chapter 7
ધોરણ 10 | విષય: Maths
અંતરસૂત્ર: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
(i) $(2, 3), (4, 1)$
ધારો કે $P(2, 3)$ અને $Q(4, 1)$ છે.
$PQ = \sqrt{(4 - 2)^2 + (1 - 3)^2}$
$PQ = \sqrt{(2)^2 + (-2)^2} = \sqrt{4 + 4} = \sqrt{8} = \mathbf{2\sqrt{2}\text{ એકમ}}$
(ii) $(-5, 7), (-1, 3)$
ધારો કે $P(-5, 7)$ અને $Q(-1, 3)$ છે.
$PQ = \sqrt{(-1 - (-5))^2 + (3 - 7)^2}$
$PQ = \sqrt{(-1 + 5)^2 + (-4)^2} = \sqrt{(4)^2 + 16} = \sqrt{16 + 16} = \sqrt{32} = \mathbf{4\sqrt{2}\text{ એકમ}}$
(iii) $(a, b), (-a, -b)$
ધારો કે $P(a, b)$ અને $Q(-a, -b)$ છે.
$PQ = \sqrt{(-a - a)^2 + (-b - b)^2}$
$PQ = \sqrt{(-2a)^2 + (-2b)^2} = \sqrt{4a^2 + 4b^2} = \sqrt{4(a^2 + b^2)} = \mathbf{2\sqrt{a^2 + b^2}\text{ એકમ}}$
ઊગમબિંદુ $O(0, 0)$ અને બિંદુ $B(36, 15)$ વચ્ચેનું અંતર:
$OB = \sqrt{(36 - 0)^2 + (15 - 0)^2}$
$OB = \sqrt{36^2 + 15^2} = \sqrt{1296 + 225} = \sqrt{1521} = \mathbf{39\text{ કિમી}}$
ઉત્તર: હા, વિભાગ 7.2 ના બે શહેરો $A$ અને $B$ વચ્ચેનું અંતર 39 કિમી થાય.
ધારો કે $A(1, 5)$, $B(2, 3)$ અને $C(-2, -11)$ છે.
$AB = \sqrt{(2 - 1)^2 + (3 - 5)^2} = \sqrt{1^2 + (-2)^2} = \sqrt{1 + 4} = \sqrt{5}$
$BC = \sqrt{(-2 - 2)^2 + (-11 - 3)^2} = \sqrt{(-4)^2 + (-14)^2} = \sqrt{16 + 196} = \sqrt{212} = 2\sqrt{53}$
$AC = \sqrt{(-2 - 1)^2 + (-11 - 5)^2} = \sqrt{(-3)^2 + (-16)^2} = \sqrt{9 + 256} = \sqrt{265}$
અહીં, કોઈપણ બે અંતરનો સરવાળો ત્રીજા અંતર જેટલો થતો નથી ($AB + BC \neq AC$).
ઉત્તર: આપેલા બિંદુઓ સમરેખ નથી.
ધારો કે $A(5, -2)$, $B(6, 4)$ અને $C(7, -2)$ છે.
$AB = \sqrt{(6 - 5)^2 + (4 - (-2))^2} = \sqrt{1^2 + 6^2} = \sqrt{1 + 36} = \sqrt{37}$
$BC = \sqrt{(7 - 6)^2 + (-2 - 4)^2} = \sqrt{1^2 + (-6)^2} = \sqrt{1 + 36} = \sqrt{37}$
$AC = \sqrt{(7 - 5)^2 + (-2 - (-2))^2} = \sqrt{2^2 + 0^2} = \sqrt{4} = 2$
અહીં, $AB = BC = \sqrt{37}$ છે (બે બાજુઓની લંબાઈ સમાન છે).
ઉત્તર: હા, આપેલા બિંદુઓ સમદ્વિબાજુ ત્રિકોણનાં શિરોબિંદુઓ છે.
આલેખ પરથી બિંદુઓના યામ:
$A(3, 4)$, $B(6, 7)$, $C(9, 4)$, $D(6, 1)$
બાજુઓની લંબાઈ:
$AB = \sqrt{(6-3)^2 + (7-4)^2} = \sqrt{3^2 + 3^2} = \sqrt{18} = 3\sqrt{2}$
$BC = \sqrt{(9-6)^2 + (4-7)^2} = \sqrt{3^2 + (-3)^2} = \sqrt{18} = 3\sqrt{2}$
$CD = \sqrt{(6-9)^2 + (1-4)^2} = \sqrt{(-3)^2 + (-3)^2} = \sqrt{18} = 3\sqrt{2}$
$DA = \sqrt{(3-6)^2 + (4-1)^2} = \sqrt{(-3)^2 + 3^2} = \sqrt{18} = 3\sqrt{2}$
વિકર્ણોની લંબાઈ:
$AC = \sqrt{(9-3)^2 + (4-4)^2} = \sqrt{6^2 + 0} = 6$
$BD = \sqrt{(6-6)^2 + (1-7)^2} = \sqrt{0 + (-6)^2} = 6$
ચારેય બાજુઓ સમાન છે ($AB = BC = CD = DA$) અને બંને વિકર્ણો સમાન છે ($AC = BD$).
ઉત્તર: $ABCD$ એક ચોરસ છે, તેથી ચંપા સાચી છે.
આલેખ પરથી બિંદુઓના યામ:
$A(3, 4)$, $B(6, 7)$, $C(9, 4)$, $D(6, 1)$
બાજુઓની લંબાઈ:
$AB = \sqrt{(6-3)^2 + (7-4)^2} = \sqrt{3^2 + 3^2} = \sqrt{18} = 3\sqrt{2}$
$BC = \sqrt{(9-6)^2 + (4-7)^2} = \sqrt{3^2 + (-3)^2} = \sqrt{18} = 3\sqrt{2}$
$CD = \sqrt{(6-9)^2 + (1-4)^2} = \sqrt{(-3)^2 + (-3)^2} = \sqrt{18} = 3\sqrt{2}$
$DA = \sqrt{(3-6)^2 + (4-1)^2} = \sqrt{(-3)^2 + 3^2} = \sqrt{18} = 3\sqrt{2}$
વિકર્ણોની લંબાઈ:
$AC = \sqrt{(9-3)^2 + (4-4)^2} = \sqrt{6^2 + 0} = 6$
$BD = \sqrt{(6-6)^2 + (1-7)^2} = \sqrt{0 + (-6)^2} = 6$
ચારેય બાજુઓ સમાન છે ($AB = BC = CD = DA$) અને બંને વિકર્ણો સમાન છે ($AC = BD$).
ઉત્તર: $ABCD$ એક ચોરસ છે, તેથી ચંપા સાચી છે.
(i) $(-1, -2), (1, 0), (-1, 2), (-3, 0)$
ધારો કે $A(-1, -2), B(1, 0), C(-1, 2), D(-3, 0)$
$AB = \sqrt{2^2 + 2^2} = \sqrt{8} = 2\sqrt{2}$
$BC = \sqrt{(-2)^2 + 2^2} = \sqrt{8} = 2\sqrt{2}$
$CD = \sqrt{(-2)^2 + (-2)^2} = \sqrt{8} = 2\sqrt{2}$
$DA = \sqrt{2^2 + (-2)^2} = \sqrt{8} = 2\sqrt{2}$
વિકર્ણો: $AC = \sqrt{0^2 + 4^2} = 4$, $BD = \sqrt{(-4)^2 + 0^2} = 4$
ઉત્તર: ચારેય બાજુઓ અને બંને વિકર્ણો સમાન હોવાથી આ ચોરસ (Square) છે.
(ii) $(-3, 5), (3, 1), (0, 3), (-1, -4)$
ધારો કે $A(-3, 5), B(3, 1), C(0, 3), D(-1, -4)$
$AB = \sqrt{6^2 + (-4)^2} = \sqrt{52} = 2\sqrt{13}$
$AC = \sqrt{3^2 + (-2)^2} = \sqrt{13}$
$CB = \sqrt{3^2 + (-2)^2} = \sqrt{13}$
અહીં $AC + CB = \sqrt{13} + \sqrt{13} = 2\sqrt{13} = AB$. આનો અર્થ એ થયો કે $A, C, B$ એક જ રેખા પર (સમરેખ) છે.
ઉત્તર: આ બિંદુઓ વડે કોઈ ચતુષ્કોણ રચાતો નથી.
(iii) $(4, 5), (7, 6), (4, 3), (1, 2)$
ધારો કે $A(4, 5), B(7, 6), C(4, 3), D(1, 2)$
$AB = \sqrt{3^2 + 1^2} = \sqrt{10}$
$BC = \sqrt{(-3)^2 + (-3)^2} = \sqrt{18} = 3\sqrt{2}$
$CD = \sqrt{(-3)^2 + (-1)^2} = \sqrt{10}$
$DA = \sqrt{3^2 + 3^2} = \sqrt{18} = 3\sqrt{2}$
વિકર્ણો: $AC = \sqrt{0^2 + (-2)^2} = 2$, $BD = \sqrt{(-6)^2 + (-4)^2} = \sqrt{52}$
સામસામેની બાજુઓ સમાન છે ($AB = CD$ અને $BC = DA$), પરંતુ વિકર્ણો અસમાન છે ($AC \neq BD$).
ઉત્તર: આ સમાંતરબાજુ ચતુષ્કોણ (Parallelogram) છે.
$x$-અક્ષ પરનું બિંદુ $P(x, 0)$ સ્વરૂપમાં હોય.
ધારો કે $A(2, -5)$ અને $B(-2, 9)$ છે. $PA = PB \implies PA^2 = PB^2$
$(x - 2)^2 + (0 - (-5))^2 = (x - (-2))^2 + (0 - 9)^2$
$x^2 - 4x + 4 + 25 = x^2 + 4x + 4 + 81$
$-4x + 29 = 4x + 85$
$-8x = 56 \implies x = -7$
ઉત્તર: માંગેલ બિંદુ $(-7, 0)$ છે.
$PQ = 10 \implies PQ^2 = 100$
$(10 - 2)^2 + (y - (-3))^2 = 100$
$(8)^2 + (y + 3)^2 = 100$
$64 + (y + 3)^2 = 100$
$(y + 3)^2 = 36$
$y + 3 = \pm 6$
જો $y + 3 = 6 \implies y = 3$
જો $y + 3 = -6 \implies y = -9$
ઉત્તર: $y$ ની કિંમત $3$ અથવા $-9$ થાય.
$QP = QR \implies QP^2 = QR^2$
$(0 - 5)^2 + (1 - (-3))^2 = (0 - x)^2 + (1 - 6)^2$
$25 + 16 = x^2 + 25$
$x^2 = 16 \implies \mathbf{x = \pm 4}$
જો $x = 4$ હોય:
$QR = \sqrt{(4 - 0)^2 + (6 - 1)^2} = \sqrt{16 + 25} = \mathbf{\sqrt{41}}$
$PR = \sqrt{(4 - 5)^2 + (6 - (-3))^2} = \sqrt{(-1)^2 + 9^2} = \mathbf{\sqrt{82}}$
જો $x = -4$ હોય:
$QR = \sqrt{(-4 - 0)^2 + (6 - 1)^2} = \sqrt{16 + 25} = \mathbf{\sqrt{41}}$
$PR = \sqrt{(-4 - 5)^2 + (6 - (-3))^2} = \sqrt{(-9)^2 + 9^2} = \sqrt{81 + 81} = \mathbf{9\sqrt{2}}$
ધારો કે $P(x, y)$, $A(3, 6)$ અને $B(-3, 4)$ છે.
$PA = PB \implies PA^2 = PB^2$
$(x - 3)^2 + (y - 6)^2 = (x - (-3))^2 + (y - 4)^2$
$(x^2 - 6x + 9) + (y^2 - 12y + 36) = (x^2 + 6x + 9) + (y^2 - 8y + 16)$
दोन्ही બાજુથી $x^2$ અને $y^2$ કટ થશે:
$-6x - 12y + 45 = 6x - 8y + 25$
$12x + 4y - 20 = 0$
4 વડે ભાગતા:
$\mathbf{3x + y - 5 = 0}$ (અથવા $3x + y = 5$)
બિંદુઓ $(x_1, y_1)$ અને $(x_2, y_2)$ ને જોડતા રેખાખંડનું $m_1 : m_2$ ગુણોત્તરમાં વિભાજન કરતા બિંદુ $P(x, y)$ ના યામ:
$$P(x, y) = \left( \frac{m_1 x_2 + m_2 x_1}{m_1 + m_2}, \frac{m_1 y_2 + m_2 y_1}{m_1 + m_2} \right)$$
ધારો કે બિંદુઓ $A(-1, 7)$ અને $B(4, -3)$ છે. ગુણોત્તર $m_1 : m_2 = 2 : 3$ છે.
વિભાજન સૂત્ર મુજબ:
$$x = \frac{2(4) + 3(-1)}{2 + 3} = \frac{8 - 3}{5} = \frac{5}{5} = 1$$
$$y = \frac{2(-3) + 3(7)}{2 + 3} = \frac{-6 + 21}{5} = \frac{15}{5} = 3$$
ઉત્તર: માંગેલ બિંદુના યામ $(1, 3)$ છે.
ધારો કે $A(4, -1)$ અને $B(-2, -3)$ છે. ત્રિભાગ બિંદુઓ $P$ અને $Q$ છે, જ્યાં $AP = PQ = QB$.
બિંદુ $P$ માટે: $P$ એ $AB$ નું $1 : 2$ ગુણોત્તરમાં અંતઃવિભાજન કરે છે.
$$P(x, y) = \left( \frac{1(-2) + 2(4)}{1 + 2}, \frac{1(-3) + 2(-1)}{1 + 2} \right) = \left( \frac{-2 + 8}{3}, \frac{-3 - 2}{3} \right) = \mathbf{\left( 2, -\frac{5}{3} \right)}$$
બિંદુ $Q$ માટે: $Q$ એ $AB$ નું $2 : 1$ ગુણોત્તરમાં અંતઃવિભાજન કરે છે (અથવા $PB$ નું મધ્યબિંદુ છે).
$$Q(x, y) = \left( \frac{2(-2) + 1(4)}{2 + 1}, \frac{2(-3) + 1(-1)}{2 + 1} \right) = \left( \frac{-4 + 4}{3}, \frac{-6 - 1}{3} \right) = \mathbf{\left( 0, -\frac{7}{3} \right)}$$
ઉત્તર: ત્રિભાગ બિંદુઓના યામ $\left(2, -\frac{5}{3}\right)$ અને $\left(0, -\frac{7}{3}\right)$ છે.
કુલ કુંડાં = $100$ (પ્રત્યેક 1 મીટરના અંતરે), તેથી કુલ લંબાઈ $AD = 100\text{ મીટર}$.
નિહારિકાનું સ્થાન (લીલો ધ્વજ): $x_1 = 2$, $y_1 = \frac{1}{4} \times 100 = 25 \implies \mathbf{G(2, 25)}$
પ્રિતનું સ્થાન (લાલ ધ્વજ): $x_2 = 8$, $y_2 = \frac{1}{5} \times 100 = 20 \implies \mathbf{R(8, 20)}$
બંને ધ્વજ વચ્ચેનું અંતર:
$$GR = \sqrt{(8 - 2)^2 + (20 - 25)^2} = \sqrt{6^2 + (-5)^2} = \sqrt{36 + 25} = \mathbf{\sqrt{61}\text{ મીટર}}$$
રશ્મિના વાદળી ધ્વજનું સ્થાન ($GR$ નું મધ્યબિંદુ):
$$M = \left( \frac{2 + 8}{2}, \frac{25 + 20}{2} \right) = \left( \frac{10}{2}, \frac{45}{2} \right) = \mathbf{(5, 22.5)}$$
ઉત્તર: બંને ધ્વજ વચ્ચેનું અંતર $\sqrt{61}\text{ મીટર}$ છે. રશ્મિએ 5મી હરોળમાં 22.5 મીટરના અંતરે વાદળી ધ્વજ ફરકાવવો જોઈએ.
ધારો કે બિંદુ $P(-1, 6)$ એ $A(-3, 10)$ અને $B(6, -8)$ ને $k : 1$ ગુણોત્તરમાં વિભાજન કરે છે.
$x$-યામ માટે વિભાજન સૂત્ર:
$$-1 = \frac{k(6) + 1(-3)}{k + 1}$$
$$-1(k + 1) = 6k - 3 \implies -k - 1 = 6k - 3$$
$$2 = 7k \implies k = \frac{2}{7}$$
ઉત્તર: માંગેલ ગુણોત્તર $2 : 7$ છે.
$x$-અક્ષ પરના કોઈ બિંદુના યામ $(x, 0)$ સ્વરૂપમાં હોય. ધારો કે તે $k : 1$ ગુણોત્તરમાં વિભાજન કરે છે.
$y$-યામ સરખાવતાં ($y = 0$):
$$0 = \frac{k(5) + 1(-5)}{k + 1} \implies 5k - 5 = 0 \implies 5k = 5 \implies \mathbf{k = 1}$$
તેથી ગુણોત્તર $1 : 1$ છે (જે દર્શાવે છે કે વિભાજન બિંદુ મધ્યબિંદુ છે).
વિભાજન બિંદુના $x$-યામ:
$$x = \frac{1(-4) + 1(1)}{1 + 1} = \frac{-3}{2}$$
ઉત્તર: ગુણોત્તર $1 : 1$ છે અને વિભાજન બિંદુના યામ $\left(-\frac{3}{2}, 0\right)$ છે.
સમાંતરબાજુ ચતુષ્કોણના વિકર્ણો પરસ્પર દુભાગે છે, તેથી વિકર્ણ $AC$ નું મધ્યબિંદુ = વિકર્ણ $BD$ નું મધ્યબિંદુ.
ધારો કે $A(1, 2), B(4, y), C(x, 6), D(3, 5)$.
$$\left( \frac{1 + x}{2}, \frac{2 + 6}{2} \right) = \left( \frac{4 + 3}{2}, \frac{y + 5}{2} \right)$$
$$\left( \frac{1 + x}{2}, 4 \right) = \left( \frac{7}{2}, \frac{y + 5}{2} \right)$$
$x$-યામ સરખાવતાં: $\frac{1 + x}{2} = \frac{7}{2} \implies 1 + x = 7 \implies \mathbf{x = 6}$
$y$-યામ સરખાવતાં: $4 = \frac{y + 5}{2} \implies 8 = y + 5 \implies \mathbf{y = 3}$
ઉત્તર: $x = 6$ અને $y = 3$.
વર્તુળનું કેન્દ્ર $C(2, -3)$ એ વ્યાસ $AB$ નું મધ્યબિંદુ થાય.
ધારો કે $A(x, y)$ છે.
$$\left( \frac{x + 1}{2}, \frac{y + 4}{2} \right) = (2, -3)$$
$x$-યામ સરખાવતાં: $\frac{x + 1}{2} = 2 \implies x + 1 = 4 \implies \mathbf{x = 3}$
$y$-યામ સરખાવતાં: $\frac{y + 4}{2} = -3 \implies y + 4 = -6 \implies \mathbf{y = -10}$
ઉત્તર: બિંદુ $A$ ના યામ $(3, -10)$ છે.
$AP = \frac{3}{7}AB \implies PB = AB - AP = AB - \frac{3}{7}AB = \frac{4}{7}AB$.
તેથી $AP : PB = 3 : 4$ થાય.
બિંદુ $P$ એ $A(-2, -2)$ અને $B(2, -4)$ નું $3 : 4$ ગુણોત્તરમાં વિભાજન કરે છે.
$$x = \frac{3(2) + 4(-2)}{3 + 4} = \frac{6 - 8}{7} = -\frac{2}{7}$$
$$y = \frac{3(-4) + 4(-2)}{3 + 4} = \frac{-12 - 8}{7} = -\frac{20}{7}$$
ઉત્તર: બિંદુ $P$ ના યામ $\left(-\frac{2}{7}, -\frac{20}{7}\right)$ છે.
ધારો કે ચાર સમાન ભાગ કરતાં બિંદુઓ $P_1, P_2, P_3$ છે.
$P_2$ (જે $AB$ નું મધ્યબિંદુ છે):
$$P_2 = \left( \frac{-2 + 2}{2}, \frac{2 + 8}{2} \right) = \mathbf{(0, 5)}$$
$P_1$ (જે $AP_2$ નું મધ્યબિંદુ છે):
$$P_1 = \left( \frac{-2 + 0}{2}, \frac{2 + 5}{2} \right) = \mathbf{\left(-1, \frac{7}{2}\right)}$$
$P_3$ (જે $P_2B$ નું મધ્યબિંદુ છે):
$$P_3 = \left( \frac{0 + 2}{2}, \frac{5 + 8}{2} \right) = \mathbf{\left(1, \frac{13}{2}\right)}$$
ઉત્તર: વિભાજન કરતાં બિંદુઓના યામ $\left(-1, \frac{7}{2}\right)$, $(0, 5)$, અને $\left(1, \frac{13}{2}\right)$ છે.
ધારો કે A(3,0),B(4,5),C(−1,4),D(−2,−1).
વિકર્ણોની લંબાઈ:
AC=(−1−3)2+(4−0)2
![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.28em" viewBox="0 0 400000 1296" preserveAspectRatio="xMinYMin slice"><path d="M263,681c0.7,0,18,39.7,52,119<br />
c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120<br />
c340,-704.7,510.7,-1060.3,512,-1067<br />
l0 -0<br />
c4.7,-7.3,11,-11,19,-11<br />
H40000v40H1012.3<br />
s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232<br />
c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1<br />
s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26<br />
c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z<br />
M1001 80h400000v40h-400000z"></path></svg>)
=(−4)2+42=16+16![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702<br />
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14<br />
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54<br />
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10<br />
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429<br />
c69,-144,104.5,-217.7,106.5,-221<br />
l0 -0<br />
c5.3,-9.3,12,-14,20,-14<br />
H400000v40H845.2724<br />
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7<br />
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z<br />
M834 80h400000v40h-400000z"></path></svg>)
=32=42
BD=(−2−4)2+(−1−5)2
=(−6)2+(−6)2=36+36=72=62
ક્ષેત્રફળનું સૂત્ર: ક્ષેત્રફળ=21×d1×d2
ક્ષેત્રફળ=21×42×62=21×24×2=24 ચોરસ એકમ
ઉત્તર: સમબાજુ ચતુષ્કોણનું ક્ષેત્રફળ 24 ચોરસ એકમ થાય.
destiny — fate [S]
rural — urban [A]
sturdy — strong [S]
desire — wish [S]
cheap — costly [A]
benefit — disadvantage [A]
resolution — decision [S]
curious — incurious [A]
opportunity — chance [S]
reside
(a) Mr. P. G. Pathak is a resident of Shastrinagar area.
(b) The police inquired of his residence in Delhi.
(c) You can't have a ration card of this city as you are residing in another city.
strong
(a) You must strengthen your body to face such hardships as you are going to join our army next month.
(b) The inner strength of our father of the nation, Gandhiji, made the Britishers quit India.
(c) Bhim gave such a strong blow of his mace on Duryodhan's thigh that he was injured.
construct
(a) Dr. Babasaheb Ambedkar is one of the constructors of the constitution of our country.
(b) Students should be given constructive education rather than theoretical.
(c) The construction of the Tajmahal began in 1632 by Shahjahan at Agra.
power
(a) Our government is trying its best for women empowerment in every walk of life.
(b) Don't you think that India needs some powerful leaders like Sardar Patel nowadays?
(c) The new law of RTI empowers us to get any information.
inform
(a) Information: We collected useful information for our science project.
(b) Informative: The documentary on nature was very informative.
(c) Informant: The police got a clue from an anonymous informant.
direct
(a) Direction: We should walk in the right direction to reach our goal.
(b) Director: The director guided all actors efficiently.
(c) Directly: She addressed her concerns directly to the principal.
beauty
(a) Beautiful: The sunrise over the mountains looked beautiful.
(b) Beautify: The municipality planted trees to beautify the city streets.
(c) Beautifully: The students decorated the assembly hall beautifully.
Aarzu wanted a job of an officer. So she applied for the job.
Our society pooled in Rs. 3,50,000/- for relief fund.
Aanandnagar has no electricity so the GEB is going to establish mini grid there.
The Loksansar launched a new scheme of flats.
The people of Bhavnagar have raised the demand for 'Bhavnagar Tarapur railway line' for many years.
Our government has started a scheme of giving LED bulbs to the people.
Very soon Gujarat Government will recruit about 45000 persons in various administrative departments.
In Gujarat, we face the scorching heat of sun during May and June.
We visited Ghogha last week because we wanted to launch a new project. — T
There are lunar panels in our village. — F
Correction: There are solar panels in our village.
Solar power is a smokeful source of light. — F
Correction: Solar power is a smokeless source of light.
In recent times, most people use fluorescent lamps to save electricity. — F
Correction: In recent times, most people use LED lamps to save electricity.
Most of our women squander in watching TV serials of family drama. — T
The climate (metalic) of this region is humid; so being an asthma patient you can't stay here.
Dr. Batra's counsel (unclose) to Aastha for her choosing a career proved fruitful.
It was Dashrath's destiny (density) that he would die when none of his sons was present there.
Mr. Khan is a resident (inserted) of this society so he must pay the maintenance charges.
Brinda's resolution (reside) to educate her daughter in an English medium school was fulfilled as they shifted to Baroda.
They have signed (design) the contract, so it's a bit late to change their minds now
Sudha Murthy found that Hanumanthappa was a brilliant boy. But unfortunately, he was not able to study further because of his poverty. She wanted to contribute in his study. She talked about this issue in her staff and they pooled in one lakh rupees. They had dispute over the course of his choice. They lobbied a senior colleague to take decision. Finally, the issue was resolved by formulating a plan for empowering the boy and providing him necessary resources.
The Government funded twenty one lakh rupees to build the railway station. — F
Majority of people living in Taj Nagar are businessmen. — F
Ranjitsingh is the sarpanch of Taj Nagar village. — F
Azaz, the electrician, was given the job of a technician. — F
Out of thousand members of the library, three hundred are women. — T
The library arranged seminars to solve the family problems of women. — T
Separate reading room for women was set up to give them safe space. — T
The wish of villagers was to:
(c) build a railway station.
Railway authorities refused a railway station because of:
(a) lack of fund.
What is the source of smokeless light?
(c) solar power.
Palakkad's library is unique for its:
(a) women members.
The library set up a separate reading room for women because:
(b) the women could feel safe.
The solar panels are installed:
(b) on the roof of the strong walled homes.
Most of the three thousand people living in the village are farmers. But such was the burning desire to have a station in the village, everybody contributed according to their capacity. Ranging from three thousand rupees to seventy five thousand rupees, they donated money for the station and we started the construction in January 2008," said Ranjeet Singh, a former village Sarpanch.
A (Palakkad's district library...) — 7 (The library provides the women the strength to empower them.)
B (Installing a micro-grid...) — 5 (Villagers watched with surprise the set up of grid...)
C (Village by village...) — 4 (An organization arranged for power at a low cost.)
D (For twenty five...) — 1 (The villagers collected 21 lakh rupees...)
E (The library was also...) — 6 (The library started to settle all kinds of disputes of women.)
F (There are a large...) — 2 (The villagers had to go six kilometers to catch a train...)
G (In Sitapur district...) — 3 (A place in Sitapur got transformed with solar energy...)
They pooled in twenty one lakh rupees. — (c) Who gave the money?
We had to either go to Halimandi or Patli to catch a train. — (e) What was the problem in that?
In Sitapur district one such place with no power, a small social enterprise is trying to change things. — (d) What are they doing?
But it has recently been in the news for different reasons. — (a) What is that?
The unit got together to discuss methods of empowering women. — (b) How did they do it?
How long did the people of Taj Nagar try to persuade the railway authorities for a railway station?
Ans: The people of Taj Nagar tried to persuade the railway authorities for twenty-five years.
Where did the villagers have to go to board a train?
Ans: The villagers had to go to either Halimandi or Patli to board a train.
What is the main problem in rural Uttar Pradesh?
Ans: Over sixty percent of households in rural Uttar Pradesh are without power.
In just one year's time, what has MGP achieved in Sitapur district?
Ans: MGP has connected more than 3,500 customers to solar power mini-grids at a village level.
What is the main advantage of solar light according to a village farmer?
Ans: Solar light saves the environment and keeps homes free from smoke and pollution.
For what can people use Palakkad's District Library?
Ans: People can use it as a center for information, knowledge, wisdom, cultural activities, research, and reference.
Why did the women unit get together?
Ans: The women's unit got together to discuss methods and plans for empowering women.
What did the Library open its halls for?
Ans: It opened its halls for film screening, workshops, child care, arts, and resolving family or legal disputes.
What does the Palakkad's Library stand for?
Ans: It stands tall as a beacon to encourage women's empowerment through classes, clubs, workshops, and reading rooms.
What was the burning desire of the people of Taj Nagar? What did they do for it?
Ans: The burning desire of the people was to have a railway station in their village. When the railways refused, they pooled in 21 lakh rupees and built a station on their own.
Why did people raise their demand for a railway station in their village? How did the authorities respond?
Ans: Railway lines passed right through Taj Nagar, but residents had to walk 6 km to Halimandi or Patli to catch a train. When they demanded a station, the railway authorities responded that they lacked funds.
What is MGP doing in Sitapur district? Why?
Ans: MGP is connecting rural households to low-cost solar microgrids. They do this because over 60% of homes in Sitapur have no electricity, and solar energy provides a cheap, clean light source.
How were the panels installed?
Ans: Panels were installed on the sturdy, brick-walled roof of a village home. Local electrician Azaz installed them facing a southerly direction to capture maximum sunlight.
How have solar micro grids helped the village people?
Ans: Solar microgrids provided cheap light and phone charging, saved the environment from pollution, allowed children to study at night, and enabled adults to run night businesses like weaving.
What did the secretary of the library point out?
Ans: The secretary pointed out that through reading, women would realize their inner strength and forge unity, preventing them from wasting hours in front of televisions.
What did the library do for women?
Ans: The library set up a dedicated women's unit, arranged separate reading rooms, and organized workshops on home management, child care, and legal counseling.
1. Palakkad's District Library
The Palakkad District Public Library was established in September 2013 in Kerala. It serves as a modern center for information, knowledge, research, and cultural activities. One-third of its members are women, leading to the creation of a special women’s unit in February 2014. The library opened its halls for film screenings, workshops in gardening, child care, and resolving family or legal disputes. By offering a safe venue and separate reading rooms for female members, Palakkad's library stands tall as a beacon of women's empowerment.
2. Dream of Railway Station Comes True
The residents of Taj Nagar near Gurgaon faced great hardship as they had to travel 6 km to Halimandi or Patli to catch a train. Despite railway lines passing through their village, their 25-year demand for a station was rejected due to lack of funds. Driven by strong determination, the villagers took matters into their own hands, pooled 21 lakh rupees, and formed an 11-member team. Construction began in 2008, and on January 7, 2010, the country’s first community-funded railway station started operations.
3. MGP's Drive for Solar Power in Sitapur District
In rural Sitapur district, over 60% of homes lacked power. A social enterprise named Mera Gao Power (MGP) tackled this challenge by setting up low-cost solar microgrids. In just over a year, MGP connected over 3,500 customers to solar mini-grids. For 25 rupees a week, households received two LED lights and a mobile charging point. This smokeless light proved beneficial for health, saved fuel costs compared to kerosene, and opened up night-time business opportunities like sari weaving and plastic tablecloth making.
Where is Saputara located?
Ans: Saputara is located on a plateau of the Western Ghats (Sahyadri range) in the Dang District of Gujarat.
What is the altitude of the hill station?
Ans: It is situated at an altitude of about 900 meters above sea level.
How far is the hill station from Surat?
Ans: It is 156 km away from Surat.
What is the atmosphere in monsoon like?
Ans: The monsoon atmosphere is filled with fog, clouds dispersed over hills, mighty waterfalls, and soothing green surroundings.
When is the Monsoon Festival organized?
Ans: The Monsoon Festival is organized every year in the month of August.
What are the main attractions of the Monsoon Festival?
Ans: Water sports, heritage walks, rides, and cultural programs that last till midnight are the main attractions.
Answers to Questions:
What happened in the morning?
Ans: A bank robbery took place in the morning on S P Road.
Where did the robbery take place?
Ans: In a bank on S P Road and later in a nearby jewellery shop.
Where was the money kept?
Ans: The money was kept inside a box in the bank's strong room.
When did the police get the first clue?
Ans: The police got the first clue at 1:00 PM when the jeweler reported the escape car.
What did Vadodara police find? When? Where?
Ans: Vadodara police found an abandoned white car at 4:30 PM at a circle on Airport Road.
"...extremely busy that day." → T
"...sixth day of overtime." → T
"...near Gurgaon..." → L
"...in their village." → L
"...morning of the year 1887." → T
"...to our house..." → L
"...into her room..." → L
"...In 1890..." → T
"...at the age of about ten..." → T
"...to the Perkins Institution." → L
"...in India..." → L
"...in the North." → L
"...in the night sky..." → L/T
"...Six minutes to six..." → T
"...above the Information desk..." → L
"...in New York's Grand Central Station." → L
"...past thirteen months." → T
Where were you born? — Answer: At Porbandar.
What is your date of birth? — Answer: On 5th September.
At what time were you born? — Answer: At midnight (12:00 AM).
When do you get up everyday? — Answer: At 6:00 AM.
Where exactly is your house? — Answer: In Agra.
Where do you live? — Answer: In Ahmedabad.
Where exactly is the book? — Answer: On the dining table.
When do you learn photography? — Answer: On Fridays.
Where have you kept your TV? — Answer: In my bedroom.
Where is the photograph? — Answer: Behind my back / wall.
A: On MG Road → Q: Where is the main shopping center located?
A: At 12.30 pm → Q: At what time do you usually have lunch?
A: In the room → Q: Where is your younger brother studying?
A: Near Gandhinagar → Q: Where is the new IT park situated?
A: On the banks of the Narmada → Q: Where is the Statue of Unity built?
A: Between Baroda and Surat → Q: Where is Bharuch located?
A: At Dandi → Q: Where did Gandhiji break the salt law?
A: In the evening → Q: When do children go out to play?
A: At midnight → Q: When did the express train reach the station?
A: On Sunday → Q: When will your school organize the annual picnic?