The equation 2 a x - 3 + a x + 1 + 5 - a x = 1 2 possesses

Infinite number of real solutions for some a ∈ R

Finitely many real solutions for some a ∈ R +

No real solutions for some a ∈ R

Measurement is defined as a comparison of a physical quantity to a given standard unit. It is the determination of the size or magnitude of something. Measurement provide us with a means of describing various phenomenon in quantitative terms. It can also e considered as the process by which one can convert physical parameters to meaningful numbers.

EASY

Earn 100

Define true value of measurement. The true value is $252.14$ mm and the measured value is $249.02$ mm. Find the absolute error.

Important Questions on Measurement

HARD

Mathematics>Geometry>Measurement>More on Absolute Values

Students

A, B

and

C

measure the length of a room using

25 m

long measuring tape of least count

LC

0.5 cm,

meter-scale of

LC 0.1 cm

and a foot-scale of

LC 0.05 cm,

respectively. If the specified length of the room is

9.5 m,

then which of the following students will report the lowest relative error in the measured length?

(1 foot = 30.48 cm)

MEDIUM

Mathematics>Geometry>Measurement>More on Absolute Values

The error in the measurement of the radius of a sphere is

0.1 %

. The error in the measurement of its volume is

MEDIUM

Mathematics>Geometry>Measurement>More on Absolute Values

The uncertainty in measurement is called as _____.

HARD

Mathematics>Geometry>Measurement>More on Absolute Values

The equation

|2 a x - 3| + |a x + 1| + |5 - a x| = \frac{1}{2}

possesses

HARD

Mathematics>Geometry>Measurement>More on Absolute Values

Find the percentage error in kinetic energy of a body having mass

60.0 \pm 0.3 g

moving with a velocity

25.0 \pm 0.1 \frac{c m}{s}

HARD

Mathematics>Geometry>Measurement>More on Absolute Values

|x^{2} - 2 x - 8| + |x^{2} + x - 2| = 3 | x + 2 |

, then the set of all real values of

x

EASY

Mathematics>Geometry>Measurement>More on Absolute Values

If $f (x) = 2 | x | + 3 x$ , then find the value of $f (- 5)$ .

EASY

Mathematics>Geometry>Measurement>More on Absolute Values

A physical quantity,

X = \frac{a^{2} b^{2}}{\sqrt{c}}

. if

%

error in

a, b

and

c

are

1 %, 2 %

and

4 %

respectively, then the

%

error in

X

EASY

Mathematics>Geometry>Measurement>More on Absolute Values

“To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary :

"A jet plane moves with great speed".

MEDIUM

Mathematics>Geometry>Measurement>More on Absolute Values

The error in the measurement of the sides of a rectangle is