Since  ∆ACO ~ ∆BOD, AC/BD = CO/ OD = AO/BO [Ratio of corresponding sides of similar triangles are equal] Taking AC/BD = CO/ OD or,  10/ BD = 8 / 12 [Given] or, 10 x 12 = BD x 8 or, BD = (10 x 12)/8 = 15 cm. Hence .....

Here,  y = 610,  Vertacally opposite angles are equale. Again, x = y  , alternate angles. So,  x  = 61o. Hence,  x= y  = .....

Here, Total earning = Rs. 1505000 Divident percent = 7% Number of emplyoee = 75 Hence,  Total money divided =  7% of 1505000 = 7/100 x 1505000 = Rs. 10530 Noe, Sum got by each employer = 10530/75 = Rs. .....

Here,  3: 2 = 9 : x or, 3/2 = 9 / x or, x = 9 X 2 / 3          = 3X 2 = 6 Hence,  x  = .....

We have to find x,  So,  3x + 2 = 11 or, 3x =  11 - 2 or, 3x = 9 or, x = 9/ 3 or, x = 3 Hence,  x = 2   is required .....

To beundefined, denomerator of given function must be zero, i.e; x - 5 = 0  or, x = 0 + 5  Or, x = 5. Hence rquired value of x is .....

a) To beundefined, denomerator of given function must be zero, i.e; x - 5 = 0  or, x = 0 + 5  Or, x = 5. Hence rquired value of x is .....

Let his total yearly earning be 'x'. Since there is an allowance of Rs. 40,000 , The Taxable income = Rs. (x - 40,000) Also, Tax % = 15% Tax amount = Rs. 30,000 or, 30,000 =  (x - 40,000) * 15/100 or, 200000 = x - .....

Here,  P =,{ 1, 2, 3, 4} Q = { 3, 4, 5,6} P - Q  = { 1, 2, 3, 4} -  { 3, 4, 5,6}           = { 1,2 } Is required .....

We have to find mode of   70,75,80,60,70,90 As we know, mode = data which repeat most                                  = .....

The advantage of series combination is: The current is increased with the increase in the number of cells and  the brightness of the cell increases with the increase in the number of cells in the series .....

Here,  Radius of circle = R = rcm We know, area of circle  = π R2                                          = π [r .....

You know each magnet possess magnetic field. This field is represented by magnetic lines of force. The properties of magnetic lines of force are 1. They are directef from north poles to south. 2.The direction of the field lines inside the .....

The instrument which is used to measure the heat is a thermometer. Two liquids used inside the thermometer are alcohol and mercury. A narrow constriction is made near the bulb of a clinical thermometer so that the mercury will not drop down .....

Here, Co - interior angle of < BGH is < DHG. Hence, Co - interior angle of < BGH is < .....

Here, GIven, mass (m) = 300 kg Surface area (A) = 150 m2 Gravity (g) = 10 m/s2 Pressure exerted (P) =? we have, from formula, Force (F) = m × g                 = .....

Here,  We have given, x2 - 6x - 72 = 0 or, x2 - 12x + 6x - 72 = 0 or, x ( x - 12 ) + 6 ( x - 12) = 0 or, (x - 12 ) ( x + 6 ) = 0 Either, x - 12 = 0   ==>  x = 12\ Or, x + 6 = 0   ==>  x = - .....

You know that in lever, the product of load to the load distance (Lx LD) is equal to the product of an effort to the effort distance (E x ED). This shows that greater the effort distance, lesser will be the effort required.  In a .....

Solution; =1 / [x - 1] - 1/ [ x + 1] + 2 / [x2+ 1] =[ x + 1 - ( x - 1) ] / [ (x -1) (x +1)] + 2 / [ x2 + 1] = [ x + 1 -  x + 1 ] / [ (x -1) (x +1)] + 2 / [ x2 + 1] = 2  /  (x2 -1)  + 2 / [ x2 + 1] = [2 ( x2 + .....

VR = effort distance (ED)           load distance (LD)        = 40           20        = 2 Therefore, VR of the lever is .....

Frist expression = x4 - 8x                            = x [ x3 - 8]                            = .....

Here, Velocity of first car (VA) = 40 m/s Velocity of second car (VB) = 25 m/s we have, Relative velocity of the first car with respect to the second car when both are moving in the same direction (V AB) =? VAB = VA - VB   .....

You know that when you go to a shop, A shopkeeper gives you only after measuring it on a beam balance. Hence, a mass of a body is measured by using a beam balance and a set of standard masses. Here, a mass is measured by putting the .....

We need to factorise,  ( x + y)2 + 11( x + y) + 30 Let, x + y = a, then  ( x + y)2 + 11( x + y) + 30 = a2 + 11a + 30 = a2 + 5a + 6a + 30 = a( a + 5) + 6 ( a + 5) = ( a+5) ( a + 6) Replace, a = x + y, = ( x +  + 5) ( x + .....

.....

Solution, 16/√2 - 24/√32 - 2√48 - 3√(8×54) = 16/√2 x √2 / √2  - 24/√[ 2 x 2 x 2 x 2 x 2]  - 2√[ 2 x 2 x 2 x 2 x 3] - 3√(2 x 2 x2 ×3 x 3 x 3 x 2) = .....

Here,  Interest= I = Rs. 162 Time = T = 3 yrs. Rate = R = 12% We know,  P = I x 100 / [T x R]     = Rs.162 x 100 / [ 3 x 12]    =  Rs.450. Hence sum is Rs. .....

Here,  14 men can do a work in 3 days. or, 1 man can do a work in 3x 14 days. So, 6 men can do a work in 3 x 14 / 6 = 7 .....

Here,  Final SP = SP + VAT % of SP or, Rs. 18080 = SP + 13/ 100 x SP or, SP = 18080 x 100 / 113              = Rs.16000. Again,  SP = MP - Discount % of MP or, 16000 = MP - 20 / 100 x MP or, 16000 .....

Here, a2 - ( b -2) a - 2b =  a2 - a b + 2a - 2b = a( a - b) +2 (a- b) = (a -b) ( a .....

Here, We need to find, 60% of Rs.900  = 60 / 100 X Rs.900 = Rs. 60 x 9 = Rs. .....

Here,  Side of triangle = a = 6cm We know,  Area of equilateral triangle = √3/ 4 a2                                         .....

Here,  A ={ 1,2,3,4,5} B = { 4, 5, 6, 7,8} C = { 4,6,9,10} Now, AU(B∩C) = { 1,2,3,4,5} U [ { 4, 5, 6, 7,8} ∩ { 4,6,9,10}]                         .....

Solution, Here, [ 83 x 153 ] / [ 64 x 103] = [(2x2x2)3 x (5 x 3)3 ] / [ ( 2 x3 )4 x ( 2x 5)3] = [ 23 x 23 x 23 x 53x 33 ] / [ 24 x 34 x 23 x 53] Now using indices rule,  = 23 + 3 + 3 .....

Here,  [ a2 - 2ab + b2 ] / [ a2 - b2 ]  Using, a2 - 2ab + b2 = (a - b )2   and  a2 - b2 = ( a + b) ( a -b ) , we get, = (a - b )2 / [( a + b) ( a -b )] = (a - b) / ( a + .....

Here, AC = 6,  BC = 8 AB = ? From the pythagoras theorem,  In right angled triangle, ABC, AB = √[ AC2 + BC2]        = √[ 62 + 82]        = √[ .....

Here,  Radius of circle = r  = 2cm We know, area of circle  = π r2                                         = 22/ 7 x[ .....

Here,  We know, 360o = total students. So, 1o = 540/ 360             =  3/2. So, Class 8 = 120o = 120 x 3/2 = 180 Hence 180 students are in class .....

Here,   U = { x : 1 ≦ x ≤ 10 } = { 1, 2, 3 ,4, 5, 6, 7,8 ,9 ,10} A= { 1,2 ,3 }  B = { 3,4 7} Now, AUB =  { 1,2 ,3 } U { 3,4 7} = { 1 , 2, 3 ,4 , 7 } SO, (AUB ) ' = U - ( AUB)     .....

In △ADB and  △ADC,  i) AB = AC   (S)   [ given] ii) < BAD = < CAD  (A)   [ given] iii) AD = AD  (S)     [ common side] So,△ADB  ≅  .....

Here,  2 / √3  = 2/ √3  x  √3 / √3  = 2x √3  / [ √3 x√3 ] = 2√3 / 3.         Since, √3x .....

6.b) In triangle ABC,  B = C = 40o  [ As, AB = BC is given]  A + B + C = 180o  [ sum of angles of a triangle is 180o] or, A + 40 + 40 = 180 or, A = 180 - 80 = 100o Hence, <BAC .....

Here,  x2 = 81 or, x2 - 81 = 0 or, x2 - 92 = 0 or, [ x + 9] [ x - 9 ] = 0 Either, x + 9 = 0 ==> x = -9 Or, x -9 = 0 ==> x = 9 Hence values of x  are, - 9 and .....

Here,  x2 = 81 or, x2 - 81 = 0 or, x2 - 92 = 0 or, [ x + 9] [ x - 9 ] = 0 Either, x + 9 = 0 ==> x = -9 Or, x -9 = 0 ==> x = 9 Hence values of x  are, - 9 and .....

Here,  9x2 - 16y2 = ( 3x) 2- ( 4y) 2    We know, a2 - b 2 = (a + b) ( a-b ) So,  ( 3x) 2- ( 4y) 2           = ( 3x + 4y) ( 3x - 4y)  is required .....

Here,  Smallest data = S  = 2 Largest data = L = 80 We know,  Range  = L - S              = 80 - 2              = 78,   which is required .....

Here,  x  = 20o . [ Because,  vertically opposite angles are equal] Again, x + y = 180o  [ AB is a stright line and angle on st.line is 180o ] or, 20o+ y = 180o  or, y = 180 - 20 .....

Sound always needs some kind of medium such as air, water, or metal to travel through. In a vacuum, there is no air. Hence, sound does not propagate in a .....

During chemical reaction within the cell, hydrogen gas bubbles gather around the copper plate. These bubbles prevent the flow of current. Thus, the bulb does not glow for a longer time.   This effect is called polarization. Hence, .....

Here, we have, from formula, F- 32  = C    180       100      or, F-32 = 40  ⨉ 180                  100 or, F = 104 Therefore, 400C is .....