Question Set C

CBSE 11th Mathematics Introduction to Three Dimensional Geometry Model Questions Papers Study Material - QB365

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Questions:

Multiple Choice Question

42 x 1 = 42

If Z \(\ne\) 0 is a complex number, then _______.

(a)

Re(z) = 0 \(\Rightarrow\) Im (Z²) = 0

(b)

Re(z2) = 0 \(\Rightarrow\)Im (Z²) = 0

(c)

Re(z) = 0 \(\Rightarrow\) Re(z²) = 0

(d)

None of the above

If \(\sqrt{5} x^{2}+x+\sqrt{5}=0\) then which of the following is/are correct?
I. Discriminant, D = -19.
\(\text { II. } x=\frac{-1 \pm \sqrt{19} i}{2 \sqrt{5}} \text { . }\)

(a)

Only I is correct

(b)

Only II is correct

(c)

Both are correct

(d)

Both are incorrect

The value of (z + 3) (\(\bar{z}\) + 3) is equivalent to _______.

(a)

\(|z+3|^{2}\)

(b)

\(|z-3|\)

(c)

\(z^{2}+3\)

(d)

None of these

\(\text { If }|1-i|^{n}=2^{n}, \text { then } n \text { is equal to }\)_______.

(a)

(b)

(c)

-1

(d)

None of these

If z is non-zero complex number and z = a + ib, then inverse of z is _______.

(a)

\(\frac{a}{a^{2}+b^{2}}+\frac{-b i}{a^{2}+b^{2}}\)

(b)

\(\frac{a}{a^{2}-b^{2}}+\frac{-b i}{a^{2}-b^{2}}\)

(c)

\(\frac{a}{a^{2}-b^{2}}+\frac{i b}{a^{2}-b^{2}}\)

(d)

\(\frac{-a}{a^{2}+b^{2}}+\frac{-b i}{a^{2}+b^{2}}\)

If the origin is the centroid of a \(\Delta\)ABC having vertices A(a, 1, 3), B(-2, b, -5) and C(4, 7, c), then ______.

(a)

a = -2

(b)

b = 8

(c)

c = -2

(d)

None of these

Which of the following statements is correct?

(a)

The coordinates of the origin 0 are (0, 0, 0)

(b)

The coordinates of any point on the X-axis will be as (0,y',z)

(c)

The coordinates of any point in the YZ-plane will be (x, 0, 0)

(d)

All of the above are correct

The coordinates of the point R, which divides the segment joining P(x₁,y₁,z₁) and Q(x₂,y₂,z₂) internally in the ratio k : 1,are ______.

(a)

\(\left(\frac{k x_{2}-x_{1}}{1-k}, \frac{k y_{2}-y_{1}}{1-k}, \frac{k z_{2}-z_{1}}{1-k}\right) \)

(b)

\(\left(\frac{k x_{2}+x_{1}}{1+k}, \frac{k y_{2}+y_{1}}{1+k}, \frac{k z_{2}+z_{1}}{1+k}\right) \)

(c)

\(\left(\frac{k x_{2}+x_{1}}{1-k}, \frac{k y_{2}+y_{1}}{1-k}, \frac{k z_{2}+z_{1}}{1-k}\right)\)

(d)

None of the above

Points P(2, 4, 6), Q(-2, -2, -2) and R(6, io, 14) are ______.

(a)

verticesof a triangle

(b)

collinear

(c)

non-collinear

(d)

Both(a)and (b)

10.

The three numbers representing the perpendicular distances of the point from three mutually perpendicular planes are called the ______.

(a)

coordinates of the point with respect to the two coordinate planes

(b)

coordinates of the origin with respect to the three coordinate planes

(c)

coordinates of the point with reference to the three coordinate planes

(d)

None of the above

11.

The last digit in 7³⁰⁰ is _____.

(a)

(b)

(c)

(d)

12.

The remainder left out when 8²ⁿ - (62)^{2n + 1}is divided by 9, is _____.

(a)

(b)

(c)

(d)

13.

If the term free from x in the expansion of \(\left(\sqrt{x}-\frac{k}{x^{2}}\right)^{15}\) is 455, then the values of k are _____.

(a)

(b)

(c)

(d)

-1

14.

If \(x \neq 0, \text { then }\left(x^{2}+\frac{3}{x}\right)\) is equal to _____.

(a)

\(x^{8}+12 x^{5}+\frac{108}{x}+\frac{81}{x^{4}} \)

(b)

\(x^{8}+12 x^{5}+54 x^{3}+\frac{180}{x}+\frac{81}{x^{3}} \)

(c)

\(x^{8}+12 x^{5}+54 x^{2}+\frac{108}{x}+\frac{81}{x^{4}}\)

(d)

None of the above

15.

The number of combinations of 4 different objects A, B, C,D taken 2 at a time is _____.

(a)

(b)

(c)

(d)

16.

The number of natural numbers smaller than 10⁴, in the decimal notation of which all the digits are distinct is _____.

(a)

5274

(b)

5275

(c)

5276

(d)

5277

17.

The total number of 9-digits numbers which have all different digits is _______.

(a)

10!

(b)

(c)

9 x 9!

(d)

10 x 10!

18.

Consider the following statements
Statement I \({ }^{n} P_{r}=\frac{n !}{(n-r) !}, 0 \leq r \leq n\)
Statement II \({ }^{n} P_{r}=n(n-1)(n-2) \ldots \ldots . .(n-r+1)\), \(0 \leq r \leq n\)
Which of the above statement (s) is/are true?

(a)

Only I

(b)

Only II

(c)

Both I and II

(d)

Neither I nor II

19.

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

20.

The graphical solution of the system of linear inequalities 3x + 4y \(\ge\) 12,y\(\ge\) 1,x \(\ge\) 0 is _______.

(a)

(b)

(c)

(d)

21.

The solution set of \(\frac{2 x-1}{3} \geq\left(\frac{3 x-2}{4}\right)-\left(\frac{2-x}{5}\right)\) is _______.

(a)

\((-\infty, 2)\)

(b)

\((-\infty, 2]\)

(c)

\(\left(-\infty,-\frac{1}{2}\right)\)

(d)

\(\left(-\infty,-\frac{1}{2}\right]\)

22.

Two real numbers or two algebraic expressions related by the symbol '<', '>', '\(\le\)' or '\(\ge\)'forms an _______.

(a)

equation

(b)

inequality

(c)

set

(d)

None of the above

23.

The all pairs of consecutive even positive integers, both of which are larger than 5, such that their sum is less than 23, are _______.

(a)

(2, 4), (5, 7) and (8, 10)

(b)

(3, 5), (6, 8) and (9, 11)

(c)

(6, 8), (8, 10) and (10, 12)

(d)

None of the above

24.

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

25.

If \(\sqrt{3} \cos \theta+\sin \theta=\sqrt{2}, \text { then } \theta\) is equal to ______.

(a)

\(2 m \pi+\frac{5 \pi}{12}, m \in Z \)

(b)

\(2 m \pi-\frac{\pi}{12}, m \in Z\)

(c)

Both (a) and (b) are correct

(d)

Both (a) and (b) are incorrect

26.

The value of \(\cos \frac{2 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{8 \pi}{15} \cos \frac{16 \pi}{15} \mathrm{is}\) ______.

(a)

\(\frac{1}{4}\)

(b)

\(\frac{1}{8}\)

(c)

\(\frac{1}{12}\)

(d)

\(\frac{1}{16}\)

27.

The value of \(\cos \theta \cdot \cos \frac{\theta}{2}-\cos 3 \theta \cdot \cos \frac{9 \theta}{2}\) is equal to ______.

(a)

\(\sin 4 \theta \cdot \sin \frac{7 \theta}{2}\)

(b)

\(\sin 8 \theta\)

(c)

\(\sin 7 \theta+\sin 8 \theta\)

(d)

\(\sin 7 \theta.\sin 8 \theta\)

28.

The graph of the function, f(x) = \(\frac{1}{x^{2}}\) is ______.

(a)

(b)

(c)

(d)

None of these

29.

The value of tan 3A - tan2A - tan A is ______.

(a)

tan3A tan2A tanA

(b)

- tan3A tan2A tanA

(c)

tan A tan2A - tan2A tan3A - tan3A tanA

(d)

None of the above

30.

Let R be a relation in N defined by \(R=\left\{\left(1+x, 1+x^{2}\right): x \leq 5, x \in N\right\}\). Which of the following is false?

(a)

R = {(2, 2), (3, 5), (4, 10), (5, 17), (6, 25)}

(b)

Domain of R = {2, 3, 4, 5, 6}

(c)

Range of R = {2,5, 10, 17, 26}

(d)

None of the above

31.

If A = {1, 2, 5, 6} and B = {1, 2, 3}, then what is (A x B) n (B x A) equal to ______.

(a)

{(1, 1), (2, 1), (6, 1), (3, 2)}

(b)

{(1, 1), (1,2), (2, 1), (2, 2)}

(c)

{(1, 1), (2, 2)}

(d)

{(1, 1), (1,2), (2, 5), (2, 6)}

32.

Each set X_r contains 5 elements and each set Y_r contains 2 elements and \(\bigcup_{r=1}^{20} X_{r}=S=\bigcup_{r=1}^{n} Y_{r}\). If each element of S belongs to exactly 10 of the X_r's and to exactly 4 of the Y_r's, then n is equal to _____.

(a)

(b)

(c)

100

(d)

33.

If A = {1,2, 3}, B = {3, 4}, C = {4, 5, 6}, then \((A \times B) \cap(B \times C)\) is equal to ______.

(a)

{(l,4)}

(b)

{(3,4)}

(c)

{(I, 4), (3, 4)}

(d)

None of these

34.

The set of negative real numbers is denoted by ...Y... Here, Y refers to _____.

(a)

\((-\infty, 0)\)

(b)

\([-\infty, 0]\)

(c)

\((-\infty, 0]\)

(d)

\([-\infty, 0)\)

35.

The set of real numbers {x: a < x < b} is called _____.

(a)

open interval

(b)

closed interval

(c)

semi-open interval

(d)

semi-closed interval

36.

If f(x) = log\({1+x\over 1-x}\) and g(x) = \({3x+x^3\over 1+3x^2}\) then f(g(x)) is equal to ______.

(a)

f(2x)

(b)

\([f(x)]^2\)

(c)

3f(x)

(d)

- f(3x)

37.

Let f(x) = Ix-1I then ______.

(a)

f(x²) = [f(x)]²

(b)

f(x +y) = f(x) f(y)

(c)

f(IxI) = I f(x) I

(d)

none of these

38.

If x = r sin\(\alpha\) cos \(\beta\), y = r sin\(\alpha\) sin \(\beta\)and z = r cos\(\alpha\), then X² + y² + Z² is independent of ______.

(a)

\(\alpha , \beta\)

(b)

\(\gamma , \alpha\)

(c)

\(\gamma , \beta\)

(d)

none of these

39.

If A = {1, 2, 3, 4, 5, 6}then the number of proper sub-sets is _____.

(a)

(b)

(c)

(d)

40.

If A and B are two sets then A \(\cap\) (A \(\cap\) B') =_______.

(a)

(b)

(c)

A'\(\cap\)B'

(d)

41.

If in the expansion of (1 +x)¹⁵, the coefficient of (2x + 3)^th and (r - 1)^th terms are equal then r is equal to _____.

(a)

(b)

(c)

(d)

none of the these

42.

The points (3, 3, 3), (0, 6, 3), (1, 7, 7) and (4, 4, 7) are vertices of ______.

(a)

a rectangle

(b)

a square

(c)

a parallelogram

(d)

a rhombus

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Answers Key:

Multiple Choice Question

42 x 1 = 42

(a)
Re(z) = 0 \(\Rightarrow\) Im (Z²) = 0

(a)
\(|z+3|^{2}\)

(b)
0

(a)
\(\frac{a}{a^{2}+b^{2}}+\frac{-b i}{a^{2}+b^{2}}\)

(a)
a = -2

(a)
The coordinates of the origin 0 are (0, 0, 0)

(b)
\(\left(\frac{k x_{2}+x_{1}}{1+k}, \frac{k y_{2}+y_{1}}{1+k}, \frac{k z_{2}+z_{1}}{1+k}\right) \)

(b)
collinear

10.

11.

(d)
1

12.

(b)
2

13.

(d)
-1

14.

15.

(b)
6

16.

(a)
5274

17.

18.

19.

(b)
1023

20.

21.

(b)
\((-\infty, 2]\)

22.

(a)
equation

23.

24.

25.

26.

(d)
\(\frac{1}{16}\)

27.

(a)
\(\sin 4 \theta \cdot \sin \frac{7 \theta}{2}\)

28.

29.

(a)
tan3A tan2A tanA

30.

(a)
R = {(2, 2), (3, 5), (4, 10), (5, 17), (6, 25)}

31.

(b)
{(1, 1), (1,2), (2, 1), (2, 2)}

32.

(b)
20

33.

34.

(a)
\((-\infty, 0)\)

35.

(a)
open interval

36.

37.

(d)
none of these

38.

(a)
\(\alpha , \beta\)

39.

(d)
63

40.

41.

(b)
5

42.

(b)
a square

CBSE 11th Mathematics Introduction to Three Dimensional Geometry Model Questions Papers Study Material - QB365 Set C

QB365 Student Learing Managemnet System

Std: 11th Standard CBSE - Mathematics

chapter: Introduction to Three Dimensional Geometry - Model Questions Papers

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Questions:

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Answers Key:

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Mathematics CBSE Class 11 MCQ Practice Test

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