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A regular octagon is formed by cutting an Isosceles right triangle from each of the corners of a square with side $15 cm$ . The area $(in {cm}^{2})$ of the octagon is

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Important Questions on Perimeter and Area

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Mathematics>Geometry>Perimeter and Area>Area

A

is a square matrix such that

A^{2} = I

, then

(A - I)^{3} + (A + I)^{3} - 7 A

is equal to

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Directions: Each of the following sentences in this section has a blank space and four words or group of words given after the sentence. Select the word or group of words you consider most appropriate for the blank space and indicate your response on the Answer Sheet accordingly.

Every rash driver becomes a ____ killer.

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Mathematics>Geometry>Perimeter and Area>Area

Given:

f (x) = \{\begin{matrix} \begin{matrix} x, 0 \leq x < \frac{1}{2} \\ \frac{1}{2}, x = \frac{1}{2} \end{matrix} \\ 1 - x, \frac{1}{2} < x \leq 1 \end{matrix}

and

g (x) = {(x - \frac{1}{2})}^{2}, x \in R .

Then, the area (in sq. units) of the region bounded by the curves,

y = f (x)

and

y = g (x)

between the lines

2 x = 1

and

2 x = \sqrt{3},

is:

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For the binary operation

*

defined on

R - \{1\}

by the rule

a * b = a + b + a b

for all

a, b \in R - \{1\}

, the inverse of

a

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A

and

B

are any two events such that

P (A) + P (B) - P (A a n d B) = P (A)

, then

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Mathematics>Geometry>Perimeter and Area>Area

Which of the following is not a pair of prime numbers ?

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Two balls are projected at an angle

θ

and

(90 ° - θ)

with respect to the horizontal with the same speed. The ratio of their maximum vertical heights is

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Mathematics>Geometry>Perimeter and Area>Area

For the following probability distribution:

$X$	$1$	$2$	$3$	$4$
$P (X)$	$\frac{1}{10}$	$\frac{1}{5}$	$\frac{3}{10}$	$\frac{2}{5}$

$E (X^{2})$ is equal to

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Two sentences are given below and you are required to find the correct sentence which combines both the sentences.

Which is the correct combination of the given two sentences?

He is too tired. He could not stand.

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A proton, a deuteron and an

α

-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

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In the following sentence, a blank space with four options is given. Select whichever preposition or determiner you consider the most appropriate for the blank space.

These are the good rules to live _____.

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A particle

A

of mass

m

and charge

q

is accelerated by a potential difference of

50 V .

Another particle

B

of mass

4 m

and charge

q

is accelerated by a potential difference of

2500 V .

The ratio of de-Broglie wavelengths

\frac{λ_{A}}{λ_{B}}

is close to:

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A galvanometer of resistance

50 Ω

is connected to battery of

3 V

along with a resistance of

2950 Ω

in series. A full scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection to

20

divisions, the resistance in series should be

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Mathematics>Geometry>Perimeter and Area>Area

Let

f : [2, \infty) \to R

be the function defined by

f (x) = x^{2} - 4 x + 5

, then the range

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Mathematics>Geometry>Perimeter and Area>Area

If the tangent at the point

P

on the circle

x^{2} + y^{2} + 6 x + 6 y = 2

meets

the

straight

line

5 x - 2 y + 6 = 0

at a point

Q

on the

Y

-axis, then the length of

P Q

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The probability that two randomly selected subsets of the set

{1, 2, 3, 4, 5}

have exactly two elements in their intersection, is:

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The coordinates of the foot of the perpendicular drawn from the origin to plane

2 x - 3 y + 4 z - 6 = 0

, are

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Mathematics>Geometry>Perimeter and Area>Area

For

a \in R, |a| > 1,

let

\lim_{n \to \infty} (\frac{1 + \sqrt[3]{2} + \dots + \sqrt[3]{n}}{n^{7 / 3} (\frac{1}{{(a n + 1)}^{2}} + \frac{1}{{(a n + 2)}^{2}} + \dots + \frac{1}{{(a n + n)}^{2}})}) = 54 .

Then the possible value(s) of

a

is/are:

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Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed

1 .0 m s^{- 1}

and the man behind walks at a speed

2 .0 m s^{- 1}

. A third man is standing at a height

12 m

above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency

1430 Hz

. The speed of sound in air is

330 m s^{- 1}

. At the instant, when the moving men are

10 m

apart, the stationary man is equidistant from them. The frequency of beats in

Hz

, heard by the stationary man at this instant, is __________.

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Sum of the areas of two squares is

850 m^{2}

.If the difference of their perimeter is

40 m

.Find the sides of two squares.

A regular octagon is formed by cutting an Isosceles right triangle from each of the corners of a square with side 15 cm. The area in cm2 of the octagon is

Important Questions on Perimeter and Area

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A regular octagon is formed by cutting an Isosceles right triangle from each of the corners of a square with side $15 cm$ . The area $(in {cm}^{2})$ of the octagon is