Diagrammatically indicate the location of the various endocrine glands in our body.
Question: Diagrammatically indicate the location of the various endocrine glands in our body. Solution: The location of various endocrine glands in the human body can be illustrated as follows:...
Read More →The radii of two circles are 19 cm and 9 cm respectively.
Question: The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles. Solution: The circumference of the circle having radius $19 \mathrm{~cm}=2 \pi \times 19 \mathrm{~cm}=38 \pi \mathrm{cm}(\because \mathrm{r}=19 \mathrm{~cm})$ The circumference of the circle having radius $9 \mathrm{~cm}=2 \pi \times 9 \mathrm{~cm}=18 \pi \mathrm{cm} \quad(\because \mathrm{r}=9 \mathrm{~cm})$ Sum of t...
Read More →Define the following:
Question: Define the following: (a)Exocrine gland (b)Endocrine gland (c)Hormone Solution: (a)Exocrine glands: Glands that discharge secretions into ducts are known as exocrine glands. Sebaceous gland in the skin, salivary gland in the buccal cavity, etc. are examples of exocrine glands. (b)Endocrine glands: Glands that do not discharge their secretions into ducts are known as endocrine glands. Instead, these glands discharge their secretions directly into the blood. Pituitary gland, thyroid glan...
Read More →Show that A ∩ B = A ∩ C need not imply B = C.
Question: Show that A B = A C need not imply B = C. Solution: Let $A=\{0,1\}, B=\{0,2,3\}$, and $C=\{0,4,5\}$ Accordingly, $A \cap B=\{0\}$ and $A \cap C=\{0\}$ Here, $A \cap B=A \cap C=\{0\}$ However, $B \neq C[2 \in B$ and $2 \notin C]$...
Read More →Draw a circle with the help of a bangle.
Question: Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle. Solution: Steps of construction : 1. Locate the centre O of the circle by drawing right bisectors of two non-parallel chords of the circle. These right bisectors intersect each other at the centre of the circle. (i.e., at O). 2. Take point P outside the circle and join OP. 3. Locate mid-point M of OP. 4. Taking M as centre and radius equal to MP, draw ...
Read More →Pay load is defined as the difference between the mass of displaced air and the mass of the balloon.
Question: Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load when a balloon of radius $10 \mathrm{~m}$, mass $100 \mathrm{~kg}$ is filled with helium at $1.66$ bar at $27^{\circ} \mathrm{C}$. (Density of air $=1.2 \mathrm{~kg} \mathrm{~m}^{-3}$ and $\mathrm{R}=0.083$ bar $\mathrm{dm}^{3} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ ). Solution: Given, Radius of the balloon,r= 10 m $\therefore$ Volume of the balloon $=\frac{4}{3} \p...
Read More →Let ABC be a right triangle in which AB = 6 cm,
Question: Let $\mathrm{ABC}$ be a right triangle in which $\mathrm{AB}=6 \mathrm{~cm}, \mathrm{BC}=8 \mathrm{~cm}$ and $\angle \mathrm{B}=90^{\circ} . \mathrm{BD}$ is the perpendicular from $\mathrm{B}$ on $\mathrm{AC}$. The circle through B, C,D is drawn. Construct the tangents from A to this circle. Solution: Consider the following situation. If a circle is drawn through $\mathrm{B}, \mathrm{D}$, and $\mathrm{C}, \mathrm{BC}$ will be its diameter as $\angle \mathrm{BDC}$ is of measure $90^{\ci...
Read More →Using properties of sets show that
Question: Using properties of sets show that (i) $A \cup(A \cap B)=A$ (ii) $A \cap(A \cup B)=A$. Solution: (i) To show: $A \cup(A \cap B)=A$ We know that $A \subset A$ $A \cap B \subset A$ $\therefore A \cup(A \cap B) \subset A \ldots(1)$ Also, $A \subset A \cup(A \cap B) \ldots$ (2) $\therefore$ From $(1)$ and $(2), A \cup(A \cap B)=A$ (ii) To show: $A \cap(A \cup B)=A$ $A \cap(A \cup B)=(A \cap A) \cup(A \cap B)$ $=A \cup(A \cap B)$ $=A\{$ from $(1)\}$...
Read More →Draw a line segment AB of length 8 cm.
Question: Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Constuct tangents to each circle from the centre of the other circle. Solution: Steps of construction : 1. Draw a line segment AB of 8 cm. Taking A and B as centre, draw two circles of 4 cm and 3 cm radius. 2. Bisect the line AB. Let the mid-point of AB be C. Taking C as centre, draw a circle of AC radius which will intersect the circles at...
Read More →Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.
Question: Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60. Solution: Steps of construction : 1. Draw circle with centre at O and radius 5 cm. 2. Construct radii $\mathrm{OA}$ and $\mathrm{OB}$ such that $\angle \mathrm{AOB}=120^{\circ}$. 3. Draw perpendiculars to OA and OB at A and B respectively and let they intersect at P. Now, PA and PB is a pair of tangents inclined to each other at an angle of 60....
Read More →Show that for any sets A and B,
Question: Show that for any sets A and B, $A=(A \cap B) \cup(A-B)$ and $A \cup(B-A)=(A \cup B)$ Solution: To show: A = (A B) (A B) Letx A We have to show thatx (A B) (A B) Case I x A B Then,x (A B) (A B) (A B) Case II x A B ⇒x A orx B x B [x A] x A B (A B) (A B) A (A B) (A B) (1) It is clear that A B A and (A B) A (A B) (A B) A (2) From (1) and (2), we obtain A = (A B) (A B) To prove: A (B A) A B Letx A (B A) ⇒x A orx (B A) ⇒x A or (x B andx A) ⇒ (x A orx B) and (x A orx A) ⇒x (A B) A (B A) (A B...
Read More →Draw a circle of radius 3 cm.
Question: Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q. Solution: Steps of construction : 1. Taking any point O on the given plane as centre, draw a circle of 3 cm radius. 2. Take one of its diameters, RS, and extend it on both sides. Locate two points on this diameter such that OP = OQ = 7 cm 3. Bisect OP and OQ. Let T and U be the mid-points of OP and O...
Read More →Is it true that for any sets A and B, P (A) ∪ P (B) = P (A ∪ B)?
Question: Is it true that for any sets A and B, P (A) P (B) = P (A B)? Justify your answer. Solution: False Let A = {0, 1} and B = {1, 2} A B = {0, 1, 2} P(A) = {Φ, {0}, {1}, {0, 1}} P(B) = {Φ, {1}, {2}, {1, 2}} P(A B) = {Φ, {0}, {1}, {2}, {0, 1}, {1, 2}, {0, 2}, {0, 1, 2}} P(A) P(B) = {Φ, {0}, {1}, {0, 1}, {2}, {1, 2}} P(A) P(B) P(A B)...
Read More →Assume that P (A) = P (B). Show that A = B.
Question: Assume that P (A) = P (B). Show that A = B. Solution: Let P(A) = P(B) To show: A = B Letx A A P(A) = P(B) x C, for some C P(B) Now, C B x B A B Similarly, B A A = B...
Read More →Show that if A ⊂ B, then C – B ⊂ C – A.
Question: Show that if A B, then C B C A. Solution: Let A B To show: C B C A Letx C B ⇒x C andx B ⇒x C andx A [A B] ⇒x C A C B C A...
Read More →Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length.
Question: Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation. Solution: Steps of construction : 1. Draw two concentric circles having radii 4 cm and 6 cm. O is the centre of the circles. 2. Take any point P on the larger circle. 3. Join OP and mark mid-point M of OP. 4. Taking M as centre and radius = MP = MO, draw circle which intersects the smaller circle in two points Q a...
Read More →Calculate the total pressure in a mixture of 8 g of dioxygen and 4 g of dihydrogen confined in a vessel of 1 dm3 at 27°C.
Question: Calculate the total pressure in a mixture of $8 \mathrm{~g}$ of dioxygen and $4 \mathrm{~g}$ of dihydrogen confined in a vessel of $1 \mathrm{dm}^{3}$ at $27^{\circ} \mathrm{Cl} \mathrm{R}=0.083 \mathrm{bar} \mathrm{dm}^{3} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$. Solution: Given, Mass of dioxygen $\left(\mathrm{O}_{2}\right)=8 \mathrm{~g}$ Thus, number of moles of $\mathrm{O}_{2}=\frac{8}{32}=0.25$ mole Mass of dihydrogen $\left(\mathrm{H}_{2}\right)=4 \mathrm{~g}$ Thus, number of moles ...
Read More →Distinguish between:
Question: Distinguish between: (a) afferent neurons and efferent neurons (b) impulse conduction in a myelinated nerve fibre and unmyelinated nerve fibre (c) aqueous humor and vitreous humor (d) blind spot and yellow spot (f) cranial nerves and spinal nerves. Solution: (a)Afferent neurons and efferent neurons (b) Impulse conduction in a myelinated nerve fibre and an unmyelinated nerve fibre (c)Aqueous humour and vitreous humour (d)Blind spot and yellow spot (f) Cranial nerves and spinal nerves...
Read More →Show that the following four conditions are equivalent:
Question: Show that the following four conditions are equivalent: (i)A B (ii)A B = Φ (iii)A B = B (iv)A B = A Solution: First, we have to show that (i) ⇔ (ii). Let A B To show: A B Φ If possible, suppose A B Φ This means that there existsx A,x B, which is not possible as A B. A B = Φ A B ⇒ A B = Φ Let A B = Φ To show: A B Letx A Clearly,x B because ifx B, then A B Φ A B = Φ ⇒ A B (i) ⇔ (ii) Let A B To show: $\mathrm{A} \cup \mathrm{B}=\mathrm{B}$ Clearly, $\mathrm{B} \subset \mathrm{A} \cup \mat...
Read More →Draw a circle of radius 6 cm. From a point 10 cm away from its centre,
Question: Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. Solution: Steps of construction : 1. Taking any point O of the given plane as centre, draw a circle of 6 cm radius. Locate a point P, 10 cm away from O. Join OP. 2. Bisect OP. Let M be the mid-point of PO. 3. Taking M as centre and MO as radius, draw a circle. 4. Let this circle intersect the previous circle at point Q and R. 5. Join PQ and PR. ...
Read More →The region of the vertebrate eye, where the optic nerve passes out of the retina,is called the
Question: The region of the vertebrate eye, where the optic nerve passes out of the retina,is called the (a) fovea (b) iris (c) blind spot (d) optic chaisma Solution: Answer: (c)Blind spot Blind spot is the part where the optic nerve passes out of the retina. Photoreceptors are absent from this region....
Read More →How much time would it take to distribute one Avogadro number of wheat grains,
Question: How much time would it take to distribute one Avogadro number of wheat grains, if 1010grains are distributed each second? Solution: Avogadro number $=6.02 \times 10^{23}$ Thus, time required $=\frac{6.02 \times 10^{23}}{10^{10}} \mathrm{~s}$ $=6.02 \times 10^{23} \mathrm{~s}$ $=\frac{6.02 \times 10^{23}}{60 \times 60 \times 24 \times 365}$ years $=1.909 \times 10^{6}$ years Hence, the time taken would be $1.909 \times 10^{6}$ years....
Read More →The region of the vertebrate eye, where the optic nerve passes out of the retina,
Question: The region of the vertebrate eye, where the optic nerve passes out of the retina,is called the (a) fovea (b) iris (c) blind spot (d) optic chaisma Solution: Answer: (c)Blind spot Blind spot is the part where the optic nerve passes out of the retina. Photoreceptors are absent from this region....
Read More →Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm.
Question: Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm.Then construct another triangle whose sides are $\frac{\mathbf{5}}{\mathbf{3}}$ times the corresponding sides of the given triangle. Solution: Steps of construction : 1. Draw a line segment AB = 4 cm. Draw a ray SA making 90 with it. 2. Draw an arc of 3 cm radius while taking A as its centre to intersect SA at C. Join BC. $\triangle \mathrm{ABC}$ is the required triangle. 3. Draw a ray AX maki...
Read More →Answer the following:
Question: Answer the following: (a) Which part of the ear determines the pitch of a sound? (b) Which part of the human brain is the most developed? (c) Which part of our central neural system acts as a master clock? Solution: (a)Cochlea determines the pitch of a sound. (b)Forebrain is largest and the most developed part of the human brain. (c)Hypothalamus acts as a master clock in the human body....
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