Q. What is the result of mixing equal volumes of 0.1 M HCl and 0.1 M NaOH?
-
A.
pH < 7
-
B.
pH = 7
-
C.
pH > 7
-
D.
Cannot be determined
Solution
Mixing equal volumes of 0.1 M HCl and 0.1 M NaOH results in a neutral solution with pH = 7.
Correct Answer:
B
— pH = 7
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Q. What is the result of multiplying 2.5 by 3.456, considering significant figures?
-
A.
8.64
-
B.
8.6
-
C.
8.65
-
D.
8.7
Solution
2.5 has 2 significant figures and 3.456 has 4 significant figures. The result should be rounded to 2 significant figures, giving 8.6.
Correct Answer:
B
— 8.6
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Q. What is the role of antioxidants in nutrition? (2022)
-
A.
Energy production
-
B.
Cell protection
-
C.
Muscle growth
-
D.
Hormone regulation
Solution
Antioxidants play a role in cell protection by neutralizing free radicals that can cause cellular damage.
Correct Answer:
B
— Cell protection
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Q. What is the role of auxins in plant growth?
-
A.
Promote flowering
-
B.
Stimulate root growth
-
C.
Inhibit growth
-
D.
Promote cell elongation
Solution
Auxins are plant hormones that promote cell elongation, which is crucial for growth and development in plants.
Correct Answer:
D
— Promote cell elongation
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Q. What is the role of enzymes in biological reactions? (2023)
-
A.
Increase temperature
-
B.
Decrease activation energy
-
C.
Change the pH
-
D.
Provide energy
Solution
Enzymes act as catalysts that lower the activation energy required for biochemical reactions, thus speeding them up.
Correct Answer:
B
— Decrease activation energy
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Q. What is the role of ribosomes in a cell?
-
A.
Energy production
-
B.
Protein synthesis
-
C.
DNA replication
-
D.
Cell division
Solution
Ribosomes are the sites of protein synthesis, translating mRNA into polypeptide chains.
Correct Answer:
B
— Protein synthesis
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Q. What is the role of the circulatory system? (2019)
-
A.
To break down food
-
B.
To transport nutrients and oxygen
-
C.
To produce hormones
-
D.
To protect against diseases
Solution
The circulatory system's role is to transport nutrients, oxygen, and hormones to cells and remove waste products.
Correct Answer:
B
— To transport nutrients and oxygen
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Q. What is the role of the endoplasmic reticulum?
-
A.
Energy production
-
B.
Synthesis of lipids and proteins
-
C.
Storage of genetic information
-
D.
Cell division
Solution
The endoplasmic reticulum is involved in the synthesis of lipids and proteins.
Correct Answer:
B
— Synthesis of lipids and proteins
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Q. What is the role of the Golgi apparatus in the cell?
-
A.
Energy production
-
B.
Modification and packaging of proteins
-
C.
Cell division
-
D.
Photosynthesis
Solution
The Golgi apparatus modifies, sorts, and packages proteins for secretion or use within the cell.
Correct Answer:
B
— Modification and packaging of proteins
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Q. What is the role of the respiratory system?
-
A.
To break down food
-
B.
To exchange gases
-
C.
To circulate blood
-
D.
To protect against pathogens
Solution
The respiratory system is responsible for the exchange of gases, primarily oxygen and carbon dioxide, between the body and the environment.
Correct Answer:
B
— To exchange gases
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Q. What is the role of xylem in plants?
-
A.
Transport of nutrients
-
B.
Transport of water
-
C.
Photosynthesis
-
D.
Storage of food
Solution
Xylem is responsible for the transport of water and dissolved minerals from the roots to the rest of the plant.
Correct Answer:
B
— Transport of water
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Q. What is the scalar product of A = 1i + 2j + 3k and B = 4i + 5j + 6k?
Solution
A · B = (1)(4) + (2)(5) + (3)(6) = 4 + 10 + 18 = 32.
Correct Answer:
A
— 32
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Q. What is the scalar product of the vectors A = 1i + 2j + 3k and B = 4i + 5j + 6k?
Solution
A · B = (1)(4) + (2)(5) + (3)(6) = 4 + 10 + 18 = 32.
Correct Answer:
A
— 32
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Q. What is the scalar projection of vector H = 6i + 8j onto vector I = 3i + 4j?
Solution
Scalar projection = (H · I) / |I| = (6*3 + 8*4) / √(3^2 + 4^2) = (18 + 32) / 5 = 50 / 5 = 10.
Correct Answer:
C
— 10
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Q. What is the scalar triple product of vectors A = i + j + k, B = 2i + 3j + k, and C = 3i + j + 2k?
Solution
Scalar triple product = A · (B × C) = |i j k| |1 1 1| |2 3 1| |3 1 2| = 0.
Correct Answer:
D
— 0
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Q. What is the second derivative of f(x) = 2x^4 - 3x^3 + x?
-
A.
24x^2 - 18x + 1
-
B.
24x^2 - 9
-
C.
12x^2 - 9
-
D.
8x^3 - 9
Solution
First derivative f'(x) = 8x^3 - 9x^2 + 1. Second derivative f''(x) = 24x^2 - 18x.
Correct Answer:
A
— 24x^2 - 18x + 1
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Q. What is the second derivative of f(x) = 2x^4 - 4x^3 + 3?
-
A.
24x^2 - 24x
-
B.
12x^2 - 12
-
C.
24x^3 - 12x^2
-
D.
8x^2 - 12
Solution
First derivative f'(x) = 8x^3 - 12x^2. Second derivative f''(x) = 24x^2 - 24x.
Correct Answer:
A
— 24x^2 - 24x
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Q. What is the second derivative of the function f(x) = 2x^4 - 4x^3 + 3?
-
A.
24x^2 - 24x
-
B.
24x^2 - 12
-
C.
12x^2 - 12
-
D.
8x^2 - 12
Solution
First derivative f'(x) = 8x^3 - 12x^2. Second derivative f''(x) = 24x^2 - 24x.
Correct Answer:
A
— 24x^2 - 24x
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Q. What is the shape of an s orbital? (2023)
-
A.
Spherical
-
B.
Dumbbell
-
C.
Double dumbbell
-
D.
Linear
Solution
The s orbital has a spherical shape.
Correct Answer:
A
— Spherical
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Q. What is the significance of August 15 in India?
-
A.
Constitution Day
-
B.
Independence Day
-
C.
Republic Day
-
D.
Gandhi Jayanti
Solution
August 15 is celebrated as Independence Day in India.
Correct Answer:
B
— Independence Day
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Q. What is the slope of the line perpendicular to the line 4x - 5y + 10 = 0? (2022)
-
A.
5/4
-
B.
-4/5
-
C.
4/5
-
D.
-5/4
Solution
The slope of the line is 4/5, so the slope of the perpendicular line is -5/4.
Correct Answer:
B
— -4/5
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Q. What is the slope of the line perpendicular to the line 4x - 5y = 10? (2022)
-
A.
5/4
-
B.
-4/5
-
C.
4/5
-
D.
-5/4
Solution
The slope of the line is 4/5, so the slope of the perpendicular line is -5/4.
Correct Answer:
B
— -4/5
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Q. What is the slope of the line represented by the equation 4x - 2y + 8 = 0? (2021)
Solution
Rearranging gives y = 2x + 4, so slope = 2.
Correct Answer:
C
— -2
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Q. What is the slope of the line represented by the equation y = 2x + 3?
Solution
The slope of the line in the equation y = mx + b is m, which is 2.
Correct Answer:
B
— 2
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Q. What is the slope of the line represented by the equation y = 3x + 2? (2021)
Solution
In the equation y = mx + b, m is the slope. Here, m = 3.
Correct Answer:
A
— 3
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Q. What is the slope of the line represented by the equation y = 3x + 4? (2022)
Solution
The slope of the line in the equation y = mx + b is m. Here, m = 3.
Correct Answer:
A
— 3
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Q. What is the slope of the tangent line to the curve y = x^2 + 2x at x = 1?
Solution
The derivative y' = 2x + 2. At x = 1, y' = 2(1) + 2 = 4.
Correct Answer:
A
— 3
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Q. What is the slope of the tangent line to the curve y = x^2 at the point (1,1)? (2023)
Solution
The derivative y' = 2x; At x = 1, slope = 2(1) = 2.
Correct Answer:
B
— 2
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Q. What is the slope of the tangent line to the curve y = x^2 at the point (2, 4)?
Solution
The derivative y' = 2x. At x = 2, the slope is y'(2) = 2(2) = 4.
Correct Answer:
A
— 2
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Q. What is the slope of the tangent line to the curve y = x^2 at the point (3, 9)? (2020)
Solution
The derivative y' = 2x. At x = 3, y' = 2(3) = 6.
Correct Answer:
B
— 6
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