The journey to becoming a proficient and successful teacher begins with robust preparation. For aspirants aiming to secure admission in the B.Ed (Bachelor of Education) programs in Odisha, a key component of the preparation strategy is practicing through full-length mock tests. These tests simulate the actual exam environment and help candidates gauge their readiness, identify strengths and weaknesses, and build confidence.
Odisha B.Ed 2024 Science Practice Full Length Mock Test 2
Section I
- Leela worked hard—————- she passed her exam.
(a) so
(b) although
(c) because
(d) through
Ans:- [ Option A ] So. - ————–he was very tired, and he helped his sister with her homework.
(a) Because
(b) whether
(c)Although
(d) so
Ans:- [Option C ] Although - It’s raining hard,———— they can’t go to the playground.
(a) or
(b) but
(c) so
(d) through
Ans:- [Option C ] So. - She was absent from class yesterday———- she felt sick.
(a) so
(b) because
(c) although
(d) but
Ans:- [Option B ] because. - Pamela has a car,———– she doesn’t use it.
(a) or
(b) as
(c) because
(d) but
Ans:- [Option D ] but. - To accustom oneself to a foreign climate
(a) Adapt
(b) Adopt
(c) Accustom
(d) Acclimatise
Ans:- (d) Acclimatise - One who knows everything
(a) Literate
(b) Scholar
(c) Omnipotent
(d) Omniscient
Ans:- (d) Omniscient - Detailed plan of journey
(a) Travelogue
(b)Travel kit
(c) Schedule
(d) Itinerary
Ans:- (d) Itinerary - Giving undue favours to one’s own kith and kin
(a) Nepotism
(b) Favouritism
(c) Worldliness
(d) Corruption
Ans:- (a) Nepotism - Hater of learning and knowledge
(a) Misologist
(b) Bibliophile
(c) Misogynist
(d) Misanthropist
Ans:- (a) Misologist - What is the missing number in the series: 13, 17, ?, 25, 29?
A) 19
B) 21
C) 22
D) 23
ANS:- B) 21
Sol:- To identify the pattern in the series, let’s examine the differences between consecutive numbers:
The difference between 17 and 13 is 17 − 13 = 4
The difference between 29 and 25 is 29 − 25 = 4
It seems like the differences alternate between 4 Let’s continue this pattern:
The difference between the missing number and 17 should be 4.
Adding 4 to 17 gives us 17 + 4 = 21
Then, the difference between 21 and 29 is 29 − 21 = 4
Adding 4 to 25 gives us 25 +4 = 29
Therefore, the missing number in the series is 21 - What is the next number in the series: 1, 4, 9, 16, 25, …?
A) 36
B) 49
C) 64
D) 81
ANS:- A) 36
Sol:- The given series consists of perfect squares of consecutive natural numbers:
12 =1 (1 ×1)
22 = 4 (1 ×1)
32 = 9 (1 ×1)
42 = 16 (1 ×1)
52 = 25 (1 ×1)
To find the next number in the series, we square the next consecutive natural number:
62 = 36
Therefore, the next number in the series is 36 - What is the next number in the series: 1, 4, 9, 16, …?
A) 20
B) 24
C) 25
D) 28
ANS:- C) 25
Sol:- The given series consists of the squares of consecutive natural numbers:
1 = 12 (i.e. 1 ×1)
4 = 22 (i.e. 2 × 2)
9 = 32 (i.e. 3× 3)
16 = 42 (i.e. 4× 4)
To find the next number in the series, we square the next consecutive natural number:
25 = 52 (i.e. 5 × 5)
Therefore, the next number in the series is 25 - Complete the analogy:
3: 9:: 4:?
Options:
a) 8
b) 12
c) 16
d) 6
ANS:- b) 12
Sol:- The relationship between 3 and 9 is that 3 squared equals 9. Similarly, 4 squared equals 16. Therefore, the correct answer is 12 because it is the square of 4. - Complete the analogy:
5 : 25:: 6:?
Options:
a) 31
b) 36
c) 30
d) 29
ANS:- b) 36
Sol:- The relationship between 5 and 25 is that 5 squared equals 25. Similarly, 6 squared equals 36. Therefore, the correct answer is 36. - Complete the analogy:
8: 64:: 10:?
Options:
a) 100
b) 80
c) 120
d) 64
ANS:- a) 100
Sol:- The relationship between 8 and 64 is that 8 squared equals 64. Similarly, 10 squared equals 100. Therefore, the correct answer is 100. - Evaluate: (7 + 3) × (6 – 4)
a) 20
b) 14
c) 10
d) 8
ANS:- a) 20
Sol:- To evaluate the expression (7 + 3) × (6 – 4), we first perform the operations inside the parentheses:
(7 + 3) = 10
(6 – 4) = 2
Then, we multiply the results:
10 × 2 = 20
So, the correct answer is a) 20 - Evaluate: 8 ÷ (2 + 2) × 3
a) 3
b) 6
c) 9
d) 12
ANS:- b) 6
Sol:- To evaluate the expression 8÷(2+2)×3, we follow the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction):
First, we perform the operations inside the parentheses:
2 + 2 = 4
Then, we perform division and multiplication from left to right:
8 ÷ 4 = 2
2 × 3 = 6
So, the correct answer is b) 6 - In a survey, 150 people were asked about their preferred mode of transportation. 80 people said they prefer cars, 70 people said they prefer bicycles, and 50 people said they prefer both cars and bicycles. How many people didn’t prefer either cars or bicycles?
Options:
a) 50
b) 20
c) 30
d) 40
ANS:- a) 50
Sol:- To find out how many people didn’t prefer either cars or bicycles, we need to subtract the number of people who prefer both cars and bicycles from the total number of people surveyed.
Given:
n(U) = 150 (Total number of people surveyed)
n(C) = 80 (Number of people who prefer cars)
n(B) = 70 (Number of people who prefer bicycles)
n(B∩C) = 50 (Number of people who prefer both cars and bicycles)
We can calculate the number of people who didn’t prefer either cars or bicycles as follows:
Number of people who didn’t prefer either = n(U) – [n(C) + n(B) – n(B∩C)]
=150−(80+70−50)
=150 – (150 – 50)
=150−100
=50
So, 50 people didn’t prefer either cars or bicycles. - If ‘BIRD’ is coded as ‘FLUG’, then ‘FISH’ would be coded as:
A) JLUM
B) GJQK
C) JMWL
D) JLVK
ANS:- D) JLVK
Sol:- To find the code for “FISH” based on the given coding pattern, let’s analyze the relationship between the letters in “BIRD” and their corresponding letters in the code “FLUG”:
B -> F
I -> L
R -> U
D -> G
It appears that each letter in the word “BIRD” is shifted forward by a certain position in the alphabet to get the code.
Applying the same pattern to the word “FISH”:
F -> J
I -> L
S -> V
H -> K
So, the code for “FISH” would be “JLVK”. The correct answer is D) JLVK - What does the Latin term ‘educare’ mean?
a) To nourish
b) To lead out (of ignorance)
c) To draw out
d) Act of training
Answer: a) To nourish - Which Greek term is sometimes used synonymously with ‘education’?
a) Philos
b) Ethos
c) Pedagogy
d) Logos
Answer: c) Pedagogy - According to Mahatma Gandhi, what does education signify?
a) Intellectual growth only
b) Physical and mental faculties
c) Holistic cultivation
d) Spiritual enlightenment
Answer: c) Holistic cultivation - Who emphasized education as empowering the mind to discover profound truths?
a) Mahatma Gandhi
b) Rabindranath Tagore
c) Zakir Husain
d) Swami Vivekananda
Answer: b) Rabindranath Tagore - What did Aristotle believe education fosters?
a) A balanced mind within a healthy body
b) Mastery of physical skills
c) Spiritual enlightenment
d) Political prowess
Answer: a) A balanced mind within a healthy body - Rousseau’s perspective on education emphasizes:
a) Academic excellence
b) Discipline and obedience
c) Natural development
d) Technological innovation
Answer: c) Natural development - Education facilitates both individual and ______ advancement.
a) Religious
b) Cultural
c) Political
d) Societal
Answer: d) Societal - What is central to education’s aim according to the article?
a) Intellectual superiority
b) Moral and character development
c) Physical fitness
d) Technological innovation
Answer: b) Moral and character development - According to the article, education promotes:
a) Vocational aims only
b) Cultural enrichment
c) Physical development only
d) Political agenda
Answer: b) Cultural enrichment - Education aims to prepare students for:
a) Financial success only
b) Democratic values and societal responsibilities
c) Personal achievement only
d) Technological advancement
Answer: b) Democratic values and societal responsibilities - How many states of India share its border with Bhutan?
(a) 2
(b) 3
(c) 4
(d) 5
Ans: (c) 4 - What is the main reason the average temperature of the Earth remains fairly steady compared to that of the moon?
(a) Hydrosphere
(b) Biosphere
(c) Lithosphere
(d) Atmosphere
Ans: (d) Atmosphere - Who is the author of the book “Lincoln in the Bardo”?
(a) Junot Díaz
(b) George Saunders
(c) Marie Claire
(d) Zadie Smith
Ans: (b) George Saunders - Who is the author of the book “The Secret Diary of Kasturba”?
(a) Neelima Dalmia Adhar
(b) Aruna Chakravarti
(c) Som Sharma
(d) Narendra Verma
Ans: (a) Neelima Dalmia Adhar - Who is the author of the book “Gandhi in Champaran”?
(a) DG Tendulkar
(b) Anand Gandhi
(c) S Ganesan
(d) Mahadev Desai
Ans: (a) DG Tendulkar - Who is the author of the book “The Emergency-Indian Democracy’s Darkest Hour”?
(a) Surya Prakash
(b) Uma Vasudev
(c) Janardhan Thakur
(d) Uma Vasudev
Ans: (a) Surya Prakash - The Bhimbetka rock shelters are located in which state?
(a) Gujarat
(b) Madhya Pradesh
(c) Maharashtra
(d) Jharkhand
Ans: (b) Madhya Pradesh - Which feature of Indian temples resembles the pylons of the Egyptian temples?
(a) Lat
(b) Vimana
(c) Gopura
(d) Shikhara
Ans: (c) Gopura - The temples at Belur, Halebidu, and Somnathpura are supreme examples of which type of Temple Architecture?
(a) Nagara
(b) Dravida
(c) Gadag
(d) Vesara
Ans: (d) Vesara - Castle Naggar heritage site is located in which state?
(a) Himachal Pradesh
(b) Punjab
(c) Odisha
(d) Haryana
Ans: (a) Himachal Pradesh
Section II
- The phenomenon of light bending as it passes from one medium to another is called:
(a) Reflection
(b) Refraction
(c) Diffraction
(d) Dispersion
Ans. (b) Refraction - Sound cannot travel through:
(a) Solid
(b) Liquid
(c) Gas
(d) Vacuum
Ans. (d) Vacuum - The speed of light in a vacuum is approximately:
(a) 300,000 m/s
(b) 300,000 km/s
(c) 300,000 cm/s
(d) 300,000 mm/s
Ans. (b) 300,000 km/s - The process of heat transfer in fluids by the movement of particles is called:
(a) Conduction
(b) Convection
(c) Radiation
(d) Insulation
Ans. (b) Convection - Which of the following is a non-luminous object?
(a) Sun
(b) Moon
(c) Candle
(d) Bulb
Ans. (b) Moon - Echoes are produced due to:
(a) Reflection of sound
(b) Refraction of sound
(c) Diffraction of sound
(d) Absorption of sound
Ans. (a) Reflection of sound - The phenomenon of splitting of white light into its constituent colors is called:
(a) Reflection
(b) Refraction
(c) Dispersion
(d) Diffraction
Ans. (c) Dispersion - The pitch of a sound is determined by its:
(a) Amplitude
(b) Frequency
(c) Speed
(d) Wavelength
Ans. (b) Frequency - What is the value of acceleration due to gravity?
(a) Minimum at equator and maximum at poles
(b) Maximum at equator and minimum at poles
(c) Equal at poles and equator
(d) None of the above
Ans. (a) Minimum at equator and maximum at poles - The inertia of an object depend on which of the following criteria?
(a) Bulk
(b) Size
(c) Shape
(d) Mass
Ans. (d) Mass - What is the unit of force in the International System of Units (SI)?
(a) Joule
(b) Newton
(c) Pascal
(d) Watt
Ans. (b) Newton - Work is defined as:
(a) Force divided by distance
(b) Force multiplied by distance
(c) Force plus distance
(d) Distance divided by force
Ans. (b) Force multiplied by distance - The ability to do work is known as:
(a) Power
(b) Energy
(c) Momentum
(d) Pressure
Ans. (b) Energy - Pressure is measured in:
(a) Newton
(b) Joule
(c) Pascal
(d) Watt
Ans. (c) Pascal - The potential difference between two points in an electric circuit is measured in:
(a) Amperes
(b) Volts
(c) Ohms
(d) Coulombs
Ans. (b) Volts - The flow of electric charge is known as:
(a) Voltage
(b) Resistance
(c) Electric current
(d) Capacitance
Ans. (c) Electric current - A magnetic field around a current-carrying conductor is:
(a) Circular
(b) Straight
(c) Rectangular
(d) Triangular
Ans. (a) Circular - Lines of force in a magnetic field represent:
(a) The strength and direction of the field
(b) The amount of charge
(c) The speed of current
(d) The resistance in the field
Ans. (a) The strength and direction of the field - Electro-magnetic induction is the process of generating:
(a) Electric current from a magnetic field
(b) Magnetic field from electric current
(c) Heat from electric current
(d) Light from a magnetic field
Ans. (a) Electric current from a magnetic field - Heat transfer from one place to another without the movement of particles is called:
(a) Conduction
(b) Convection
(c) Radiation
(d) Induction
Ans. (c) Radiation - Which of the following is a renewable natural resource?
(a) Coal
(b) Oil
(c) Wind energy
(d) Natural gas
Ans: (c) Wind energy - Which of the following cycles involves the movement of nitrogen through the environment?
(a) Carbon cycle
(b) Nitrogen cycle
(c) Water cycle
(d) Phosphorus cycle
Ans: (b) Nitrogen cycle - The process by which green plants convert carbon dioxide and water into glucose is known as:
(a) Respiration
(b) Photosynthesis
(c) Transpiration
(d) Digestion
Ans: (b) Photosynthesis - In an ecosystem, which of the following is considered a producer?
(a) Herbivores
(b) Carnivores
(c) Plants
(d) Decomposers
Ans: (c) Plants - What is the term for the gradual buildup of pollutants in the environment?
(a) Bioaccumulation
(b) Biodegradation
(c) Biomagnification
(d) Bioremediation
Ans: (a) Bioaccumulation - Which type of pollution is caused by excessive nutrients in water bodies leading to algal blooms?
(a) Air pollution
(b) Soil pollution
(c) Water pollution
(d) Noise pollution
Ans: (c) Water pollution - Which process is involved in the breakdown of glucose to release energy in cells?
(a) Photosynthesis
(b) Respiration
(c) Fermentation
(d) Glycolysis
Ans: (b) Respiration - Which organ in the human body is primarily responsible for filtering blood?
(a) Heart
(b) Liver
(c) Kidneys
(d) Lungs
Ans: (c) Kidneys - What is the main purpose of excretion in living organisms?
(a) To obtain energy
(b) To remove waste products
(c) To reproduce
(d) To grow
Ans: (b) To remove waste products - Which of the following is a primary consumer in a food chain?
(a) Grass
(b) Deer
(c) Lion
(d) Fungi
Ans: (b) Deer - The biogeochemical cycle involving the movement of water through the environment is known as:
(a) Water cycle
(b) Carbon cycle
(c) Nitrogen cycle
(d) Phosphorus cycle
Ans: (a) Water cycle - Which type of organism breaks down dead organic matter and recycles nutrients back into the ecosystem?
(a) Producers
(b) Consumers
(c) Decomposers
(d) Predators
Ans: (c) Decomposers - In which part of the cell does respiration take place?
(a) Nucleus
(b) Chloroplast
(c) Mitochondria
(d) Ribosome
Ans: (c) Mitochondria - What is the process called when plants release water vapor into the atmosphere?
(a) Photosynthesis
(b) Respiration
(c) Transpiration
(d) Evaporation
Ans: (c) Transpiration - What type of natural resource is coal?
(a) Renewable
(b) Non-renewable
(c) Biotic
(d) Abiotic
Ans: (b) Non-renewable - Which cycle is associated with the movement of carbon through living organisms and the environment?
(a) Water cycle
(b) Carbon cycle
(c) Nitrogen cycle
(d) Sulfur cycle
Ans: (b) Carbon cycle - What is the primary function of the small intestine in animals?
(a) Digestion and absorption of nutrients
(b) Filtration of blood
(c) Production of red blood cells
(d) Excretion of waste products
Ans: (a) Digestion and absorption of nutrients - Which gas is primarily responsible for the greenhouse effect?
(a) Oxygen
(b) Nitrogen
(c) Carbon dioxide
(d) Methane
Ans: (c) Carbon dioxide - Which of the following is an abiotic component of an ecosystem?
(a) Plants
(b) Animals
(c) Soil
(d) Bacteria
Ans: (c) Soil - What is the process by which living organisms maintain a stable internal environment?
(a) Metabolism
(b) Homeostasis
(c) Adaptation
(d) Evolution
Ans: (b) Homeostasis - If 2:3 is the same as 6:x, what is the value of x?
A) 8
B) 9
C) 12
D) 18
ANS:- B) 9
Sol:- To find the value of x, we can set up a proportion using the given ratios:
2 : 3 = 6 : x
We can solve this proportion by cross-multiplication:
2 / 3 = 6 / x
2 x x = 6 x 3
2x = 18
Dividing both sides by 2 to solve for x:
2x / 2 = 18 / 2
x = 9
So, the value of x is 9
Therefore, the correct answer is B) 9. - If a recipe calls for 2 cups of flour for every 1 cup of sugar, what is the ratio of flour to sugar?
A) 2:1
B) 1:2
C) 3:1
D) 1:3
ANS:- A) 2:1
Sol:- In the given recipe, the ratio of flour to sugar is 2 cups of flour for every 1 cup of sugar. So, the ratio of flour to sugar is 2:1. The correct answer is A) 2:1. - What is the simplified form of the ratio 12:18?
A) 1:2
B) 2:3
C) 3:4
D) 4:5
ANS:- B) 2:3.
Sol:- To simplify the ratio 12:18, we can divide both terms by their greatest common divisor, which is 6.
12 / 6:18 / 6 = 2:3
So, the simplified form of the ratio 12:18 is 2:3.
Therefore, the correct answer is option B) 2:3. - Find the area of a parallelogram with a base of 12 cm and a height of 8 cm.
A) 80 square cm
B) 96 square cm
C) 100 square cm
D) 64 square cm
ANS:- B) 96 square cm.
Sol:- The area A of a parallelogram is given by the formula:
A = base × height
Given:
Base = 12 cm
Height = 8 cm
Substituting these values into the formula:
A = 12 × 8
A = 96square cm
So, the area of the parallelogram with a base of 12 cm and a height of 8 cm is 96 square cm
Therefore, the correct option is B) 96 square cm. - What is the formula for the volume of a cone?
A) πrl
B) πr²h
C) 1/3 πr²h
D) 4/3 πr³
ANS:- C) 1/3 πr²h
Sol:- The correct formula for the volume of a cone is 1/3πr²h, where r is the radius of the base of the cone and h is the height of the cone. This formula represents the volume of a cone as one-third of the product of the base area (πr²) and the height (h). So the correct answer is C) 1/3 πr²h - Calculate the volume of a cone with a radius of 6 cm and a height of 9 cm. (Take π = 3.14)
A) 254.52 cubic cm
B) 339.12 cubic cm
C) 377.52 cubic cm
D) 452.16 cubic cm
ANS:- B) 339.12 cubic cm
Sol:- The formula for the volume of a cone is given by: Volume= 1/3 πr²h
Where: r is the radius of the base of the cone h is the height of the cone π is approximately 3.14
Given that the radius r is 6 cm and the height h is 9 cm, we can plug these values into the formula:
Volume = 1/3 × 3.14 × 6² × 9
Volume = 1/3 × 3.14 × 36 × 9
Volume = 1/3 × 3.14×324
Volume = 1017.36 / 3
Volume = 339.12 cubic cm
So, the volume of the cone with a radius of 6 cm and a height of 9 cm is 339.12 cubic cm.
Therefore, the correct option is B) 339.12 cubic cm. - A flagpole casts a shadow of 10 meters when the angle of elevation of the sun is 45°. What is the height of the flagpole?
a) 5 √2 meters
b) 10 meters
c) 10 √2 meters
d) 20 meters
ANS:- 10 meters
Sol:- To find the height of the flagpole, we can use the trigonometric relationship between the height of the flagpole, the length of its shadow, and the angle of elevation of the sun.
Let h be the height of the flagpole, and s be the length of its shadow.
Given that the angle of elevation of the sun is 45∘, we can use the tangent function:
tan(45∘) = h/ s
Since tan(45∘) = 1, we have:
1 = h/ 10
Multiplying both sides by 10, we get:
h = 10
So, the height of the flagpole is 10 meters, which matches option b) 10 meters - What is the relationship between the sine and cosine functions according to the Pythagorean identity?
a) sin2θ + cos2θ =1
b) 1 + tan2θ = sec2θ
c) 1 + cot2θ = csc2θ
d) sin(90°−θ) =cosθ
ANS:- a) sin2θ + cos2θ =1
Sol:- The relationship between the sine and cosine functions according to the Pythagorean identity is: a) sin2θ + cos2θ =1
This is known as the Pythagorean identity for trigonometric functions, which states that in a right triangle, the square of the length of the side adjacent to an angle added to the square of the length of the side opposite to that angle equals the square of the length of the hypotenuse.
So, the correct answer is option a) a) sin2θ + cos2θ =1 - A ladder leans against a wall at an angle of 60° to the horizontal. If the foot of the ladder is 6 meters away from the wall, how high does the ladder reach on the wall?
a) 3√3 meters
b) 6 √3 meters
c) 6 meters
d) 12 meters
ANS:- b) 3√3
Sol:- To find the height the ladder reaches on the wall, we can use trigonometry. The ladder, the wall, and the ground form a right triangle, where the ladder is the hypotenuse.
Given:
Angle of elevation = 60°
Distance from the foot of the ladder to the wall = 6 meters
Let h be the height the ladder reaches on the wall.
Using the sine rule:
sin(60∘) = h/length of the ladder
We know that the length of the ladder is the hypotenuse of the right triangle, which is also the distance from the foot of the ladder to the wall.
length of the ladder = 6
h = sin(60∘) × 6
h = (√3 / 2) × 6
h = 3√3
So, the height the ladder reaches on the wall is 3√3
meters, which matches option b) 3√3 - In a right triangle, if the length of one leg is 5 units and the length of the hypotenuse is 10 units, what is the measure of the angle of elevation?
a) 30°
b) 45°
c) 60°
d) 90°
ANS:- a) 30∘
Sol:- To find the measure of the angle of elevation in a right triangle given the lengths of one leg and the hypotenuse, we can use the trigonometric ratio of sine.
In a right triangle, the sine of an angle is the ratio of the length of the side opposite to that angle to the length of the hypotenuse.
Given:
Length of one leg (opposite side) = 5 units
Length of the hypotenuse = 10 units
Let’s denote the angle of elevation as θ.
Using the sine ratio:
sin(θ) = Opposite/Hypotenuse
sin(θ) = 5/10
sin(θ) = 1/2
To find the angle whose sine is 1/2, we can use the inverse sine function (also known as arcsine or sin−1).
θ = sin−1 (½)
θ = 30∘
So, the measure of the angle of elevation is θ = 30∘, which corresponds to option a) 30∘ - Which formula is used to find compound ratios?
A) (a + c) : (b + d)
B) (a – c) : (b – d)
C) (a + b) : (a – b)
D) (a – b) : b
ANS:- A) (a + c) : (b + d)
Sol:- The formula used to find compound ratios is (a + c) : (b + d), where “a:b” and “c:d” are two given ratios. This formula is applied when two ratios are multiplied to obtain a compound ratio. So the correct answer is A) (a + c) : (b + d) - In which type of proportion, does an increase in one quantity result in a proportional decrease in the other?
A) Direct Proportion
B) Inverse Proportion
C) Continued Proportion
D) Compound Proportion
ANS:- B) Inverse Proportion
Sol:- In inverse proportion, an increase in one quantity results in a proportional decrease in the other, and vice versa. This means that as one quantity increases, the other quantity decreases proportionally, and vice versa. So the correct answer is B) Inverse Proportion - What is the formula for the surface area of a cuboid?
A) a √3
B) a³
C) 6a²
D) 2πr²
ANS:- C) 6a²
Sol:- The formula for the surface area of a cuboid is calculated by finding the sum of the areas of all its faces. Since a cuboid has 6 faces, each with an area equal to the product of its length and breadth, the total surface area A can be calculated as:
A = 2 (lw + wh + lh)
where l, w, and h represent the length, width, and height of the cuboid respectively. Simplifying this formula, we get:
A = 2lw + 2wh + 2lh
A = 2 (lw + wh + lh)
In a cuboid, opposite faces have the same area, so each term appears twice, leading to the simplified formula:
A = 2 (lw + wh + lh) = 2 × area of one face × 6
A = 6a².
Therefore, the correct answer is C) 6a². - Calculate the area of a rhombus with diagonals of lengths 10 cm and 12 cm.
A) 120 square cm
B) 60 square cm
C) 100 square cm
D) 150 square cm
ANS:- B) 60 square cm
Sol:- To calculate the area of a rhombus given the lengths of its diagonals, you can use the formula:
Area= ½ × Product of Diagonals
Given that the diagonals are 10 cm and 12 cm, the area can be calculated as:
Area = ½ × 10 × 12
Area = ½ × 120
Area = 60 square cm
Area = 60 square cm
So, the correct answer is B) 60 square cm - A flagpole casts a shadow of 10 meters when the angle of elevation of the sun is 45°. What is the height of the flagpole?
a) 5 √2 meters
b) 10 meters
c) 10 √2 meters
d) 20 meters
ANS:- 10 meters
Sol:- To find the height of the flagpole, we can use the trigonometric relationship between the height of the flagpole, the length of its shadow, and the angle of elevation of the sun.
Let h be the height of the flagpole, and s be the length of its shadow.
Given that the angle of elevation of the sun is 45∘, we can use the tangent function:
tan(45∘) = h/ s
Since tan(45∘) = 1, we have:
1 = h/ 10
Multiplying both sides by 10, we get:
h = 10
So, the height of the flagpole is 10 meters, which matches option b) 10 meters - What is the line drawn from the observer’s eye to the point on the object being observed called?
a) Horizon
b) Angle of elevation
c) Line of sight
d) Perpendicular line
ANS:- c) Line of sight
Sol:- The line of sight is the line drawn from the observer’s eye to the point on the object being observed. So, the correct answer is c) Line of sight - A flagpole casts a shadow of 10 meters when the angle of elevation of the sun is 45°. What is the height of the flagpole?
a) 5 √2 meters
b) 10 meters
c) 10 √2 meters
d) 20 meters
S3. ANS:- 10 meters
Sol:- To find the height of the flagpole, we can use the trigonometric relationship between the height of the flagpole, the length of its shadow, and the angle of elevation of the sun.
Let h be the height of the flagpole, and s be the length of its shadow.
Given that the angle of elevation of the sun is 45∘, we can use the tangent function:
tan(45∘) = h/ s
Since tan(45∘) = 1, we have:
1 = h/ 10
Multiplying both sides by 10, we get:
h = 10
So, the height of the flagpole is 10 meters, which matches option b) 10 meters - What is the line drawn from the observer’s eye to the point on the object being observed called?
a) Horizon
b) Angle of elevation
c) Line of sight
d) Perpendicular line
S4. ANS:- c) Line of sight
Sol:- The line of sight is the line drawn from the observer’s eye to the point on the object being observed. So, the correct answer is c) Line of sight - In trigonometry, what does the angle of elevation represent?
a) Angle between two perpendicular lines
b) Angle formed between the horizontal line and the line of sight to an object above the observer’s level
c) Angle formed between the observer and the object
d) Angle between the observer’s eye and the object
ANS:- b) Angle formed between the horizontal line and the line of sight to an object above the observer’s level
Sol:- The angle of elevation in trigonometry represents the angle formed between the horizontal line and the line of sight to an object above the observer’s level. So, the correct answer is b) Angle formed between the horizontal line and the line of sight to an object above the observer’s level - Which field extensively applies trigonometry in analyzing height and distance?
a) Biology
b) Architecture
c) Literature
d) Sociology
ANS:- b) Architecture
Sol:- Architecture extensively uses trigonometry to calculate heights, distances, and angles for designing structures.
