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Maths case /data -based (4 Marks)

Exponents and Powers · Jharkhand Board (JAC) STD 7 (Jharkhand - English Medium). 3 questions.

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case /data -based (4 Marks)

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3 questions · self-marked practice — reveal the answer and mark yourself.

Question 14 Marks
A light-year is the distance light travels in one Earth year. For objects in space, we use light years to describe the distance between two heavenly bodies.
One light-year is approximately $9,500,000,000,000\ km.$
$1.$ Express one light year in metres.
$2.$ Astronomers are observing a star that is $5$ light-years away from the Earth. How far is the star from the Earth in kilometres$?$
$A. 4.75 \times 10^{11}$
$B. 47.5 \times 10^{11}$
$C. 4.75 \times 10^{12}$
$D. 4.75 \times 10^{13}$
Answer
$9. 9,500,000,000,000,000$
$9.5 × 10^{15}$
$95 × 10^{14}$
$10.$ Option $D. 4.75 ×10^{13}$
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Question 24 Marks
Nanoscience is the study of structures and materials of an ultra-small scale. The widely used
units to measure length in nanoscience are nanometre and micrometre.
The relations between different units of length are given below.
$10^3$ nanometre $(nm) = 1$ micrometre $(µm)$
$10^6$ nanometre $(nm) = 1$ millimetre $(mm)$
$10^7$ nanometre $(nm) = 1$ centimetre $(cm)$
$10^9$ nanometre $(nm) = 1$ meter $(m)$
$1.$ Electron microscopes are used to see very small particles. These microscopes can enlarge an image up to $106$ times. A laboratory developed a switch that is $1$ nanometre wide. How wide will the switch look when seen under an electron microscope$?$
$A. 1$ nanometre
$B. 1$ micrometre
$C. 1$ millimetre
$D. 1$ centimetre
$2.$ Asha measures the thickness of one sheet of newspaper. A stack of $100$ sheets of newspaper is $1\ cm$ thick. What would be the thickness of the newspaper when expressed in nanometres?
$3.$ Scalpel is an instrument used by surgeons in surgery. During an experiment it was found that the size of tip of scalpel can affect the recovery rates of patients.
Two scalpels of tip sizes $0.8$ micrometre and $12.5$ micrometre were tested.
Patients on whom the scalpel with tip radius $0.8$ micrometre was used healed faster.
What is the difference between the radii of the two tips in millimetres$?$
$A. 1.6 \times 10^{-4}$
$B.0.8 \times 10^{-3}$
$C. 1.17 \times 10^{-2}$
$D. 4.5 \times 10^{-2}$
$4.$ Deoxyribonucleic acid $(DNA)$ is found in every cell of almost all living beings including humans. One strand of human $DNA $ is $2.5$ nanometres in diameter. What is the diameter of the strand of $DNA$ in meters$?$
$A. 2.5 \times 10^{-10}$
$B. 1 \times 10^{-9}$
$C. 2.5 \times 10^{-9}$
$D. 2.5 \times 10^9$
$5$. Research says, “Human fingernail grows one nanometre in one second.”
What would be the approximate growth of the fingernail (in cm) in $24$ hours?
$A. 8.64 \times 10^{-3}$
$B.8.64 \times 10^{-2}$
$C. 8.64 \times 10^3$
$D. 8.64 \times 10^{11}$
$6.$ Rajat claims, “A negative number raised to a power is always less than the number itself.” Give an example that proves that Rajat is incorrect.
$7.$ Simplify the following.
$\{(92)^4× 9^5\} ÷ 9^8$
$8.$ Assume x and y are two negative numbers. ‘The result of the multiplication of $x$ and $y$ with the same positive power is greater than the multiplication of $x$ and $y$ with the same negative power.’
Give an example to support this statement.
Answer
$1. C. 1$ millimetre
$2. 100000$
$10^5$
$3. C. 1.17 \times 10^{-2}$
$4. C. 2.5 \times 10^{-9}$
$5. A. 8.64 \times 10^{-3}$
$6.$ The example must contain an even exponent of a negative number $(–2)^4= 16; –2 < 16$
$7. 9^5$
$9 \times 9 \times 9 \times 9 \times 9$
$59049$
$8.$ Gives example for both cases.
Let say $x=-2$ and $y=-3.$
Case $1: (-2)^2 \times(-3)^2=6^2=36$
Case $2: (-2)^{-2} \times(-3)^{-2}=6^{-2}=\frac{1}{36}$
And $\frac{1}{36}<36$
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Question 34 Marks
Nanoscience is the study of structures and materials of an ultra-small scale. The widely used
units to measure length in nanoscience are nanometre and micrometre.
The relations between different units of length are given below.
10³ nanometre (nm) = 1 micrometre (µm)
10⁶ nanometre (nm) = 1 millimetre (mm)
10⁷ nanometre (nm) = 1 centimetre (cm)
10⁹ nanometre (nm) = 1 meter (m)
1. Research says, “Human fingernail grows one nanometre in one second.”
What would be the approximate growth of the fingernail (in cm) in 24 hours?
A. $8.64 \times 10^{-3}$
B. $8.64 \times 10^{-2}$
C. $8.64 \times 10^3$
D. $8.64 \times 10^{11}$
2. Rajat claims, “A negative number raised to a power is always less than the number itself.” Give an example that proves that Rajat is incorrect.
3. Simplify the following.
{(92)⁴× 9⁵} ÷ 9⁸
4. Assume x and y are two negative numbers. ‘The result of the multiplication of x and y with the same positive power is greater than the multiplication of x and y with the same negative power.’
Give an example to support this statement.
Answer
1. A. $8.64 \times 10^{-3}$
2. The example must contain an even exponent of a negative number (–2)⁴ = 16; –2 < 16
3. 9⁵
9 × 9 × 9 × 9 × 9
59049
4. Gives example for both cases.
Let say $x=-2$ and $y=-3$.
Case 1: $(-2)^2 \times(-3)^2=6^2=36$
Case 2: $(-2)^{-2} \times(-3)^{-2}=6^{-2}=\frac{1}{36}$
And $\frac{1}{36}<36$
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