eSaral - JEE | NEET | Class 8-10 Exam Prep App

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:...

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...

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...

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 $2 \notin C]$...

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 ...

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...

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...

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 $(1)\}$...

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...

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....

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...

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...

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)...

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...

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...

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...

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 ...

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...

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...

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. ...

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....

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....

The region of the vertebrate eye, where the optic nerve passes out of the retina,

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...

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....

All Study Material