Sample paper maths

Sample Paper
Class 11 Maths
Sampl Paper 4 | Class 11 Mathematics

Maximum Marks : 100 Time Taken : 3 Hours

General Instructions:

(i) All the questions are compulsory.

(ii) This question paper consists of 4 sections A, B, C and D.

(iii) Questions from Section A carry 1 mark each.

(iv) Questions from Section B carry 2 marks each.

(v) Questions from Section C carry 4 marks each.

(vi) Questions from Section D carry 6 marks each.

(vii) Use of calculator is not permitted.

SECTION – A (1 * 4 = 4)

Question 1:

If A ⊂ B and B ⊂ C then A ∪ C = ?

Question 2:

If f(x) = x + 1x , then find [f(x)]³.

Question 3:

Find the solution of the inequality |x – 1| < 2.

Question 4:

5 flags of different colours are given. How many different signals can be generated if each signal requires the use of 2 flags one after another?

SECTION – B (2 * 8 = 16)

Question 5:

How many 4 letter code can be formed using the first 10 letter of the English

alphabet, if no letter can be repeated?

Question 6:

If f(x) = a^x, what is the value of f(x + 2) – 2f(x + 1) + f(x)?

Question 7:

What is the value of tan 1° * tan 2° * tan 3° *….. * tan 89°?

Question 8:

Express (1 + 3i)^-1 in the form of a + ib.

Question 9:

Find the value of i¹⁰ + i¹⁸.

Question 10:

If ⁿP_r = 840 and ⁿC_r = 35 then what is the value of r?

Question 11:

One card is drawn from a set of 17 cards numbered 1 to 17. Find the probability that the number is divisible by 3 or 7.

Question 12:

Using Binomial Theorem, evaluate (102)⁵

SECTION – C (4 * 11 = 44)

Question 13:

In a group of 65 people 40 like cricket, 10 like both cricket and tennis, how like tennis only and not cricket?

Question 14:

If A = {1, 2, 3, 4} and B = {3, 4, 5, 6} then find:

(a) A ∪ B (b) A ∩ B (c) A - B (d) B - A

Question 15:

If tan A + tan B + tan C = 6, then find the value of cot A * cot B * cot C

Question 16:

Find the value of cos30^o * cos 10^o * cos50^o * cos 70^o.

Question 17:

If x + iy = , then prove that x² + y² = 1

Question 18:

Find the pairs of consecutive odd natural numbers both of which are larger than 10 such that their sum is less than 50.

Question 19:

Solve the given inequality graphically in two-dimensional plane: 3x + 4y ≤ 12

Question 20:

Find a if 17^th and 18^th term of the expansion (2 + a)⁵⁰ are equal.

Question 21:

Let n be a positive integer find the integer which divides 2³ⁿ – 7n – 1.

Question 22:

Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that you both enter the same section?

Question 23:

Prove that for all n ≥ 1, 8ⁿ – 3ⁿ is divisible by 5.

SECTION – D (6 * 6 = 36)

Question 24:

Of the members of three athletic teams in a certain school, 21 are on the basketball team, 26 on hockey team and 29 on 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 25:

Solve the given quadratic equation 2x² + x + 1 = 0.

Question 26:

If the sum of a certain number of terms of the A.P. 25, 22, 19, ... is 116. Find the last term.

Question 27:

If the letters of the word RACHIT are arranged in all possible ways as listed in dictionary, then what is the rank of the word RACHIT?

Question 28:

Prove that:

cos 6x = 32cos⁶ x − 48cos⁴ x + 18cos² x − 1

Question 29:

Prove the following by using the principle of mathematical induction for all n ∈ N: 1.2 + 2.2² + 3.2² + ... + n.2ⁿ = (n – 1)2ⁿ⁺¹ + 2

**********

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