Students can access the CBSE Sample Papers for Class 11 Maths with Solutions and marking scheme Term 2 Set 4 will help students in understanding the difficulty level of the exam.

## CBSE Sample Papers for Class 11 Maths Term 2 Set 4 for Practice

Time: 2 Hours

Maximum Marks: 40

General Instructions:

- This question paper contains three sections A, B and C. Each part is compulsory.
- Section -A has 6 short answer type (SA1) questions of 2 marks each.
- Section -B has 4 short answer type (SA2) questions of 3 marks each.
- Section -C has 4 long answer type questions (LA) of 4 marls each.
- There is an internal choice in some of the questions.
- Q14 is a case-based problem having 2 sub parts of 2 marks each.

Section – A

Question 1.

Find the degree measure corresponding to the following radian measure use (π = \(\frac{22}{7}\)):

\(\left(\frac{11}{16}\right)\) (2)

Question 2.

Solve the following inequality:

-15 < \(\frac{3(x-2)}{5}\) ≤ 0 (2)

Question 3.

In how many ways can select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

OR

In how many ways can a student choose a program of 5 courses, if 9 courses are available and 2 specific courses are compulsory for every student? (2)

Question 4.

Show that:

(0, 7, -10), (1, 6, -6) and (4, 9, -6) are the vertices of an isosceles triangle. (2)

Question 5.

Find the derivative of the (x^{2} + 1) cos x function :

OR

If y = \(\frac{1+\frac{1}{x^{2}}}{1-\frac{1}{x^{2}}}\), then find \(\frac{d y}{d x}\) (2)

Question 6.

Six new employees, two of whom are married to each other, are to be assigned six desks that are lined up in a row. If the assignment of employees to desks is made randomly, what is the probability that the married couple will have non-adjacent desks ? (2)

Section – B

Question 7.

Find the equation for the ellipse that satisfies the given conditions:

Major axis on the X-axis and passes through the points (4, 3) and (6, 2). (3)

OR

Find the equation for the ellipse that satisfies the given conditions: Centre at (0, 0), major axis on the Y-axis and passes through the points (3,2) and (1, 6). (3)

Question 8.

In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct? (3)

Question 9.

Prove that:

(cos x +cos y)^{2} +(sin x – sin y)^{2} = 4 cos^{2} \(\frac{x+y}{2}\) (3)

Question 10.

Show that the following system of linear inequalities has no solution:

x + 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1. (3)

Section – C

Question 11.

A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10 m and the distance between the flag posts is 8 m. find the equation of the posts traced by the man. (4)

Question 12.

Find the derivative of the (ax + b)^{n} (cx + d)^{m} function (here, a, b ,c, d, m and n are fixed non-zero constants): (4)

Question 13.

Find the area of the triangle formed by the lines joining the vertex of the parabola x^{2} = 12y to the ends of its latus rectum.

Case-Based/Data Based

Question 14.

Reena and Ajay are playing Ludo. Reena throws the die first. (4)

Find the probability of following events :

(i) A prime number will appear and A number greater than or equal to 3 will appear.

(ii) A number less than or equal to one will appear and a number more than 6 will appear.