In the class interval 20 – 30,
Question: In the class interval 20 30, the lower class limit is . Solution: In the class interval 20 30, the lower class limit is 20....
Read More →Data available in an unorganised
Question: Data available in an unorganised form is called data. Solution: Data available in an unorganised form is called raw data....
Read More →Mark (✓) against the correct answer:
Question: Mark (✓) against the correct answer: The parallel sides of a trapezium are 54 cm and 26 cm and the distance between them is 15 cm. The area of the trapezium is (a) 702 cm2 (b) 810 cm2 (c) 405 cm2 (d) 600 cm2 Solution: (d) $600 \mathrm{~cm}^{2}$ Area of the trapezium $=\left\{\frac{1}{2} \times(54+26) \times 15\right\} \mathrm{cm}^{2}$ $=\left(\frac{1}{2} \times 80 \times 15\right) \mathrm{cm}^{2}$ $=600 \mathrm{~cm}^{2}$...
Read More →A dice is tossed two times.
Question: A dice is tossed two times. The number of possible outcomes is (a) 12 (b) 24 (c) 36 (d) 30 Solution: (c) 36 (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6) = 6 (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6) = 6 (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6) = 6 (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6) = 6 (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6) = 6 (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6) = 6 = 36 In questions 36 to 58, fill in the blanks to make the statements true....
Read More →Mark (✓) against the correct answer:
Question: Mark (✓) against the correct answer: The area of a rhombus is 120 cm2and one of its diagonals is 24 cm. Each side of the rhombus is (a) 10 cm (b) 13 cm (c) 12 cm (d) 15 cm Solution: (b) 13 cm Let $A B C D$ be a rhombus whose diagonals $A C$ and $B D$ intersect at a point $O$. Let the length of the diagonal $A C$ be $24 \mathrm{~cm}$. $A$ rea of the rhombus $=\left(\frac{1}{2} \times A C \times B D\right) \mathrm{cm}^{2}$ But the area of the rohmbus is $120 \mathrm{~cm}^{2}$ (given) $\t...
Read More →Find the modulus of each of the following complex numbers and hence
Question: Find the modulus of each of the following complex numbers and hence express each of them in polar form: 2 Solution: Let $Z=-2=r(\cos \theta+i \sin \theta)$ Now, separating real and complex part, we get -2 = rcos. eq.1 0 = rsin eq.2 Squaring and adding eq.1 and eq.2, we get $4=r^{2}$ Since r is always a positive no, therefore, r = 2, Hence its modulus is 2. Now, dividing eq.2 by eq.1, we get, $\frac{r \sin \theta}{r \cos \theta}=\frac{0}{-2}$ Tan = 0 Since $\cos \theta=-1, \sin \theta=0...
Read More →A coin is tossed three times.
Question: A coin is tossed three times. The number of possible outcomes is (a) 3 (b) 4 (c) 6 (d) 8 Solution: (d) 8 HHH, TTT, THH, HTH, HHT, HTT, THT, TTH...
Read More →Mark (✓) against the correct answer:
Question: Mark (✓) against the correct answer: Each side of a rhombus is 15 cm and the length of one of its diagonals is 24 cm. The area of the rhombus is (a) 432 cm2 (b) 216 cm2 (c) 180 cm2 (d) 144 cm2 Solution: (b) 216 cm2 Let $A B C D$ be a rhombus whose diagonals $A C$ and $B D$ intersect at a point $O$. Let the length of the diagonal $A C$ be $24 \mathrm{~cm}$ and the side of the rhombus be $15 \mathrm{~cm}$. We know that the diagonals of the rhombus bisect each other at right angles. $\the...
Read More →A coin is tossed two times.
Question: A coin is tossed two times. The number of possible outcomes is (a) 1 (b) 2 (c) 3 (d) 4 Solution: (d) 4 Head Head, Tail Tail, Tail Head, Head Tail....
Read More →Find the modulus of each of the following complex numbers and hence
Question: Find the modulus of each of the following complex numbers and hence express each of them in polar form: 4 Solution: Let Z = 4 = r(cos + isin) Now, separating real and complex part, we get 4 = rcos.eq.1 0 = rsineq.2 Squaring and adding eq.1 and eq.2, we get $16=r^{2}$ Since r is always a positive no., therefore, r = 4, Hence its modulus is 4. Now, dividing eq.2 by eq.1, we get, $\frac{r \sin \theta}{r \cos \theta}=\frac{0}{4}$ Tan = 0 Since cos = 1, sin = 0 and tan = 0. Therefore the li...
Read More →Numbers 1 to 5 are written on separate slips
Question: Numbers 1 to 5 are written on separate slips, i.e. one number on one slip and put in a box. Wahida pick a slip from the box without looking at it. What is the probability that the slip bears an odd number? (a) $\frac{1}{5}$ (b) $\frac{2}{5}$ (c) $\frac{3}{5}$ (d) $\frac{4}{5}$ Solution: (c) Numbers on the slips are 1,2, 3, 4 and 5. Odd numbers = 1,3, 5 Number of slips bears an odd number = 3 Probability that the slip bears an odd number $=\frac{\text { Numberofslipsbearsanoddnumber }}{...
Read More →Mark (✓) against the correct answer:
Question: Mark (✓) against the correct answer: The diagonal of a quadrilateral is 20 cm in length and the lengths of perpendiculars on it from the opposite vertices are 8.5 cm and 11.5 cm. The area of the quadrilateral is (a) 400 cm2 (b) 200 cm2 (c) 300 cm2 (d) 240 cm2 Solution: (b) 200 cm2 Let $A B C D$ be a quadilateral. $D$ iagonal, $A C=20 \mathrm{~cm}$ $B L \perp A C$, such that $B L=8.5 \mathrm{~cm}$ $D M \perp A C$, such that $D M=11.5 \mathrm{~cm}$ $A$ rea of the quadilateral $=(A$ rea o...
Read More →Mark (✓) against the correct answer:
Question: Mark (✓) against the correct answer: The base of a triangle is four times its height and its area is 50 m2. The length of its base is (a) 10 m (b) 15 m (c) 20 m (d) 25 m Solution: (c) 20 m Let the height of the triangle be $x \mathrm{~m}$ and its base be $4 x \mathrm{~m}$ respectively. Then, area of the triangle $=\left(\frac{1}{2} \times 4 x \times x\right) m^{2}$ $=2 x^{2} \mathrm{~m}^{2}$ But, the area of the triangle $i s 50 \mathrm{~m}^{2}$. $\therefore 2 x^{2}=50$ $\Rightarrow x^...
Read More →If a and b are real numbers such that
Question: If $a$ and $b$ are real numbers such that $a^{2}+b^{2}=1$ then show that a real value of $x$ satisfies the equation, $\frac{1-i x}{1+i x}=(a-i b)$ Solution: We have, $\frac{1-i x}{1+i x}=(a-i b)=\frac{a-i b}{1}$ Applying componendo and dividendo, we get $\frac{(1-i x)+(1+i x)}{(1-i x)-(1+i x)}=\frac{a-i b+1}{a-i b-1}$ $\Rightarrow \frac{1-i x+1+i x}{1-i x-1+i x}=\frac{a-i b+1}{a-i b-1}$ $\Rightarrow \frac{2}{-2 i x}=\frac{a-i b+1}{-(-a+i b+1)}$ $\Rightarrow i x=\frac{1-a+i b}{1+a-i b} ...
Read More →Tally marks are used to find
Question: Tally marks are used to find (a) Class intervals (b) Range (c) Frequency (d) Upper limit Solution: (c) Frequency...
Read More →Mark (✓) against the correct answer:
Question: Mark (✓) against the correct answer: The base of a triangle is 14 cm and its height is 8 cm. The area of the triangle is (a) 112 cm2 (b) 56 cm2 (c) 122 cm2 (d) 66 cm2 Solution: (b) $56 \mathrm{~cm}^{2}$ Area of the triangle $=\left(\frac{1}{2} \times 14 \times 8\right) \mathrm{cm}^{2}$ = $56 \mathrm{~cm}^{2}$...
Read More →Data represented using circles
Question: Data represented using circles is known as (a)Bar graph (b) Histogram (c) Pictograph (d) Pie chart Solution: (d) Pie chart....
Read More →A field is in the form of a right triangle with hypotenuse 50 m and one side 30 m.
Question: A field is in the form of a right triangle with hypotenuse 50 m and one side 30 m. Find the area of the field. Solution: Let the other side of the triangular field be $x \mathrm{~m}$. $\therefore x^{2}=\left\{(50)^{2}-(30)^{2}\right\}$ $\Rightarrow x^{2}=(2500-900)$ $\Rightarrow x^{2}=1600$ $\Rightarrow x=\sqrt{1600}$ $\Rightarrow x=40$ $\therefore A$ rea of the field $=\left(\frac{1}{2} \times 30 \times 40\right) \mathrm{m}^{2}$ $=600 \mathrm{~m}^{2}$...
Read More →In a throw of a dice,
Question: In a throw of a dice, the probability of getting the number 7 is (a) (b) 1/6 (c) 1 (d) 0 Solution: (d) 0 Only 1, 2, 3, 4, 5 and 6 are in the dice. So, no chance of getting number 7....
Read More →If z1 = (1 + i) and z2 = (–2 + 4i), prove that Im
Question: If $z_{1}=(1+i)$ and $z_{2}=(-2+4 i)$, prove that $\operatorname{lm}\left(\frac{z_{1} z_{2}}{z_{1}}\right)=2$ Solution: We have, $z_{1}=(1+i)$ and $z_{2}=(-2+4 i)$ Now, $\frac{z_{1} z_{2}}{\overline{z_{1}}}=\frac{(1+\mathrm{i})(-2+4 \mathrm{i})}{(1+1)}$ $=\frac{-2+4 i-2 i+4 i^{2}}{(1-i)}=\frac{-2+4 i-2 i-4}{(1-i)}=\frac{-6+2 i}{(1-i)}$ $=\frac{-6+2 i}{(1-i)} \times \frac{(1+i)}{(1+i)}$ $=\frac{-6-6 i+2 i+2 i^{2}}{1+1}$ $=\frac{-6-4 i-2}{2}=\frac{-8-4 i}{2}$ $=-4-2 i$ Hence, $\operatorn...
Read More →Find the area of a quadrilateral one of whose diagonals is 40 cm
Question: Find the area of a quadrilateral one of whose diagonals is 40 cm and the lengths of the perpendiculars drawn from the opposite vertices on the diagonal are 16 cm and 12 cm. Solution: Let $A B C D$ be a quadilateral. $D$ iagonal, $A C=40 \mathrm{~cm}$ $B L \perp A C$, such that $B L=16 \mathrm{~cm}$ $D M \perp A C$, such that $D M=12 \mathrm{~cm}$ $A$ rea of the quadilateral $=(A$ rea of $\Delta D A C)+(A$ rea of $\Delta A C B)$ $=\left[\left(\frac{1}{2} \times A C \times D M\right)+\le...
Read More →Size of the class 150 –175 is
Question: Size of the class 150 175 is (a) 150 (b) 175 (c) 25 (d) 25 Solution: (c) 25 The difference between the upper class limit and lower class limit of a class is called the Size of the class. = Upper limit lower limit = 175 150 = 25...
Read More →A graph showing two sets of data
Question: A graph showing two sets of data simultaneously is known as (a) Pictograph (b) Histogram (c) Pie chart (d) Double bar graph Solution: (d) Double bar graph...
Read More →The area of a trapezium is 216 m
Question: The area of a trapezium is 216 m2and its height is 12 m. If one of the parallel sides is 14 m less than the other, find the length of each of the parallel sides. Solution: Let the length of the parallel sides be $\mathrm{x} \mathrm{m}$ and $(x-14) \mathrm{m}$. Then, area of the trapezium $=\left\{\frac{1}{2} \times(x+x-14) \times 12\right\} \mathrm{m}^{2}$ $=6(2 x-14) m^{2}$ $=(12 x-84) m^{2}$ But it is given that the area of the trapezium is $216 \mathrm{~m}^{2} .$ $\therefore 12 x-84...
Read More →Total number of outcomes,
Question: Total number of outcomes, when a ball is drawn from a bag which contains 3 red, 5 black and 4 blue balls is (a) 8 (b) 7 (c) 9 (d) 12 Solution: (d) 12...
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