By what number should
Question: By what number should 51be multiplied so that the product may be equal to (7)1? Solution: Expressing in fraction form, we get: 51= 1/5 (using the propertya1= 1/a) and (7)1= 1/7 (using the propertya1= 1/a). We have to find a numberxsuch that $\frac{1}{5} x=\frac{-1}{7}$ Multiplying both sides by 5, we get: $x=-\frac{5}{7}$ Hence, 51should be multiplied by 5/7 to obtain(7)1....
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Question: If $2 \sin 2 \theta=\sqrt{3}$ then $\theta=?$ (a) 30(b) 45(c) 60(d) 90 Solution: As we know that, $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$ Thus, if $2 \sin 2 \theta=\sqrt{3}$ $\Rightarrow \sin 2 \theta=\frac{\sqrt{3}}{2}$ $\Rightarrow 2 \theta=60^{\circ}$ $\Rightarrow \theta=30^{\circ}$ Hence, the correct option is (a)....
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Question: (i) $\left\{\left(\frac{1}{3}\right)^{-3}-\left(\frac{1}{2}\right)^{-3}\right\} \div\left(\frac{1}{4}\right)^{-3}$ (ii) $\left(3^{2}-2^{2}\right) \times\left(\frac{2}{3}\right)^{-3}$ (iii) $\left\{\left(\frac{1}{2}\right)^{-1} \times(-4)^{-1}\right\}^{-1}$ (iv) $\left[\left\{\left(\frac{-1}{4}\right)^{2}\right\}^{-2}\right]^{-1}$ (v) $\left\{\left(\frac{2}{3}\right)^{2}\right\}^{3} \times\left(\frac{1}{3}\right)^{-4} \times 3^{-1} \times 6^{-1}$ Solution: (i) $\left(\left(\frac{1}{3}\r...
Read More →Why do Helium, Neon and Argon have zero valency?
Question: Why do Helium, Neon and Argon have zero valency? Solution: All the three elements have completely filled valence shells, according to Bohr Bury scheme. Therefore, their valencies are zero....
Read More →Simplify:
Question: (i) $\left\{\left(\frac{1}{3}\right)^{-3}-\left(\frac{1}{2}\right)^{-3}\right\} \div\left(\frac{1}{4}\right)^{-3}$ (ii) $\left(3^{2}-2^{2}\right) \times\left(\frac{2}{3}\right)^{-3}$ (iii) $\left\{\left(\frac{1}{2}\right)^{-1} \times(-4)^{-1}\right\}^{-1}$ (iv) $\left[\left\{\left(\frac{-1}{4}\right)^{2}\right\}^{-2}\right]^{-1}$ (v) $\left\{\left(\frac{2}{3}\right)^{2}\right\}^{3} \times\left(\frac{1}{3}\right)^{-4} \times 3^{-1} \times 6^{-1}$ Solution: (i) $\left(\left(\frac{1}{3}\r...
Read More →An element $X$ has a mass number 4 and atomic number 2 .
Question: An element $X$ has a mass number 4 and atomic number 2 . Write the valency of this element. Solution: The element $X$ with mass number 4 and atomic number 2 is helium $(H e)$. It has 2 electrons (maximum possible) in its only shell which is K-shell. Therefore, the valency of the element is zero....
Read More →A and B are square matrices of the same order,
Question: $A$ and $B$ are square matrices of the same order, then______ (i) $(A B)^{\top}=$________ (ii) $(K A)^{\top}=$_______ (iii) $(k(A-\bar{B}))^{\top}=$_______ where $k$ is any scalar. Solution: It is given that, $A$ and $B$ are square matrices of the same order. (i) $(A B)^{\top}=\quad B^{T} A^{T}$ (ii) $(k A)^{\top}=k(A)^{T}$, where $k$ is any scalar (iii) $[K(A-B)]^{T}$ $=k(A-B)^{T} \quad\left[(k A)^{T}=k(A)^{T}\right]$ $=k\left(A^{T}-B^{T}\right) \quad\left[(A+B)^{T}=A^{T}+B^{\top}\rig...
Read More →Fill in the blanks in the following statements :
Question: Fill in the blanks in the following statements : (a) Rutherfords a-particle scattering experiment led to the discovery of the . (b) Isotopes have same but different (c) Neon and chlorine have atomic numbers 10 and 17 respectively. Their valencies will be and respectively. (d) The electronic configuration of silicon is and that of sulphur is Solution: (a) nucleus (b) atomic numbers, mass numbers (c) zero and one (d) $2,8,4$ and $2,8,6$....
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Question: If $\sqrt{3} \tan 2 \theta-3=0$ then $\theta=?$ (a) 15(b) 30(c) 45(d) 60 Solution: As we know that, $\tan 60^{\circ}=\sqrt{3}$ Thus, if $\sqrt{3} \tan 2 \theta-3=0$ $\Rightarrow \sqrt{3} \tan 2 \theta=3$ $\Rightarrow \tan 2 \theta=\frac{3}{\sqrt{3}}$ $\Rightarrow \tan 2 \theta=\sqrt{3}$ $\Rightarrow 2 \theta=60^{\circ}$ $\Rightarrow \theta=30^{\circ}$ Hence, the correct option is (b)....
Read More →Helium atom has 2 electrons in its valence shell but its valency is not 2 . Explain.
Question: Helium atom has 2 electrons in its valence shell but its valency is not 2 . Explain. Solution: Helium (He) atom with atomic number (Z) equal to two has only one shell (K-shell). It can have a maximum of two electrons which it has. Therefore, the valence shell is complete and valency of the atom is zero....
Read More →If tan x = 3 cot x then x = ?
Question: If tanx= 3 cotxthenx= ?(a) 60(b) 45(c) 30(d) 15 Solution: Given:tanx= 3cotx $\tan x=3 \cot x$ $\Rightarrow \tan x=3 \frac{1}{\tan x} \quad\left(\because \cot x=\frac{1}{\tan x}\right)$ $\Rightarrow \tan ^{2} x=3$ $\Rightarrow \tan x=\sqrt{3}$ $\Rightarrow x=60^{\circ} \quad\left(\because \tan 60^{\circ}=\sqrt{3}\right)$ Hence, the correct option is (a)....
Read More →Complete the following table on the basis
Question: Complete the following table on the basis of information available in the symbols given below: (a) ${ }_{17}^{35} \mathrm{Cl}$ (b) ${ }_{6}^{12} \mathrm{C}$ (c) ${ }_{35}^{81} \mathrm{Br}$ Solution:...
Read More →The sum of two skew-symmetric matrices is always matrix.
Question: The sum of two skew-symmetric matrices is always_______ matrix. Solution: Let $A$ and $B$ be two skew-symmetric matrices. $\therefore A^{\top}=-A$ and $B^{\top}=-B$ ......(1) Now, $(A+B)^{T}$ $=A^{T}+B^{T}$ $=-A-B \quad[$ From (1) $]$ $\therefore(A+B)^{T}=-(A+B)$ Thus, the sum of two skew-symmetric matrices is always skew-symmetric matrix. The sum of two skew-symmetric matrices is always skew-symmetric matrix....
Read More →The atomic numbers of calcium and argon
Question: The atomic numbers of calcium and argon are 20 and 18 respectively, but the mass number of both these elements is 40 . What is the name given to such a pair of elements? Solution: The elements having same mass number but different atomic numbers are known as isobars....
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Question: If $\sqrt{2} \sin \left(60^{\circ}-\alpha\right)=1$ then $\alpha=?$ (a) 15(b) 30(c) 45(d) 60 Solution: As we know that, $\sin 45^{\circ}=\frac{1}{\sqrt{2}}$ Thus, if $\sqrt{2} \sin \left(60^{\circ}-\alpha\right)=1$ $\Rightarrow \sin \left(60^{\circ}-\alpha\right)=\frac{1}{\sqrt{2}}$ $\Rightarrow 60^{\circ}-\alpha=45^{\circ}$ $\Rightarrow \alpha=60^{\circ}-45^{\circ}$ $\Rightarrow \alpha=15^{\circ}$ Hence, the correct option is (a)....
Read More →Match the names of the Scientists given
Question: Match the names of the Scientists given in column A with their contributions towards the understanding of the atomic structure as given in column $B$. Solution: (a) - (iii); (b) - (iv); (c) $-$ (i); (d) $-$ (ii) (e) $-$ (vi); (f) - (vii); (g) $-(\mathrm{v})$....
Read More →Express each of the following rational numbers with a positive exponent:
Question: Express each of the following rational numbers with a positive exponent: (i) $\left(\frac{3}{4}\right)^{-2}$ (ii) $\left(\frac{5}{4}\right)^{-3}$ (iii) $4^{3} \times 4^{-9}$ (iv) $\left\{\left(\frac{4}{3}\right)^{-3}\right\}^{-4}$ (v) $\left\{\left(\frac{3}{2}\right)^{4}\right\}^{-2}$ Solution: $(i)\left(\frac{3}{4}\right)^{-2} \quad \cdots\left(a^{-1}=1 / a\right)$ $=\left(\frac{4}{3}\right)^{2}$ $(i i)\left(\frac{5}{4}\right)^{-3} \quad \cdots\left(a^{-1}=1 / a\right)$ $=\left(\frac{...
Read More →A matrix which is not a square matrix
Question: A matrix which is not a square matrix is called_______ matrix. Solution: A matrix in which number of rows equals the number of columns is called a square matrix whereas a matrix in which number of rows is not equal to the number of columns is called a rectangular matrix. Thus, a matrix which is not a square matrix is called rectangular matrix. A matrix which is not a square matrix is called rectangular matrix...
Read More →Express each of the following rational numbers with a positive exponent:
Question: Express each of the following rational numbers with a positive exponent: (i) $\left(\frac{3}{4}\right)^{-2}$ (ii) $\left(\frac{5}{4}\right)^{-3}$ (iii) $4^{3} \times 4^{-9}$ (iv) $\left\{\left(\frac{4}{3}\right)^{-3}\right\}^{-4}$ (v) $\left\{\left(\frac{3}{2}\right)^{4}\right\}^{-2}$ Solution: $(i)\left(\frac{3}{4}\right)^{-2} \quad \cdots\left(a^{-1}=1 / a\right)$ $=\left(\frac{4}{3}\right)^{2}$ $(i i)\left(\frac{5}{4}\right)^{-3} \quad \cdots\left(a^{-1}=1 / a\right)$ $=\left(\frac{...
Read More →If tan2 45° – cos230° = x sin 45° cos 45° then x = ?
Question: If tan245 cos230 =xsin 45 cos 45 thenx= ? (a) 2(b) 2 (c) $\frac{1}{2}$ (d) $-\frac{1}{2}$ Solution: As we know that, $\cos 45^{\circ}=\frac{1}{\sqrt{2}}$ $\cos 30^{\circ}=\frac{\sqrt{3}}{2}$ $\tan 45^{\circ}=1$ $\sin 45^{\circ}=\frac{1}{\sqrt{2}}$ By substituting these values, we get $\tan ^{2} 45^{\circ}-\cos ^{2} 30^{\circ}=x \sin 45^{\circ} \cos 45^{\circ}$ $\Rightarrow(1)^{2}-\left(\frac{\sqrt{3}}{2}\right)^{2}=x\left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{\sqrt{2}}\right)$ $\Righ...
Read More →The product of any matrix
Question: The product of any matrix by the scalar________ is the : matrix. Solution: Let $A$ be any matrix and $k$ is any scalar. The matrix obtained by multiplying every element of matrix $A$ by $k$ is called the scalar multiplication of matrix $A$ by $k$. It is denoted by $k A$. It is given that, $k A=O$ We know that, a matrix whose all elements are zero is called a : matrix. Here, $A$ is any matrix. So, when all the element of the matrix $A$ are multiplied by 0 , we will get a matrix whose al...
Read More →Calculate the number of neutrons present
Question: Calculate the number of neutrons present in the nucleus of an element ${ }^{31}{ }_{15} \mathrm{X}$ which is represented as. Solution: Mass no. of the element (A) $=31$ Atomic no. of the element $(Z)=15$ No. of neutrons $(n)=A-Z=31-15=16$....
Read More →Express each of the following rational numbers with a negative exponent:
Question: Express each of the following rational numbers with a negative exponent: (i) $\left(\frac{1}{4}\right)^{3}$ (ii) $3^{5}$ (iii) $\left(\frac{3}{5}\right)^{4}$ (iv) $\left\{\left(\frac{3}{2}\right)^{4}\right\}^{-3}$ (v) $\left\{\left(\frac{7}{3}\right)^{4}\right\}^{-3}$ Solution: (i) . $\left(\frac{1}{4}\right)^{3}$ $=\left(\frac{4}{1}\right)^{-3} \quad\left[\because a^{-\mathrm{n}}=\frac{1}{\mathrm{a}^{\mathrm{n}}}\right]$ (ii) $(3)^{5}$ $=\left(\frac{1}{3}\right)^{-5} \quad\left[\becau...
Read More →In response to a question,
Question: In response to a question, a student stated that in an atom, the number of protons is greater than the number of neutrons, which in turn is greater than the number of electrons. Do you agree with the statement ? Justify your answer. Solution: The statement is wrong. In an atom, number of protons and electrons are always equal. These can be different only in an ion (positive or negative)....
Read More →What information do you get from
Question: What information do you get from the following electronic distribution about the atomic number, mass number and valency of atoms $X, Y$ and $Z$ ? Give your answer in a tabular form. Solution: - In atom $X$, valency is equal to number of valence electrons $(2,3)=3$ - Atom Y has electronic configuration 2,6 . Valency is eight - No. of valence electrons (8-6) - In atom Z, valency is equal to number of valence electrons $(2,8,5)$, or eight - no. of valence electrons $(8-5)=3$....
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