Students can access the CBSE Sample Papers for Class 11 Maths with Solutions and marking scheme Term 2 Set 5 will help students in understanding the difficulty level of the exam.

## CBSE Sample Papers for Class 11 Maths Term 2 Set 5 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.

Prove that:

tan 13x = tan 4x + tan 9x + tan 4x ∙ tan 9x ∙ tan 13x (2)

Question 2.

In how many of distinct permutations of the letters in MISSISSIPPI do the four I’s not come together ? (2)

OR

In how many ways can the letters of the word PERMUTATIONS be arranged if the:

(i) Words start with P and end with S,

(ii) Vowels are all together

Question 3.

5(2x – 7) – 3(2x + 3) ≤ 0, 2x + 19 ≤ 6x + 47. (2)

Question 4.

Find the centre and radius of the circle whose equation is

3x^{2} + 3y^{2} + 6x – 4y -1 = 0 (2)

Question 5.

Find the derivatives of x^{-3}(5 + 3x)

OR

Find the derivatives of x^{5}(3 – 6x^{-9}) (2)

Question 6.

Consider the experiment of rolling a die. Let A be the event ‘getting a prime number’ and B be the event ‘getting an odd number’. Write the sets representing the events.

(i) A and B,

(ii) A or B

Section – B

Question 7.

Find the equation of a circle of radius 5 which is touching another circle x^{2} + y^{2} – 2x – 4y – 20 = 0 at (5, 5).

OR

Find the equation of the set of all points wherein the sum of whose distances from the points (3, 0), (9, 0) is 12. (3)

Question 8.

Find the solution for given inequalities 2x + y ≥ 6, 3x + 4y ≤ 12. (3)

Question 9.

Proved that:

\(\frac{(\sin 7 x+\sin 5 x)+(\sin 9 x+\sin 3 x)}{(\cos 7 x+\cos 5 x)+(\cos 9 x+\cos 3 x)}\) = tan 6x

Question 10.

Prove that:

cos \(\left(\frac{3 \pi}{4}+x\right)\) – cos \(\left(\frac{3 \pi}{4}-x\right)\) = – √2 sin x (3)

Section – C

Question 11.

If a convex polygon has 44 diagonals, then find the number of its sides.

OR

A committee of 6 is to be chosen from 10 men and 7 women, so as to contain at least 3 men and 2 women. In how many different ways can this be done, if two particular women refuse to serve on the same committee? (4)

Question 12.

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The Roadway which is horizontal and 100 m long is supported by vertical wires attached to the Cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle. (4)

Question 13.

Find the derivative of the \(\frac{\sec x-1}{\sec x+1}\) function. (4)

Case-Based/Data Based

Question 14.

Two customer Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day.

Based on the given information, answer the following questions

(i) What are the total number of favourable outcomes and what is the probability that both will visit the shop on same day ? (2)

(ii) What are the total number of favourable outcomes if both will

visit the shop on consecutive days and what is the probability that both will visit the shop on different days ? (2)