Mathematics seems to be a nightmare for the majority of students, as they lack the confidence and practice of the subject. We at BYJUâ€™S provide students of class 11th with important mark-wise questions for practice. Practising these questions would give you an idea about the pattern of examination. Here we provide a few important 6 marks questions for practice. As these questions are a little tricky, thus this section requires a good practice of different long type questions, which can appear in the final examination.

**Important 6 Marks Questions for Class 11 Maths exam are as follows-**

**Question 1-** In a survey of 5,000 people in a town, 2,250 were listed as reading English newspaper, 1,750 are reading Hindi newspaper and 875 were listed as reading both Hindi as well as English. Find how many people neither read Hindi nor English newspaper. Also, find how many read-only English newspaper.

**Question 2- **Using binomial theorem, find the value of \((52)^{4}\).

**Question 3- **Show that-

\(\frac{1.2^{2} + 2.3^{2} + …….. + n(n+1)^{2}}{1^{2}.2+ 2^{2}.3+ ………+ n^{2}.(n+1)} = \frac{3n+5}{3n+1}\)

**Question 4- **Describe the set of complex number z such that

\(\left | \frac{z+2-i}{z+5+4i} \right | = 5\)

**Question 5- **A family of 4 members planner to go for Goa by train during summer for adventures. On the day of Journey all the auto/taxi drivers were on strike due to price hike of petrol. So the family couldn’t get any transport to railway station. Now family is standing at the crossing of two straight roads represented by equations 2x – 3y – 4 = 0Â and 3x – 4y – 5 = 0,Â want to reach the path whose equation is 6x – 7y + 8 = 0Â in least time. Find the equation of path that they should follow any why.

**Question 6- **Find the value of n, if the ratio of the fifth term from the beginning to the fifth term from end in the

\(\left ( 2^{\frac{1}{4}} + \frac{1}{3^{\frac{1}{4}}} \right )^n\) is \(\sqrt{6} : 1\).

**Question 7- **Of the members of three athletic teams in a certain school, 21 axes in the basketball team, 26 in hockey team and 20 in the football team. 14 play hockey and basketball, 15 play hockey and football, 12 play football and basketball and 8 play all the three games. How many members are there in all?

**Question 8- **Find the fourth term in G.P. in which the third term is greater than the first by 9 and the second term is 3 greater than the fourth by 18.

**Question 9- **Solve the given system of inequalities graphically:

\(x-2y \leq 3\)

\(3x + 4y \geq 12\)

\(x \geq 1\)

\(y \geq 1\)

**Question 10- **Show that area of the triangle formed by the lines \(y = m_{1}x + c_{1}\), \(y = m_{2}x + c_{1}\) and \(x = 0\) is

\(\frac{(c_{1} – c_{2})^{2}}{2\left | m_{1} – m_{2} \right |}\)

**Question 11- **Using binomial theorem, prove that \(6^{n} – 5n -1\) is always divisible by 25.

**Question 12- **A student wants to arrange 3 Mathematics, 4 Hindi and 5 Physics book on a shelf. In how many ways the book can be arranged? How many arrangements are possible if all the books in the same subject are to be all together?

**Question 13- **In any triangle ABC, prove that:

(i) \(\left ( \frac{\sin(B-C)}{\sin (B + C)} \right ) = \frac{b^{2} – c^{2}}{a^{2}}\)

(ii) \(b \cos B + c \cos C = a \cos (B-C)\)

**Question 14- **Prove that the diagonals formed by the four straight lines

\(\sqrt{3}x+ y = 0; \sqrt{3}y+ x = 0, \sqrt{3}x+ y = 1\) and \(\sqrt{3}y + x = 1\) are at right angles to one another.

**Question 15- **Prove that there is no term involving \(x^{5}\) in the expansion of \(\left ( 2x^{2} – 3/x \right )^{11}\).

**Question 16- **Find the equation of the circle which passes through the points (2,-2) and (3,4) and whose centre lies on \(x + y = 1\).

**Question 17- **Find the coefficient of \(x^{5}y^{7}\) in the equation \((x – 7y)^{12}\).

**Question 18- **If the sum of n terms of two arithmetic progressions are in the ratio \(14 – 5n: 3n+5\), then find the ratio of their 8th terms.

**Question 19- **In a survey, it was found that people encourage their wards for science/commerce streams, and it looks commonly at school/college labels, there are 40 students in chemistry class and 60 students in physics class. Find the number of students who are either in physics or chemistry class in the following cases:

(i) The two classes meet at the same hour.

(ii) The two classes meet at different hours and 20 students enrolled in both subjects,

**Question 20- **An analysis of monthly wages paid to workers in two firms A and B belonging to the same industry, gives the following results:

Firm A | Firm B | |

No. of wage earners | 586 | 648 |

Mean of monthly wages | Rs. 5253 | Rs. 5253 |

The variance of the distribution of the wages | 100 | 121 |

(i) Which firm A or B pays a larger amount as monthly wages?

(ii) Which firm A or B shows greater variability in individual wages?