Find the distance between the following pairs of points :
[question] Question. Find the distance between the following pairs of points : (a) (2,3), (4, 1) (b) (–5, 7), (–1,3) (c) (a, b), (– a, – b) [/question] [solution] Solution: (a) The given points are : A (2, 3), B (4, 1). Required distance $=\mathrm{AB}=\mathrm{BA}=\sqrt{\left(\mathbf{x}_{2}-\mathbf{x}_{1}\right)^{2}+\left(\mathbf{y}_{2}-\mathbf{y}_{1}\right)^{2}}$ $A B=\sqrt{(4-2)^{2}+(1-3)^{2}}=\sqrt{(2)^{2}+(-2)^{2}}$ $=\sqrt{4+4}=\sqrt{8}=2 \sqrt{2}$ units (b) Here $x_{1}=-5, y_{1}=7$ and $x_{...
Read More →Give the number of electrons in the species
[question] Question. Give the number of electrons in the species $\mathrm{H}_{2}^{+}, \mathrm{H}_{2}$ and $\mathrm{O}_{2}^{+}$ [/question] [solution] Solution: $\mathrm{H}_{2}^{+}$: Number of electrons present in hydrogen molecule (H2) = 1 + 1 = 2 $\therefore$ Number of electrons in $\mathrm{H}_{2}^{+}=2-1=1$ H2: Number of electrons in H2 = 1 + 1 = 2 $\mathrm{O}_{2}^{+}$ Number of electrons present in oxygen molecule $\left(\mathrm{O}_{2}\right)=8+8=16$ $\therefore$ Number of electrons in $\math...
Read More →What are the following and where do you find them in animal body
[question] Question. What are the following and where do you find them in animal body (a) Chondriocytes (b) Axons (c) Ciliated epithelium [/question] [solution] Solution: Chondriocytes: They are cells of cartilages, and are present in small cavities within the matrix secreted by them. Axons: They are long, slender projections of neurons that help in carrying nerve impulses from the neuron body. Axons aggregate in bundles which make up the nerves. Ciliated epithelium: It consists of simple column...
Read More →An atom of an element contains 29 electrons and 35 neutrons. Deduce
[question] Question. An atom of an element contains 29 electrons and 35 neutrons. Deduce (i) the number of protons and (ii) the electronic configuration of the element. [/question] [solution] Solution: (i) For an atom to be neutral, the number of protons is equal to the number of electrons. Number of protons in the atom of the given element = 29 (ii) The electronic configuration of the atom is $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10}$ [/solution]...
Read More →What are the cellular components of blood?
[question] Question. What are the cellular components of blood? [/question] [solution] Solution: Components of blood include erythrocytes (RBCs), leucocytes (WBCs), and thrombocytes (platelets). These components form 45% of blood. They are suspended in the remaining fluid portion, called plasma. Mammalian erythrocytes are biconcave, coloured cells devoid of a nucleus. They help in transporting respiratory gases. Leucocytes or white blood cells are nucleated cells. They can be divided into two ty...
Read More →Tick the correct answer and justify :
[question] Question. Tick the correct answer and justify : In $\Delta \mathrm{ABC}, \mathrm{AB}=6 \sqrt{3} \mathrm{~cm}, \mathrm{AC}=12 \mathrm{~cm}$ and $\mathrm{BC}=6 \mathrm{~cm}$. The angle $\mathrm{B}$ is : (1) 120° (2) 60° (3) 90° (4) 45° [/question] [solution] Solution: $\mathrm{AB}^{2}=(6 \sqrt{3})^{2}=108$ $\mathrm{BC}^{2}=6^{2}=36$ $A C^{2}=12^{2}=144$ So, $\mathrm{AB}^{2}+\mathrm{BC}^{2}=\mathrm{AC}^{2}$ $\Delta \mathrm{ABC}$ is right $\Delta$, right angled at $\mathrm{B}$ $\angle \ma...
Read More →Distinguish between the following
[question] Question. Distinguish between the following (a) Prostomium and peristomium (b) Septal nephridium and pharyngeal nephridium [/question] [solution] Solution: [/solution]...
Read More →An aircraft executes a horizontal loop at a speed
[question] Question. An aircraft executes a horizontal loop at a speed of $720 \mathrm{~km} / \mathrm{h}$ with its wings banked at $15^{\circ}$. What is the radius of the loop? [/question] [solution] solution: Speed of the aircraft, $v=720 \mathrm{~km} / \mathrm{h}=720 \times \frac{5}{18}=200 \mathrm{~m} / \mathrm{s}$ Acceleration due to gravity, $g=10 \mathrm{~m} / \mathrm{s}^{2}$ Angle of banking, $\theta=15^{\circ}$ For radius $r$, of the loop, we have the relation: $\tan \theta=\frac{v^{2}}{...
Read More →An electron is in one of the 3d orbitals
[question] Question. An electron is in one of the $3 d$ orbitals. Give the possible values of $n, I$ and $m_{1}$ for this electron. [/question] [solution] Solution: For the $3 d$ orbital: Principal quantum number $(n)=3$ Azimuthal quantum number $(I)=2$ Magnetic quantum number $\left(m_{i}\right)=-2,-1,0,1,2$ [/question]...
Read More →In an equailateral triangle,
[question] Question. In an equailateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes. [/question] [solution] Solution: Altitude of equilateral $\Delta=\frac{\sqrt{3}}{2}$ side $h=\frac{\sqrt{3}}{2} a$ $h^{2}=\frac{3}{4} a^{2}$ $4 h^{2}=3 a^{2}$ [/solution]...
Read More →Ten one-rupee coins are put on top of each other on a table.
[question] Question. Ten one-rupee coins are put on top of each other on a table. Each coin has a mass m. Give the magnitude and direction of (a) the force on the $7^{\text {th }}$ coin (counted from the bottom) due to all the coins on its top, (b) the force on the $7^{\text {th }}$ coin by the eighth coin, (c) the reaction of the 6 th coin on the $7^{\text {th }}$ coin. [/question] [solution] solution: (a) Force on the seventh coin is exerted by the weight of the three coins on its top. Weight ...
Read More →In an equailateral triangle ABC,
[question] Question. In an equailateral triangle $\mathrm{ABC}, \mathrm{D}$ is a point on side $\mathrm{BC}$ such that $\mathrm{BD}=\frac{1}{3} \mathrm{BC}$. Prove that $9 \mathrm{AD}^{2}=7 \mathrm{AB}^{2}$. [/question] [solution] Solution: AB = BC = CA = a (say) $B D=\frac{1}{3} B C=\frac{1}{3} a$ $\Rightarrow C D=\frac{2}{3} B C=\frac{2}{3} a$ $\mathrm{AE} \perp \mathrm{BC}$ $\Rightarrow B E=E C=\frac{1}{2} a$ $\mathrm{DE}=\frac{1}{2} \mathrm{a}-\frac{1}{3} \mathrm{a}=\frac{1}{6} \mathrm{a}$ $...
Read More →What is the lowest value of n that allows g orbitals to exist?
[question] Question. What is the lowest value of n that allows g orbitals to exist? [/question] [solution] Solution: For $\mathrm{q}$-orbitals, $I=4$. As for any value ' $n$ ' of principal quantum number, the Azimuthal quantum number $(I)$ can have a value from zero to $(n-1)$. $\therefore$ For $I=4$, minimum value of $n=5$ [/solution]...
Read More →Draw a labelled diagram of alimentary canal of a cockroach.
[question] Question. Draw a labelled diagram of alimentary canal of a cockroach. [/question] [solution] Solution: [/solution]...
Read More →Write the electronic configurations of the following ions:
[question] Question. (i) Write the electronic configurations of the following ions: (a) $\mathrm{H}^{-}$ (b) $\mathrm{Na}^{+}$ (c) $\mathrm{O}^{2-}$ (d) $\mathrm{F}^{-}$ (ii) What are the atomic numbers of elements whose outermost electrons are represented by (a) $3 s^{1}$ (b) $2 p^{3}$ and (c) $3 p^{5} ?$ (iii) Which atoms are indicated by the following configurations? (a) $[\mathrm{He}] 2 s^{1}$ (b) [Ne] $3 s^{2} 3 p^{3}$ (c) $[\mathrm{Ar}] 4 s^{2} 3 d^{1}$. [/question] [solution] Solution: (i...
Read More →The perpendicular from $A$ on side $B C$ of a $\triangle A B C$ intersects $B C$ at $D$ such that $D B=3 C D(s e e$ figure).
[question] Question. The perpendicular from $A$ on side $B C$ of a $\Delta A B C$ intersects $B C$ at $D$ such that $D B=3 C D(s e e$ figure). Prove that $2 \mathrm{AB}^{2}=2 \mathrm{AC}^{2}+\mathrm{BC}^{2}$. [/question] [solution] Solution: DB = 3 CD $\Rightarrow \mathrm{CD}=\frac{1}{4} \mathrm{BC}$ ...(1) and $D B=\frac{3}{4} B C$ In $\triangle \mathrm{ABD}, \quad \mathrm{AB}^{2}=\mathrm{DB}^{2}+\mathrm{AD}^{2}$ In $\Delta \mathrm{ACD}, \quad \mathrm{AC}^{2}=\mathrm{CD}^{2}+\mathrm{AD}^{2}$ Su...
Read More →Draw a labelled diagram of the reproductive organs of an earthworm.
[question] Question. Draw a labelled diagram of the reproductive organs of an earthworm. [/question] [solution] Solution: [/solution]...
Read More →A helicopter of mass 1000 kg rises with a vertical acceleration
[question] Question. A helicopter of mass $1000 \mathrm{~kg}$ rises with a vertical acceleration of $15 \mathrm{~m} \mathrm{~s}^{-2}$. The crew and the passengers weigh $300 \mathrm{~kg}$. Give the magnitude and direction of the (a) force on the floor by the crew and passengers, (b) action of the rotor of the helicopter on the surrounding air, (c) force on the helicopter due to the surrounding air. [/question] [solution] solution: (a) Mass of the helicopter, $m_{\mathrm{h}}=1000 \mathrm{~kg}$ Ma...
Read More →Answer the following:
[question] Question. Answer the following: (i) What is the function of nephridia? (ii) How many types of nephridia are found in earthworm based on their location? [/question] [solution] Solution: (i) Nephridia are segmentally arranged excretory organs present in earthworms. (ii) On the basis of their location, three types of nephridia are found in earthworms. They are: (a) Septal nephridia: These are present on both sides of the inter-segmental septa behind the 15th segment. They open into the i...
Read More →A stone of mass m tied to the end of a string revolves in a vertical circle of radius R.
[question] Question. A stone of mass m tied to the end of a string revolves in a vertical circle of radius R. The net forces at the lowest and highest points of the circle directed vertically downwards are: [Choose the correct alternative] [/question] $T_{1}$ and $v_{1}$ denote the tension and speed at the lowest point. $T_{2}$ and $v_{2}$ denote corresponding values at the highest point. [/question] [solution] solution: (a)The free body diagram of the stone at the lowest point is shown in the f...
Read More →Describe the internal structure of a dorsiventral leaf with the help of labelled diagrams.
[question] Question. Describe the internal structure of a dorsiventral leaf with the help of labelled diagrams. [/question] [solution] Solution: Dorsiventral leaves are found in dicots. The vertical section of a dorsiventral leaf contains three distinct parts. [1] Epidermis: Epidermis is present on both the upper surface (adaxial epidermis) and the lower surface (abaxial epidermis). The epidermis on the outside is covered with a thick cuticle. Abaxial epidermis bears more stomata than the adaxia...
Read More →D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C.
[question] Question. $\mathrm{D}$ and $\mathrm{E}$ are points on the sides $\mathrm{CA}$ and $\mathrm{CB}$ respectively of a triangle $\mathrm{ABC}$ right angled at $\mathrm{C}$. Prove that $\mathrm{AE}^{2}+\mathrm{BD}^{2}=\mathrm{AB}^{2}+\mathrm{DE}^{2}$. [/question] [solution] Solution: In right angled $\triangle \mathrm{ACE}$, $\mathrm{AE}^{2}=\mathrm{CA}^{2}+\mathrm{CE}^{2}$ ...(1) and in right angled $\triangle B C D$, $\mathrm{BD}^{2}=\mathrm{BC}^{2}+\mathrm{CD}^{2}$ ...(2) Adding (1) and ...
Read More →What is periderm?
[question] Question. What is periderm? How does periderm formation take place in dicot stem? [/question] [solution] Solution: Periderm is composed of the phellogen, phellem, and phelloderm. During secondary growth, the outer epidermal layer and the cortical layer are broken because of the cambium. To replace them, the cells of the cortex turn meristematic, giving rise to cork cambium or phellogen. It is composed of thin-walled, narrow and rectangular cells. Phellogen cuts off cells on its either...
Read More →Two poles of height 6 m and 11 m stand on a plane ground.
[question] Question. Two poles of height 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops. [/question] [solution] Solution: Let AD and BE be two poles of height 6 m and 11 m and AB = 12 m In $\triangle \mathrm{DEC}$, by pythagoras theorem $\mathrm{DE}^{2}=\mathrm{CD}^{2}+\mathrm{CE}^{2}$ $\mathrm{DE}^{2}=12^{2}+5^{2}(\mathrm{DC}=\mathrm{AB}=12 \mathrm{~m})$ $\mathrm{DE}=\sqrt{144+25}=\sqrt{169}=13 \mathrm{~m}$ Thus,...
Read More →The mass of an electron is $9.1 \times 10^{-31} \mathrm{~kg}$.
[question] Question. The mass of an electron is $9.1 \times 10^{-31} \mathrm{~kg}$. If its K.E. is $3.0 \times 10^{-25} \mathrm{~J}$, calculate its wavelength. [/question] [solution] Solution: From de Broglie’s equation, $\lambda=\frac{\mathrm{h}}{m \mathrm{v}}$ Given, Kinetic energy (K.E) of the electron $=3.0 \times 10^{-25} \mathrm{~J}$ Since $\mathrm{K} . \mathrm{E}=\frac{1}{2} m v^{2}$ $\therefore$ Velocity $(v)=\sqrt{\frac{2 K \cdot E}{m}}$ $=\sqrt{\frac{2\left(3.0 \times 10^{-25} \mathrm{...
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