## Filters

Sort by :
Clear All
Q

Q : 5     A small terrace at a football ground comprises of   steps each of which is m long and   built  of solid concrete. Each step has a rise of      and a tread of    . (see Fig. ).  Calculate the total volume of concrete required to build the terrace.
[Hint : Volume of concrete required to build the first step    ] It is given that  football ground comprises of   steps each of which is m long and Each step has a rise of      and a tread of    Now, Volume required to make first step =  Similarly, Volume required to make 2nd step =  And Volume required to make 3rd step =  And so on We can clearly see that this is an AP with  Now,  total volume of concrete required to build the terrace of 15 such...

Q : 4    The houses of a row are numbered consecutively from to . Show that there is a value of   such that the sum of the numbers of the houses preceding the house numbered is equal to the  sum of the numbers of the houses following it. Find this value of .                                                              [Hint :

It is given that the sum of the numbers of the houses preceding the house numbered is equal to the  sum of the numbers of the houses following it And 1,2,3,.....,49 form an AP with a = 1 and d = 1 Now, we know that Suppose their exist an n term such that ( n < 49) Now, according to given conditions  Sum of first n - 1 terms of AP = Sum of terms following the nth term Sum of first n - 1...

Q : 3    A ladder has rungs cm apart. (see Fig. ). The rungs decrease uniformly in length from  cm at the bottom to cm at the top. If the top and the bottom rungs are    m apart, what is  the length of the wood required for the rungs?

[Hint : Number of rungs It is given that Total distance between top and bottom rung  Distance between any two rungs = 25 cm Total number of rungs =   And it is also given that bottom-most rungs is of 45 cm length and topmost is of 25 cm length.As it is given that the length of rungs decrease uniformly, it will form an AP with  Now, we know that  Now, total  length of the wood required for the rungs is equal...

Q : 2    The sum of the third and the seventh terms of an AP is and their product is . Find the sum of first sixteen terms of the AP.

It is given that  sum of the third and the seventh terms of an AP is and their product is Now, And  put value from equation (i) in (ii) we will get  Now, case (i)    Then, case (ii)   Then,

Q : 1     Which term of the AP :   is its first negative term?  [Hint : Find for  ]

Given AP is  Here  Let suppose nth term of the AP is first negative term  Then, If nth term is negative then  Therefore, first negative term must be 32nd term
Exams
Articles
Questions