If A and B are two sets such that A ⊂ B, then what is A ∪ B?

Question: If A and B are two sets such that AB, then what is AB? Solution: If A and B are two sets such that AB, then AB = B....

Draw a circle and two lines parallel to a given

Question: Draw a circle and two lines parallel to a given line such that one is tangent and other a secant to the circle. Solution: We have the required figure, as shown Here, $\ell$ is the given line and a circle with centre $\mathrm{O}$ is drawn. The line $\mathrm{n}$ is drawn which is parallel to $\ell$ and tangent to the circle. Also, $\mathrm{m}$ is drawn parallel to line $\ell$ and is a secant to the circle....

If X = {a, b, c, d} and Y = {f, b, d, g}, find

Question: If X = {a,b,c,d} and Y = {f,b,d, g}, find (i)X Y (ii)Y X (iii)XY Solution: (i)X Y = {a,c} (ii)Y X = {f,g} (iii)XY = {b,d}...

Question: Write true or false. If false change the statement so that it is true. (a) Actin is present in thin filament (b) H-zone of striated muscle fibre represents both thick and thin filaments. (c) Human skeleton has 206 bones. (d) There are 11 pairs of ribs in man. (e) Sternum is present on the ventral side of the body. Solution: (a) Answer:True (b)Answer:False H -zone of striated muscle fibre is the central part of the thick filament that is not overlapped by the thin filament. (c) Answer:T...

A tangent PQ at a point P of a circle of radius

Question: A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is. (1) 12 cm (2) 13 cm (3) 8.5 cm (4) $\sqrt{119} \mathrm{~cm}$ Solution: O is the centre of the circle. The radius of the circle is 5 cm. PQ is tangent to the circle at P. Then $\mathrm{OP}=5 \mathrm{~cm}$ and $\angle \mathrm{OPQ}=90^{\circ}$ We are given that $\mathrm{OQ}=12 \mathrm{~cm}$. By Pythagoras Theorem, we have $\mathrm{PQ}^{2}=\mathrm{OQ}^{2}-\m...

Write true or false. If false change the statement so that it is true.

Question: Write true or false. If false change the statement so that it is true. (a) Actin is present in thin filament (b) H-zone of striated muscle fibre represents both thick and thin filaments. (c) Human skeleton has 206 bones. (d) There are 11 pairs of ribs in man. (e) Sternum is present on the ventral side of the body. Solution: (a) Answer:True (b)Answer:False H -zone of striated muscle fibre is the central part of the thick filament that is not overlapped by the thin filament. (c) Answer:T...

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20},

Question: If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}; find (i)A B (ii)A C (iii)A D (iv)B A (v)C A (vi)D A (vii)B C (viii)B D (ix)C B (x)D B (xi)C D (xii)D C Solution: (i)A B = {3, 6, 9, 15, 18, 21} (ii)A C = {3, 9, 15, 18, 21} (iii)A D = {3, 6, 9, 12, 18, 21} (iv)B A = {4, 8, 16, 20} (v)C A = {2, 4, 8, 10, 14, 16} (vi)D A = {5, 10, 20} (vii)B C = {20} (viii)B D = {4, 8, 12, 16} (ix)C B = {2, 6, 10, 14} (x)D B = {5, 10, 15} (xi)...

A vessel of 120 mL capacity contains a certain amount of gas at 35 °C and 1.2 bar pressure

Question: A vessel of 120 mL capacity contains a certain amount of gas at 35 C and 1.2 bar pressure. The gas is transferred to another vessel of volume 180 mL at 35 C. What would be its pressure? Solution: Given, Initial pressure,p1= 1.2 bar Initial volume,V1= 120 mL Final volume,V2= 180 mL Since the temperature remains constant, the final pressure (p2) can be calculated using Boyles law. According to Boyles law, Therefore, the pressure would be 0.8 bar....

Which of the following pairs of sets are disjoint

Question: Which of the following pairs of sets are disjoint (i){1, 2, 3, 4} and {x:xis a natural number and 4x6} (ii){a,e,i,o,u}and {c,d,e,f} (iii){x:xis an even integer} and {x: xis an odd integer} Solution: (i){1, 2, 3, 4} {x:xis a natural number and 4x6} = {4, 5, 6} Now, {1, 2, 3, 4}{4, 5, 6} = {4} Therefore, this pair of sets is not disjoint. (ii){a,e,i,o,u}(c,d,e,f} = {e} Therefore, {a,e,i,o,u} and (c,d,e,f} are not disjoint. (iii){x:xis an even integer}{x:xis an odd integer} =Φ Therefore, ...

Describe the important steps in muscle contraction.

Question: Describe the important steps in muscle contraction. Solution: During skeletal muscle contraction, the thick filament slides over the thin filament by a repeated binding and releases myosin along the filament. This whole process occurs in a sequential manner. Step 1: Muscle contraction is initiated by signals that travel along the axon and reach the neuromuscular junction or motor end plate. Neuromuscular junction is a junction between a neuron and the sarcolemma of the muscle fibre. As...

If A = {x: x is a natural number}, B ={x: x is an even natural number}

Question: If A = {x:xis a natural number}, B ={x:xis an even natural number} C = {x:xis an odd natural number} and D = {x:xis a prime number}, find (i)AB (ii)AC (iii)AD (iv)BC (v)BD (vi)CD Solution: A = {x:xis a natural number} = {1, 2, 3, 4, 5 } B ={x:xis an even natural number} = {2, 4, 6, 8 } C = {x:xis an odd natural number} = {1, 3, 5, 7, 9 } D = {x:xis a prime number} = {2, 3, 5, 7 } (i)AB = {x:xis a even natural number} = B (ii)AC = {x:xis an odd natural number} = C (iii)AD = {x:xis a pri...

What will be the minimum pressure required to compress 500 dm3

Question: What will be the minimum pressure required to compress 500 dm3of air at 1 bar to 200 dm3at 30C? Solution: Given, Initial pressure,p1= 1 bar Initial volume,V1= 500 dm3 Final volume,V2= 200 dm3 Since the temperature remains constant, the final pressure (p2) can be calculated using Boyles law. According to Boyles law, $p_{1} V_{1}=p_{2} V_{2}$ $\Rightarrow p_{2}=\frac{p_{1} V_{1}}{V_{2}}$ $=\frac{1 \times 500}{200} \mathrm{bar}$ $=2.5 \mathrm{bar}$ Therefore, the minimum pressure required...

If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find

Question: If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find (i)AB (ii)BC (iii)ACD (iv)AC (v)BD (vi)A(BC) (vii)AD (viii)A(BD) (ix)(AB)(BC) (x)(AD)(BC) Solution: (i)AB = {7, 9, 11} (ii)BC = {11, 13} (iii)ACD = { AC}D = {11}{15, 17} =Φ (iv)AC = {11} (v)BD =Φ (vi)A(BC) = (AB)(AC) = {7, 9, 11}{11} = {7, 9, 11} (vii)AD =Φ (viii)A(BD) = (AB)(AD) = {7, 9, 11}Φ= {7, 9, 11} (ix)(AB)(BC) = {7, 9, 11}{7, 9, 11, 13, 15} = {7, 9, 11} (x)(AD)(BC) = {3, 5, 7, 9, 11, 15, 17){7,...

Define sliding filament theory of muscle contraction.

Question: Define sliding filament theory of muscle contraction. Solution: The sliding filament theory explains the process of muscle contraction during which the thin filaments slide over the thick filaments, which shortens the myofibril. Each muscle fibre has an alternate light and dark band, which contains a special contractile protein, called actin and myosin respectively. Actin is a thin contractile protein present in the light band and is known as the I-band, whereas myosin is a thick contr...

Fill in the blanks :

Question: Fill in the blanks : (i) A tangent to a circle intersects it in.....point (s). (ii) A line intersecting a circle in two points is called a....... (iii) A circle can have ....... parallel tangents at the most. (iv) The common point of a tangent to a circle and the circle is called........ Solution: (i) One (ii) Secant (iii) Two (iv) Point of contact....

If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find

Question: If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find (i)AB (ii)BC (iii)ACD (iv)AC (v)BD (vi)A(BC) (vii)AD (viii)A(BD) (ix)(AB)(BC) (x)(AD)(BC) Solution: (i)AB = {7, 9, 11} (ii)BC = {11, 13} (iii)ACD = { AC}D = {11}{15, 17} =Φ (iv)AC = {11} (v)BD =Φ (vi)A(BC) = (AB)(AC) = {7, 9, 11}{11} = {7, 9, 11} (vii)AD =Φ (viii)A(BD) = (AB)(AD) = {7, 9, 11}Φ= {7, 9, 11} (ix)(AB)(BC) = {7, 9, 11}{7, 9, 11, 13, 15} = {7, 9, 11} (x)(AD)(BC) = {3, 5, 7, 9, 11, 15, 17){7,...

Define sliding filament theory of muscle contraction.

Question: Define sliding filament theory of muscle contraction. Solution: The sliding filament theory explains the process of muscle contraction during which the thin filaments slide over the thick filaments, which shortens the myofibril. Each muscle fibre has an alternate light and dark band, which contains a special contractile protein, called actin and myosin respectively. Actin is a thin contractile protein present in the light band and is known as the I-band, whereas myosin is a thick contr...

Find the intersection of each pair of sets:

Question: Find the intersection of each pair of sets: (i)X = {1, 3, 5} Y = {1, 2, 3} (ii)A = {a,e,i,o,u} B = {a,b,c} (iii)A = {x:xis a natural number and multiple of 3} B = {x:xis a natural number less than 6} (iv)A = {x:xis a natural number and 1 x6} B = {x:xis a natural number and 6 x 10} (v)A = {1, 2, 3}, B =Φ Solution: (i)X = {1, 3, 5}, Y = {1, 2, 3} XY = {1, 3} (ii)A = {a,e,i,o,u}, B = {a,b,c} AB = {a} (iii)A = {x:xis a natural number and multiple of 3} = (3, 6, 9 } B = {x:xis a natural num...

How many tangents can a circle have?

Question: How many tangents can a circle have? Solution: There can be infinitely many tangents to a circle....

Draw the diagram of a sarcomere of skeletal muscle showing different regions.

Question: Draw the diagram of a sarcomere of skeletal muscle showing different regions. Solution: The diagrammatic representation of a sarcomere is as follows:...

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

Question: If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find (i)AB (ii)AC (iii)BC (iv)BD (v)ABC (vi)ABD (vii)BCD Solution: A = {1, 2, 3, 4], B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10} (i)AB = {1, 2, 3, 4, 5, 6} (ii)AC = {1, 2, 3, 4, 5, 6, 7, 8} (iii)BC = {3, 4, 5, 6, 7, 8} (iv)BD = {3, 4, 5, 6, 7, 8, 9, 10} (v)ABC = {1, 2, 3, 4, 5, 6, 7, 8} (vi)ABD = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (vii) BCD = {3, 4, 5, 6, 7, 8, 9, 10}...

If A and B are two sets such that A ⊂ B, then what is A ∪ B?

Question: If A and B are two sets such that AB, then what is AB? Solution: If A and B are two sets such that AB, then AB = B....

Let A = {a, b}, B = {a, b, c}. Is A ⊂ B? What is A ∪ B?

Question: Let A = {a,b}, B = {a,b,c}. Is AB? What is AB? Solution: Here, A = {a,b} and B = {a,b,c} Yes, AB. AB = {a,b,c} = B...

Find the union of each of the following pairs of sets:

Question: Find the union of each of the following pairs of sets: (i)X = {1, 3, 5} Y = {1, 2, 3} (ii)A = {a,e,i,o,u} B = {a,b,c} (iii)A = {x:xis a natural number and multiple of 3} B = {x:xis a natural number less than 6} (iv)A = {x:xis a natural number and 1 x6} B = {x:xis a natural number and 6 x 10} (v)A = {1, 2, 3}, B =Φ Solution: (i)X = {1, 3, 5} Y = {1, 2, 3} XY= {1, 2, 3, 5} (ii)A = {a,e,i,o,u} B = {a,b,c} AB = {a,b,c,e,i,o,u} (iii)A = {x:xis a natural number and multiple of 3} = {3, 6, 9 ...

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universals set (s) for all the three sets A, B and C

Question: Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universals set (s) for all the three sets A, B and C (i){0, 1, 2, 3, 4, 5, 6} (ii)Φ (iii){0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (iv){1, 2, 3, 4, 5, 6, 7, 8} Solution: (i)It can be seen that A {0, 1, 2, 3, 4, 5, 6} B {0, 1, 2, 3, 4, 5, 6} However, C {0, 1, 2, 3, 4, 5, 6} Therefore, the set {0, 1, 2, 3, 4, 5, 6} cannot be the universal set for the sets A, B, and C. (ii)A Φ, B Φ, C...