The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cm.
Question: The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle. Solution: The tangent to a circle is perpendicular to the radius through the point of contact. $\therefore \quad \angle \mathrm{OTA}=90^{\circ}$ Now, in the right $\triangle \mathrm{OTA}$, we have : $\mathrm{OA}^{2}=\mathrm{OT}^{2}+\mathrm{AT}^{2}$ [Pythagoras theorem] $\Rightarrow 5^{2}=\mathrm{OT}^{2}+4^{2}$ $\Rightarrow \mathrm{OT}^{2}=5^{2}-4^{2}$ $\Righta...
Read More →If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:
Question: If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets: (i)A = {a, b, c} (ii)B = {d, e, f, g} (iii)C = {a, c, e, g} (iv)D = {f,g,h,a} Solution: U = {a, b, c, d, e, f, g, h} (i)A = {a, b, c} (ii)B = {d, e, f, g} (iii)C = {a, c, e, g} (iv)D = {f,g,h,a}...
Read More →Name the type of joint between the following:-
Question: Name the type of joint between the following:- (a) atlas/axis (b) carpal/metacarpal of thumb (c) between phalanges (d) femur/acetabulum (e) between cranial bones (f) between pubic bones in the pelvic girdle Solution: (a)atlas/axis: Pivotal joint (b)carpal/metacarpal of thumb: Saddle joint (c)between phalanges: Hinge joint (d)femur/acetabulum: Ball and socket joint (e)between cranial bones: Fibrous joint (f)between pubic bones in the pelvic girdle: Cartilaginous joint...
Read More →Prove that the perpendicular at the point of contact
Question: Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre. Solution: In figure, line $\ell$ is tangent to the circle at $\mathrm{P} . \mathrm{O}$ is the centre of the circle. OP = radius of the circle. If we have some points $Q_{1}, Q_{2}$, etc. on $\ell$, then we find that $O P$ is the shortest distance from $\mathrm{O}$ in comparison to the distances $\mathrm{OQ}_{1}, \mathrm{OQ}_{2}$, etc. Therefore, $\mathrm{OP} \perp \ell .$ Hence, t...
Read More →How do you distinguish between a skeletal muscle and a cardiac muscle?
Question: How do you distinguish between a skeletal muscle and a cardiac muscle? Solution:...
Read More →Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Question: Prove that the tangents drawn at the ends of a diameter of a circle are parallel. Solution: In the figure, PQ is diameter of the given circle and O is its centre. Let tangents AB and CD be drawn at the end points of the diameter PQ. Since, the tangents at a point to a circle is perpendicular to the radius through the point. $\therefore \quad \mathrm{PQ} \perp \mathrm{AB}$ $\Rightarrow \mathrm{APQ}=90^{\circ}$ and $\mathrm{PQ} \perp \mathrm{CD}$ $\Rightarrow \quad \angle \mathrm{PQD}=90...
Read More →What are the different types of movements exhibited by the cells of human body?
Question: What are the different types of movements exhibited by the cells of human body? Solution: Movement is a characteristic feature of living organisms. The different types of movement exhibited by cells of the human body are: Amoeboid movement: Leucocytes present in the blood show amoeboid movement. During tissue damage, these blood cells move from the circulatory system towards the injury site to initiate an immune response. Ciliary movement: Reproductive cells such as sperms and ova show...
Read More →Let U ={1, 2, 3; 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find
Question: Let U ={1, 2, 3; 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (i) (ii) (iii) (iv) (v) (vi) Solution: U ={1, 2, 3, 4, 5, 6, 7, 8, 9} A = {1, 2, 3, 4} B = {2, 4, 6, 8} C = {3, 4, 5, 6} (i) (ii) (iii) (iv) (v) (vi)...
Read More →If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°,
Question: If tangents PA and PB from a point P to a circle with centre $\mathrm{O}$ are inclined to each other at angle of $80^{\circ}$, then $\angle \mathrm{POA}$ is equal to (A) 50 (B) 60 (C) 70 (D) 80 Solution: In figure, $\Delta \mathrm{OAP} \cong \Delta \mathrm{OBP}(\mathrm{SSS}$ congruence $)$ $\Rightarrow \angle \mathrm{POA}=\angle \mathrm{POB}$ $=\frac{\mathbf{1}}{\mathbf{2}} \angle \mathrm{AOB}$...(1) Also $\angle \mathrm{AOB}+\angle \mathrm{APB}=180$ $\Rightarrow \angle \mathrm{AOB}=10...
Read More →At 0°C, the density of a certain oxide of a gas at 2 bar is same as that of dinitrogen at 5 bar.
Question: At 0C, the density of a certain oxide of a gas at 2 bar is same as that of dinitrogen at 5 bar. What is the molecular mass of the oxide? Solution: Density (d) of the substance at temperature (T) can be given by the expression, $d=\frac{M p}{R T}$ Now, density of oxide (d1) is given by, $d_{1}=\frac{M_{1} p_{1}}{\mathrm{R} T}$ Where,M1andp1are the mass and pressure of the oxide respectively. Density of dinitrogen gas (d2) is given by, $d_{2}=\frac{M_{2} p_{2}}{R T}$ Where,M2andp2are the...
Read More →State whether each of the following statement is true or false. Justify your answer.
Question: State whether each of the following statement is true or false. Justify your answer. (i){2, 3, 4, 5} and {3, 6} are disjoint sets. (ii){a,e,i,o,u} and {a,b,c,d} are disjoint sets. (iii){2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets. (iv){2, 6, 10} and {3, 7, 11} are disjoint sets. Solution: (i)False As 3{2, 3, 4, 5}, 3{3, 6} ⇒{2, 3, 4, 5}{3, 6} = {3} (ii)False Asa{a,e,i,o,u},a{a,b,c,d} ⇒{a,e,i,o,u}{a,b,c,d} = {a} (iii)True As {2, 6, 10, 14}{3, 7, 11, 15} =Φ (iv)True As {2, 6, 10}{...
Read More →If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?
Question: IfRis the set of real numbers andQis the set of rational numbers, then what isRQ? Solution: R: set of real numbers Q: set of rational numbers Therefore, R Q is a set of irrational numbers....
Read More →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}...
Read More →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)...
Read More →In fig., if TP and TQ are the two tangents to a circle with centre O so that
Question: In fig., if TP and TQ are the two tangents to a circle with centre O so that $\angle \mathrm{POQ}=110^{\circ}$, then $\angle \mathrm{PTO}$ is equal to - (A) 60 (B) 70 (C) 80 P Q T O 110 (D) 90 Solution: $\mathrm{TQ}$ and $\mathrm{TP}$ are tangents to a circle with centre $\mathrm{O}$ and $\angle \mathrm{POQ}=110^{\circ}$ $\therefore \mathrm{OP} \perp \mathrm{PT}$ and $\mathrm{OQ} \perp \mathrm{QT}$ $\Rightarrow \angle \mathrm{OPT}=90^{\circ}$ and $\angle \mathrm{OOT}=90^{\circ}$ Now, i...
Read More →Write the difference between:
Question: Write the difference between: (a)Actin and Myosin (b)Red and White muscles (c)Pectoral and Pelvic girdle Solution: (a)Actin and Myosin (b)Red and White muscles (c) Pectoral and Pelvic girdle...
Read More →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, ...
Read More →Using the equation of state pV = nRT; show
Question: Using the equation of state $p V=n R T$; show that at a given temperature density of a gas is proportional to gas pressurep. Solution: The equation of state is given by, pV=nRT.. (i) Where, pPressure of gas V Volume of gas n Number of moles of gas R Gas constant T Temperature of gas From equation (i) we have, $\frac{n}{V}=\frac{p}{\mathrm{RT}}$ Replacing $n$ with $\frac{m}{M}$, we have $\frac{m}{M V}=\frac{p}{\mathrm{R} T}$......(ii) Where, m Mass of gas M Molar mass of gas But, $\frac...
Read More →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...
Read More →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,...
Read More →From a point Q,
Question: From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is - (A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5 cm Solution: From figure, $r^{2}=(25)^{2}-(24)^{2}$ $=625-576$ $=49$ $\Rightarrow \mathrm{r}=7 \mathrm{~cm}$ Hence, the correct option is (A)...
Read More →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...
Read More →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...
Read More →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}...
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