CBSE math

CBSE maths CBSE Sample Guess Question Papers CBSE hindi social science results X X11 syllabus



Question.106. A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contain 880/21 m3 of air.if the internal diameter of the building is equal to its total height above the floor,find the height of the building. by Osman Farooqui, answered on Dec 15, 2007 at 6:49 p.m.
Answer 106. Download answer
Question.107. A tree in each year grows 4cm less than it grew in previous year. If it grew 1 metre in the first year, in how many years will it have ceased growing and what will be its height then, by Navroop Dhillon. Answered on Dec 17, 2007 at 8:27 p.m.
Answer 107. First term              = a = 100 c.m.
                   Common Difference = d = - 4 
                   Tn = 0
            or     a + (n - 1)d = 0
            or    100 + (n - 1)(- 4) = 0
            or      25 + (n - 1)(- 1)  = 0 
            or      25 - n + 1 = 0
            or      - n   =  - 26
            or         n  =   26
            Therefore it will stop growing in 26 years
            Total height = n/2 [a + l]  
                             =  13 [100 + 0]
                             =  1300 c.m. 
Question.108.  In acute triangle PQR, PS perpendicular QR Prove that PR*PR=PQ*PQ + QR*QR - 2QR*QS, by Aashish, answered on Dec 21, 2007 at 7:21 pm IST
Answer 108.  In acute triangle PQR PS perpendicular QR. We get 2 right triangles QSP and RSP. Using Pythagoras theorem in both
                    PR^2 = PS^2 + SR^2  ......... (i)
                    PQ^2 =
PS^2 + SQ^2  ......... (ii)  
                    (ii) - (i)
                  
PR^2 - PQ^2 = SR^2 - SQ^2
                  
PR^2 - PQ^2 = (QR - SQ)^2 - SQ^2
                  
PR^2 - PQ^2 = QR^2 + SQ^2 - 2QR*SQ - SQ^2  [Since SR = QR - QS]
                  
PR^2 - PQ^2 = QR^2 - 2QR*SQ
                   PR^2 = PQ^2 + QR^2 - 2QR*SQ
Question.109. Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre of a circle by Akash Ayalani. Answered on Dec 23, 2007 at 5:38 p.m. I.S.T.                
Answer 109. Download answer
Question.110. A cylinder, cone, and hemisphere have same base and same height. find the ratio in their volumes? by siddharth
Ch
oudhary. Answered on Dec 24, 2007 at 1 : 40 p.m.
Answer 110. The three are on same base so they have equal radii. Let each be x. They have equal height and height of hemisphere = radius. So height of each = radius = x. Required ratio = pie r^2 h : 1/3 pie r^2 h : 2/3 pie r^3
                                                                          = 
r^2 h : 1/3 r^2 h : 2/3 r^3
                                                                          =  x^3 : 1/3 x^3 : 2/3 x^3
                                                                          = 1 : 1/3 : 2/3
                                                                          = 3 : 1 : 2

Question 111. Sir,usually i used to finish the exam in time,but this preboard i was not able to do so. So which section is to be answered first? Will just answers be sufficient for 1mark questions? by Sowmya. Answered on Dec 25, 2007 at 8:10 p.m.
Answer 111. (a) In our opinion you should begin with question no. 1 and try to do the questions in order if possible.    
(b) 1 mark questions have to be answered in word, one sentence or as requirement of the question. For example if you consider the 5th question of 1st Model sample paper issued by CBSE in my opinion showing calculation is must. These papers can be downloaded from here
Question 112. A river 3m deep and 10 m wide is flowing at the rate of 2km per hour.how much water will fall into the sea in a minute? by Shalu. Answered on Dec 27, 2007 at 12:54 p.m. I.S.T.
Answer 112. Distance travelled by water in 1 hour = 2 km
                                                                       = 2000 m
                    
Distance travelled by water in 1 min. = 2000/60
                                                                      = 100/3 m.
                     The river mentioned has shape of a cuboid when filled with water.
                     Volume of water falling in the sea in one minute = 100/3 
×  10  ×  3
                                                                                     = 1000 cu. m
                                                                                     = 1000 kl.
      
Question 113.A container shaped like a right circular cylinder having diameter 12cm and height 15cm is full of ice-cream.The ice-cream is to be filled into cones of height 12cm and diameter 6cm having a hemispherical shape on the top.Find the number of such cones which can be filled with ice-cream, by Saumya Jain. Answered on Jan 03, 2007 at 10:26 p.m.
Answer 113. Volume of cylinder = pie r^2 h
                                              = pie
× 6 × 6×15
                                              = 540 pie cu. cm.
                     Volume of one ice cream cone including top = 1/3 pie r^2 h + 2/3 pie r^3

                                                                               = 1/3 pie r^2 (h + 2r)
                                                                               = 1/3 pie
×3×3 (12 + 6)
                                                                               = 3 pie
× 18
                                                                               = 54 pie cu. cm
                     No. of cones = Volume of cylinder/ volume of one cone including top = 540 pie/ 54 pie
                                                                                                                 = 10
Question 114. A coin is tossed once.  Find probability of  getting  2 heads?  Jessika . Answered  on  Jan 4, 2008 at 10:18 pm IST
Answer 114.  When a coin is tossed we may get either a head or a tail.
                       Therefore total outcomes = 2
                        Favorable outcomes  = 0 (since we can have 1 head or 1 tail and never 2 heads in this case)
                        required  probability  =  0/2 
                                                    =  0
Question 115.  Determine whether the given quadratic equation has roots. If so find the roots of p(x) = 1/x+1 + 2/x+2 = 4/x+4   ( x is not equal to -1, -2, -4)  by  Himanshu Zharbade. Answered on Jan 5, 2007 at 9:05 p.m. I.S.T.
Answer 115. Download Now


    
Question 116. the sum of p terms of an AP is q and sum of q terms is p.then prove that the sum of (p+q)terms is -(p+q) by ashwin kurian philip. Answered on Jan 6, 2007 at 6:24 p.m. I.S.T.     
Answer 116. Let first term = a
                     Common difference = d
                     Sp = q
                     p/2 [2a + (p-1)d] = q
                     
   p [2a + (p-1)d] = 2q
                           2ap + pd(p-1)  = 2q  ...........(i)
                    
Sq = p
                     q/2 [2a + (q-1)d] = p
                     
q   [2a + (q-1)d] = 2p
                           2aq + qd(q-1)  = 2p  ...........(ii)
                          (i) - (ii)
                      2ap - 2aq + pd(p-1) -
qd(q-1) = 2q - 2p
                      2a(p - q) + d( p^2 - p - q^2 + q) = 2 (q - p)
                     
2a(p - q)  + d(p^2 - q^2 + q - p) = 2 (q - p)
                     
2a(p - q)  + d[(p-q) (p+q) + (q - p)] = 2 (q - p)
                      2a(p - q)  + d (p-q) [(p+q) - 1] = 2 (q - p)
                      2a + d [(p+q) - 1] = - 2        (dividing both sides by p-q)
                      2a + d (p+q - 1) = - 2  ...........(iii)
                      S(p+q) = (p+q)/2 [2a + (p+q-1)d]
                               
= (p+q)/2 (-2 )
                                =  - (p+q) 
Question 117. If cos A= 2 sin A, then what will be the value of cosec A? by Shubham Jindal. Answered on Jan 08, 2007 at 9:44 p.m.
Answer 117.   cos A= 2 sin A
                   or  cosA/sinA = 2
                   or  cot A = 2
                   or  cot^2 A = 4
                   or cosec^2 A - 1 = 4    [ since 1 + cot^2 A = cosec^2 A]
                   or cosec^2 A = 5
                   or cosec A = +- squareroot 5
Question 118. Please let me have some sample papers (chapter wise) for History & Civics for class X.  The cbsemath.com has only chapterwise for Geo, Eco and disaster Management by Noufel Arif. Answered on Jan 09, 2007 at 8:20 p.m. I.S.T.  
Answer 118. Sample papers of History, Civics and remaining chapters of geography will be added soon. We hope to add them in this month itself.
Question 119. Find the sum of first 40 integers divisible by 6, by Saiyam. Answered on Jan 12, 2007 at 6:17 p.m.
Answer 119. First integers divisible by six are 6, 12, 18, 24,...    
                     Here a = 6 and d = 12 - 6 = 6
                     S40 = 40/2 [ 2
×6 + 39×6] 
                           = 20[6(2+39)]
                           = 20[6
×41]    
                           = 20
×246
                           = 4920
Question 120. There are two tangents to a cirle from same point. the distance between the point and centre is equal to the diameter of the circle. Then prove that the triange formed when a chord is made from the point of contact of tangent is equilateral by Himanshu Zharbade. Answered on Jan 13, 2007 at 7:26 p.m.
Answer 120. Download Now

For QuesAns 121 onwards click here
{ParagraphsSidebar}