11th Standard Maths English Medium Free Online Test Book Back One Mark Questions - Part Three

11th Standard

Reg.No. :
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Maths

Time : 00:10:00 Hrs
Total Marks : 10

10 x 1 = 10
1. Let R be the set of all real numbers. Consider the following subsets of the plane R x R: S = {(x, y) : y =x + 1 and 0 < x < 2} and T = {(x,y) : x - y is an integer} Then which of the following is true?

(a)

T is an equivalence relation but S is not an equivalence relation

(b)

Neither S nor T is an equivalence relation

(c)

Both S and T are equivalence relation

(d)

S is an equivalence relation but T is not an equivalence relation.

2. Let f:Z➝Z be given by f(x)=$\begin{cases} \frac { x }{ 2 } \quad if\quad x\quad is\quad even \\ 0\quad if\quad x\quad is\quad odd \end{cases}$ . Then f is

(a)

one-one but not onto

(b)

onto but not one-one

(c)

one-one and onto

(d)

neither one-one nor onto

3. If ${ log }_{ \sqrt { x } }$ 0.25 =4 ,then the value of x is

(a)

0.5

(b)

2.5

(c)

1.5

(d)

1.25

4. $(\sqrt { 5 } -2)(\sqrt { 5 } +2)$ is equal to

(a)

1

(b)

3

(c)

23

(d)

21

5. If cospፀ + cosqፀ = 0 and if p ≠ q, then ፀ is equal to (n is any integer)

(a)

$\frac { \pi (3n+1) }{ p-q }$

(b)

$\frac { \pi (2n+1) }{ p+q }$

(c)

$\frac { \pi (n\pm 1) }{ p\pm q }$

(d)

$\frac { \pi (n+2) }{ p+q }$

6. If a is the arithmetic mean and g is the geometric mean of two numbers, then

(a)

$\le$ g

(b)

$\ge$ g

(c)

a = g

(d)

a > g

7. The equation of the line with slope 2 and the length of the perpendicular from the origin equal to $\sqrt5$ is

(a)

x+2y=$\sqrt5$

(b)

2x+y=$\sqrt5$

(c)

2x+y=5

(d)

x+2y-5=0

8. If A and B are symmetric matrices of order n, where (A $\neq$ B), then

(a)

A + B is skew-symmetric

(b)

A + B is symmetric

(c)

A + B is a diagonal matrix

(d)

A + B is a zero matrix

9. If A is skew-symmetric of order n and C is a column matrix of order n × 1, then CT AC is

(a)

an identity matrix of order n

(b)

an identity matrix of order 1

(c)

a zero matrix of order 1

(d)

an identity matrix of order 2

10. $lim_{\alpha \rightarrow {\pi/4}}{sin \alpha -cos \alpha \over \alpha -{\pi\over 4}}$ is

(a)

$\sqrt{2}$

(b)

$1\over \sqrt{2}$

(c)

1

(d)

2