves along a circular path keeping the rope tight and describe 176m when it has traced out \(72^{\circ}\) at the pole, find the length of the rope.
Question 18- Evaluate the value of \(\tan \left ( \frac{\pi}{8} \right )\)
Question 19- If \(\left ( 1 + 1/i – i\right )^{m} = 1\), then find the least integral value of m.
Question 20- Evaluate-
(i) \(\lim \limits_{x \to 0} \left [ \frac{(x+1)^{5}-1}{x} \right ]\)
(ii) \(\lim \limits_{x \to \pi} \left [ \frac{\sin (\pi + x)}{\pi( \pi -x)} \right ]\)