How many faces are there in a
Question: How many faces are there in a (i) cube (ii) pentagonal (iii) tetrahedron (iv) pentagonal pyramid? Solution: (i) A cube has 6 faces, namelyIJKL, MNOP, PLIM , OKJN, POKLandMNJI.(ii) A pentagonal prism has 7 faces, i.e. 2 pentagons and 5 rectangles, namelyABCDE, FGHIJ, ABGF, AEJF , EDIJ, DCHIandCBGH.(iii) A tetrahedron has 4 faces, namelyKLM, KLN, LMNandKMN.(iv) A pentagonal pyramid has 6 faces, i.e. 1 pentagon and 5 triangles, namelyNOPQM, SNM, SOP, SNO, SMQandSQP....
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: 1 + i Solution: Let $Z=1-i=r(\cos \theta+i \sin \theta)$ Now, separating real and complex part, we get -1 = rcos .eq.1 1 = rsin eq.2 Squaring and adding eq.1 and eq.2, we get $2=r^{2}$ Since r is always a positive no., therefore, $\mathrm{r}=\sqrt{2}$ Hence its modulus is $\sqrt{2}$. Now, dividing eq.2 by eq.1 , we get, $\frac{r \sin \theta}{r \cos \theta}=\frac{1}{-1}$ Tan = -1 Sinc...
Read More →How many edges are there in a
Question: How many edges are there in a (i) cuboid (ii) tetrahedron (iii) triangular prism (iv) square pyramid? Solution: (i) A cuboid has 12 edges, namelyAD, DC, CB, BA, EA, FB, HD, DC, CG, GH, HE, andGF.(ii) A tetrahedron has 6 edges, namelyKL, LM, MN, NL , KMandKN.(iii) A triangular prism has 9 edges, namelyQR, RS, SQ, TU, UV, VT, RU, SVandQT.(iv) A square pyramid has 8 edges, namelyOW, OX, OY , OZ , WX, XY, YZandZW....
Read More →The number of people having
Question: The number of people having books more than 20 and less than 40 is . Solution: The number of people having books more than 20 and less than 40 is 14....
Read More →Define Euler's relation between the number of faces,
Question: Define Euler's relation between the number of faces, number of edges and number of vertices for various 3-dimensional figures. Solution: The Euler's relation for a three dimensional figure can be expressed in the following manner: $F-E+V=2$ $H$ ere, $F-$ Number of faces $E-$ Number of edges $V$ - Number of vertices...
Read More →The number of people owning
Question: The number of people owning books less than 40 is . Solution: The number of people owning books less than 40 is 22....
Read More →Fill in the blanks:
Question: Fill in the blanks: (i) A cube has ....... vertices, ....... edges and ....... faces. (ii) The point at which three faces of a figure meet is known as its ....... (iii) A cuboid is also known as a rectangular ....... (iv) A triangular pyramid is called a ....... Solution: (i) A cube has8vertices,12edges and6faces. Vertices:I, J, K, L, M, N, OandP Edges :IJ, JN, NM, MI, PL, LK, KO, OP, PM, LI, KJ, andON Faces :MNJI, POKL, PLIM, OKJN, PONMandLKJI(ii) The point at which the three faces of...
Read More →Write down the number of vertices of each of the following figures:
Question: Write down the number of vertices of each of the following figures: (i) Cuboid (ii) Square pyramid (iii) Tetrahedron (iv) Triangular prism Solution: (i) A cuboid has 8 vertices, namelyA, B, C, D, E, F, GandH.(ii) A square pyramid has 5 vertices, namelyO, W, X, YandZ.(iii)A tertrahedron has 4 vertices, namelyK, L, MandN.(iv) A triangular prism has 6 vertices, namelyQ, R, S, T, UandV....
Read More →The number of people owning
Question: The number of people owningbooks more than 60 is . Solution: The number of people owning books more than 60 is 8....
Read More →Write down the number of edges of each of the following figures:
Question: Write down the number of edges of each of the following figures: (i) Tetrahedron (ii) Rectangular pyramid (iii) cube (iv) Triangular prism Solution: (i) A tetrahedron has 6 edges, namelyKL, LM, LN, MN, KNandKM.(ii) A rectangular pyramid has 8 edges, namelyAB, AE, AD, AC, EB, ED, DCandCB.(iii) A cube has 12 edges, namelyPL, LK, KO, OP, MN, NJ, JI, IM, PM, LI, ONandKJ.(iv) A triangular prism has 9 edges, namelyQR, RS, QS, TU, TV, UV, QT, RU, andSV....
Read More →The total number of people
Question: The total number of people surveyed is . Solution: Form the Histogram, The total number of people surveyed is 35....
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: 1 i Solution: Let $Z=1-i=r(\cos \theta+i \sin \theta)$ Now , separating real and complex part , we get 1 = rcos .eq.1 -1 = rsin eq.2 Squaring and adding eq.1 and eq.2, we get $2=r^{2}$ Since r is always a positive no., therefore, $r=\sqrt{2}$ Hence its modulus is $\sqrt{2}$. Now , dividing eq.2 by eq.1 , we get, $\frac{r \sin \theta}{r \cos \theta}=\frac{-1}{1}$ $\operatorname{Tan} \...
Read More →The difference between the upper
Question: The difference between the upper and lower limit of a class interval is called the of the class interval. Solution: The difference between the upper and lower limit of a class interval is called the Size/width of the class interval....
Read More →Write down the number of faces of each of the following figures:
Question: Write down the number of faces of each of the following figures: (i) Cuboid (ii) Cube (iii) Triangular prism (iv) Square pyramid (v) Tetrahedron Solution: (i) A cuboid has 6 faces, namelyABCD, EFGH, HDAE, GCBF, HDCGandEABF.(ii) A cube has 6 faces, namelyIJKL, MNOP, PLIM, OKJN, LKOPandIJNM.(iii) A triangular prism has 5 faces (3 rectangular faces and 2 triangular faces), namelyQRUT, QTVS, RUVS, QRSandTUV.(iv) A square pyramid has 5 faces (4 triangular faces and 1 square face), namelyOWZ...
Read More →An experiment whose outcomes cannot
Question: An experiment whose outcomes cannot be predicted exactly in advance is called a experiment. Solution: An experiment whose outcomes cannot be predicted exactly in advance is called a random experiment....
Read More →Each outcome or a collection
Question: Each outcome or a collection of outcomes in an experiment makes an . Solution: Each outcome or a collection of outcomes in an experiment makes an Event....
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: 2i Solution: Let $Z=2 i=r(\cos \theta+i \sin \theta)$ Now, separating real and complex part, we get 0 = rcos .eq.1 2 = 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, $\frac{r \sin \theta}{r \cos \theta}=\frac{2}{0}$ $\operatorname{Tan} \theta=\infty$ Since $\c...
Read More →When a dice is rolled,
Question: When a dice is rolled, the six possible outcomes are . Solution: When a dice is rolled, the six possible outcomes are 1, 2, 3, 4, 5 and 6....
Read More →In the experiment of tossing
Question: In the experiment of tossing a coin one time, the outcome is either or Solution: In the experiment of tossing a coin one time, the outcome is either Head or Tail....
Read More →Fill in the blanks.
Question: Fill in the blanks. (i) Area of triangle $=\frac{1}{2} \times(\ldots \ldots \ldots) \times(\ldots \ldots \ldots .)$. (ii) Area of a $\| \mathrm{gm}=\frac{1}{2} \times(\ldots \ldots . .) \times(\ldots \ldots . .)$. (iii) Area of a trapezium $=\frac{1}{2} \times(\ldots \ldots . .) \times(\ldots \ldots . .)$. (iv) The parallel sides of a trapezium are 14 cm and 18 cm and the distance between them is 8 cm. The area of the trapezium is ......... cm2. Solution: (i) Area of a triangle $=\frac...
Read More →A pie chart is used to compare to a whole.
Question: A pie chart is used to compare to a whole. Solution: A pie chart is used to compare parts to a whole....
Read More →The range of the data 6,
Question: The range of the data 6, 8, 16, 22, 8, 20, 7, 25 is . Solution: The difference between the lowest and the highest observation in a given data is called its Range. Then, Range = Highest observation Lowest observation = 25 6 = 19 The range of the data 6, 8, 16, 22, 8, 20, 7, 25 is 19....
Read More →In the class interval 26 – 33,
Question: In the class interval 26 33, 33 is known as . Solution: In the class interval 26 33, 33 is known as upper class limit....
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: i Solution: Let $Z=-i=r(\cos \theta+i \sin \theta)$ Now, separating real and complex part, we get 0 = rcos.eq.1 -1 = rsin eq.2 Squaring and adding eq.1 and eq.2, we get $1=r^{2}$ Since r is always a positive no., therefore, r = 1, Hence its modulus is 1. Now, dividing eq.2 by eq.1, we get, $\frac{r \sin \theta}{r \cos \theta}=\frac{-1}{0}$ $\operatorname{Tan} \theta=-\infty$ Since $\...
Read More →Mark (✓) against the correct answer:
Question: Mark (✓) against the correct answer: The area of a trapezium is 384 cm2. Its parallel sides are in the ratio 5 : 3 and the distance between them is 12 cm. The longer of the parallel sides is (a) 24 cm (b) 40 cm (c) 32 cm (d) 36 cm Solution: (b) $40 \mathrm{~cm}$ Let the length of the parallel sides be $5 x \mathrm{~cm}$ and $3 x \mathrm{~cm}$, respectively. $^{2}$ $A$ rea of the trapezium $=\left\{\frac{1}{2} \times(5 x+3 x) \times 12\right\} \mathrm{cm}$ $=\left(\frac{1}{2} \times 8 x...
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