Question Set C

CBSE 11th Mathematics Linear Inequalities Model Questions Papers Study Material - QB365

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Questions:

Multiple Choice Question

35 x 1 = 35

If x² + x + 1= 0, then which of the following are correct?

(a)

\(x=\frac{-1+\sqrt{3} i}{2}\)

(b)

\(x=\frac{-i-\sqrt{3}}{2}\)

(c)

\(x=\frac{1+\sqrt{3} i}{2}\)

(d)

\(x=\frac{1-\sqrt{3} i}{2}\)

The geometrical representation of complex number \(z=\frac{-16}{1+i \sqrt{3}}, \text { is }\) _______.

(a)

(b)

(c)

(d)

If z = i³⁹, then simplest form of z is equal to _______.

(a)

1+ 0i

(b)

0+ i

(c)

0+ 0i

(d)

1+ i

If Z is a complex number and z + (-z) = 0, then _______.

(a)

(-z) is called additive inverse of z

(b)

-z is additive identity of z

(c)

= z is closure of z

(d)

-z is commutative of z

Two complex numbers are equal, if and only if _____.

(a)

their real and imaginary parts are separately equal

(b)

their real parts are only equal

(c)

their imaginary parts are only equal

(d)

None of the above

If the coefficients of 2nd, 3rd and the 4th terms in the expansion of (1+ x)ⁿ are in AP then value of n is _____.

(a)

(b)

(c)

(d)

The middle term in the expansion of \(\left(\frac{x}{3}+9 y\right)^{10}\) is _____.

(a)

31236 x⁵ y⁵

(b)

61236x⁵ y⁵

(c)

31236 x⁶ y⁶

(d)

61236 x⁶ y⁶

In every term, the sum of indices of a and b in the expansion of (a + b)ⁿ is _____.

(a)

(b)

n + 1

(c)

n + 2

(d)

n - 1

The greatest integer which divides the number (101)¹⁰⁰-1, is _____.

(a)

100

(b)

1000

(c)

10000

(d)

100000

10.

If there are 5 different objects A, B, C,D, E. The number of combinations of 3 different objects is ...A.... Here, A refers to _______.

(a)

(b)

(c)

(d)

11.

The sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time, is _______.

(a)

93321

(b)

93322

(c)

93323

(d)

93324

12.

The number of ways in which 3 prize can be distributed to 4 childrens, so that no child gets all the three prizes, are ______.

(a)

(b)

(c)

(d)

None of these

13.

A telegraph has 5 arms and each arm is capable of 4 distincts positions, including the position of rest. The total number of signals that can be made is ______.

(a)

1024

(b)

1023

(c)

1022

(d)

1021

14.

A solution is to be kept between 68°F and 77°F. The range in temperature in degree Celsius (C), if the Celsius/Fahrenheit (F) conversion formula is given by \(F=\frac{9}{5} C+32\) is _______.

(a)

between 20°C and 22°C

(b)

between 20°C and 25°C

(c)

between 36°C and 45°C

(d)

between 4°C and 5°C

15.

If 3x + 8 > 2, then which of the following is true?

(a)

x \(\in\) {-I, 0, 1,2, ... }, when x is an integer

(b)

x \(\in\) [-2,\(\infty\)), when x is a real number

(c)

Both (a) and (b)

(d)

None of the above

16.

In drilling world's deepest hole it was found that the temperature Tin degree celcius, x km below the earth's surface was given by T = 30 + 25 (x - 3),3 \(\le\) x \(\le\)15.At what depth will the temperature be between 155°C and 205°C?

(a)

10 to 12 km

(b)

8 to 10 km

(c)

8 to 10 km

(d)

15 to 18 km

17.

If a point P(a, \(\beta\)) on the line ax + by = c, then _______.

(a)

\(a \alpha+b \beta>c \)

(b)

\(a \alpha+b \beta

(c)

\(a \alpha+b \beta=c\)

(d)

None of these

18.

Which of the following solution set represent the following figure?

(a)

\(x+2 y \leq 8,2 x+y \leq 8, x \geq 0, y \geq 0 \)

(b)

\(x-2 y \leq 7, x+y \leq 8, x \geq 0, y \geq 0 \)

(c)

\(x+y<82 x+y<8, r>0 y>0\)

(d)

None of the above

19.

The sides of a triangle are respectively 7 cm, \(4 \sqrt{3}\) cm and \(\sqrt{13}\)cm then the smallest angle of the triangle is ______.

(a)

\(\frac {\pi}{6}\)

(b)

\(\frac {\pi}{3}\)

(c)

\(\frac {\pi}{4}\)

(d)

\(\frac {\pi}{5}\)

20.

Which among the following is/are called Napier's Analogy in a \(\Delta\)ABC?

(a)

\(\tan \frac{B-C}{2}=\frac{b-c}{b+c} \cot \frac{A}{2}\)

(b)

\(\tan \frac{C-A}{2}=\frac{c-a}{c+a} \cot \frac{B}{2}\)

(c)

\(\tan \frac{A-B}{2}=\frac{a-b}{a+b} \cot \frac{C}{2}\)

(d)

All of the above

21.

If \(\tan \theta=\frac{a}{b}, \text { then } b \cos 2 \theta+a \sin 2 \theta\) is equal to ______.

(a)

(b)

(c)

\(\frac{a}{b}\)

(d)

None of these

22.

The value of \(\frac{1-\tan ^{2} 15^{\circ}}{1+\tan ^{2} 15^{\circ}} \) is ______.

(a)

(b)

\(\sqrt{3}\)

(c)

\(\frac{\sqrt{3}}{2}\)

(d)

23.

If a function f satisfies f{f(x)} = x + 1 for all real values of x and if f(0) = \(\frac{1}{2}\) , then f(1) is equal to ______.

(a)

\(\frac{1}{2}\)

(b)

(c)

\(\frac{3}{2}\)

(d)

24.

If f(xy) = f(x) f(y), then f(t) may be of the form ______.

(a)

t +k

(b)

ct + k

(c)

t^k+c

(d)

t^k

25.

If f(x) = \(\frac{4^{x}}{4^{x}+2}\) then \(f\left(\frac{1}{97}\right)+f\left(\frac{2}{97}\right)+\ldots+f\left(\frac{96}{97}\right)\) is equal to______.

(a)

(b)

(c)

-48

(d)

-1

26.

If f (x) = \(\frac{1}{2-\sin 3 x}\), then range (f) is equal to ______.

(a)

[ - 1, 1]

(b)

\(\left[-\frac{1}{3}, \frac{1}{3}\right]\)

(c)

\(\left[\frac{1}{3}, 1\right]\)

(d)

\(\left[-1, \frac{-1}{3}\right]\)

27.

Domain of \(\sqrt{a^{2}-x^{2}}(a>0)\) is ______.

(a)

(- a, a)

(b)

[- a, a]

(c)

[0, a]

(d)

(- a, 0]

28.

If a rapidly spinning wheel is making an angle of say 15 revolutions per second,then this is an example of ______.

(a)

smaIl angle

(b)

obtuse angle

(c)

large angle

(d)

None of these

29.

In a class of 35 students, 24 like to play cricket and 16 like to play football. Also each student likes to play at least one of the two games. How many students like to play both cricket and football is _____.

(a)

(b)

(c)

(d)

30.

Let A = {I, 2, 3, 4, 5, 6,7,8,9, 10} and B = {2, 3, 5, 7}. Then, which of following is true?

(a)

A \(\cap\) B = A

(b)

A \(\cap\) B = B

(c)

A \(\cap\) B \(\not \subset\).B

(d)

None of these

31.

Consider
X = Set of all students in your school.
Y = Set of all students in your class.
Then, which of the following is true?

(a)

Every element of Yis also an element of X

(b)

Every element of X is also an element of Y

(c)

Every element of Yis not an element of X

(d)

Every element of X is not an element of Y

32.

The set of all letters in the word 'BETTER' in roster form is _____.

(a)

{B, E, T, R}

(b)

{B, T, R}

(c)

{B,E,R}

(d)

{B, R}

33.

The set of natural numbers which divide 42 is _____.

(a)

(a) {1,2, 3}

(b)

(b) {1,2, 3, 6,7,14, 21}

(c)

(d)

(d) {42}

34.

If in the expansion of (1 +x)ⁿ, the coefficients of fifth, sixth and seventh terms are inA.P. then n is equal to _____.

(a)

5,7

(b)

7,16

(c)

7,14

(d)

8,15

35.

If C₀ + C₁ + C₂ +...+C_n = 256 then ²ⁿC₂ is equal to ______.

(a)

(b)

105

(c)

120

(d)

130

Case Study Questions

2 x 4 = 8

36.

A complex number z is purely real if and only if \(\bar{z}=z\) and is purely imaginary if and only if \(\bar{z}=-z\). Based on the above information, anwer the following qustions.
(i) If \(\frac{3+2 i \sin \theta}{1-2 i \sin \theta}\) is purely real, then \(\theta\) is equal to

(a) \(n \pi\)

(b) \(\frac{n \pi}{2}\)

(c) \(n \pi \pm \frac{\pi}{3}\)

(d) \(2 n \pi \pm \frac{\pi}{4}\)

(ii) If x and y are rol numbers and the complex number \(\frac{(2+6) x-1}{4+1}+\frac{(1-6) y+21}{4}\) is purely teal, the relation between x and y is

(a) 8x+7 y=15

(b) 8x-17 y=16

(c) 17x-8 y=15

(d) 17x+8 y=15

(iii) If z be a complex number satisfying \(|\operatorname{Re}(z)|+|m(z)|=4\), then |z| cannot be

(a) \(\sqrt{7}\)

(b) \(\sqrt{\frac{17}{2}}\)

(c) \(\sqrt{10}\)

(d) \(\sqrt{8}\)

(iv) The smallest positive integer ( n ) for which \((1+i)^{2 n}=(1-i)^{2 n}\) is

(a) 2

(b) 3

(c) 1

(d) 4

(v) If \(z_1\) and z₂ are complex numbers such that \(\left|\frac{z_1-z_2}{z_1+z_2}\right|=1\), then

(a) \(\frac{z_1}{z_2}\) is purely real

(b) \(\frac{z_1}{z_2}\) is purely imaginary

(c) z₁ is purely real

(d) z₁ and z₂ are purely imaginary

37.

Mr. Abhishek Dubey a Mathematics class XIth teacher of write a problem on black board totest the Function". preparation about the topic 'Relation and The problem is describe as following:
"Let A be a relation be set of on first A ten natural numbers and let R defined by
\((x, y) \in R \Leftrightarrow x+2 y=14\)
i.e., \(R=\{(x, y): x \in A, y \in A\) and x+2 y=14} ".
Then, answer the following questions which are based on above problem.
(i) Find the relation (R)

(a) {(2, 4), (4, 3), (6, 2), (8, 1)}

(b) {(2, 6), (4, 5), (6, 4), (8, 3)}

(c) {(4, 2), (3, 4), (2, 6), (1, 8)}

(d) None of the above

(ii) Find the R^-1.

(a) {(4, 2), (3, 4), (2, 6), (1, 8)}

(b) {(6, 2), (5, 4), (4, 6), (3, 8)}

(c) {(2, 4),(4, 3), (6, 2), (8, 1)}

(d) {(2,6), (4, 5), (6, 4), (8, 3)}

(iii) Find Dom(R)

(a) {2, 4, 6, 8}

(b) {3, 5, 6, 8}

(c) {4, 3, 2, 1}

(d) {4, 5, 6, 8)

(iv) Find Range (R).

(a) {6, 5, 4, 3)

(b) {6, 3, 8, 7}

(c) {2, 4, 8, 10}

(d) {5, 3, 1, 9}

(v) Find Dom (R^-1)

(a) {4, 3, 2, 1}

(b) {4, 5, 6, 8}

(c) {2, 4, 6, 8}

(d) {3, 5, 6, 8}

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Answers Key:

Multiple Choice Question

35 x 1 = 35

(a)
\(x=\frac{-1+\sqrt{3} i}{2}\)

(b)
0+ i

(a)
(-z) is called additive inverse of z

(a)
their real and imaginary parts are separately equal

(b)
7

(b)
61236x⁵ y⁵

(a)
n

10.

(d)
10

11.

(d)
93324

12.

13.

(b)
1023

14.

(b)
between 20°C and 25°C

15.

(a)
x \(\in\) {-I, 0, 1,2, ... }, when x is an integer

16.

(b)
8 to 10 km

17.

18.

19.

(a)
\(\frac {\pi}{6}\)

20.

(d)
All of the above

21.

(b)
b

22.

23.

24.

(d)
t^k

25.

(b)
48

26.

27.

(b)
[- a, a]

28.

29.

30.

(b)
A \(\cap\) B = B

31.

(a)
Every element of Yis also an element of X

32.

(a)
{B, E, T, R}

33.

34.

(b)
7,16

35.

Case Study Questions

2 x 4 = 8

36.

(i) (a)
(ii) (b)
(iii) (a)
(iv) (a)
(v) (b)

37.

(i) b
(ii) b
(iii) (a)
(iv) (a)
(v) (c)

CBSE 11th Mathematics Linear Inequalities Model Questions Papers Study Material - QB365 Set C

QB365 Student Learing Managemnet System

Std: 11th Standard CBSE - Mathematics

chapter: Linear Inequalities - Model Questions Papers

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Questions:

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Answers Key:

NEW MCQ Practice Test - CBSE Class 11

Mathematics CBSE Class 11 MCQ Practice Test

CBSE Class 11 MCQ Practice Test

11th Standard CBSE Study Materials