CSAT

                            Exercise 1

1.   If P/Q = 7 ;    Then find the value of  (P^2 + Q^2) / (P^2 - Q^2)

2. IF a/b = 3 /5 , Then find the value of  (9a + 4 b) / ( 9a - 4 b)

3. Find the value of      [(0.5)^4 - (0.4)^4] / [(0.5)^2 + (0.4)^2]

4. The cost of 6 Hard disk is equal to 9 printers, the cost of 27 printers is equal to 30 scanners and the cost of 300 scanners is equal to 9 computers . If the cost of 3 computers is Rs. 24000 then find the cost of a hard disc .

5.There are 2 baskets  A & B containing balls . If 10 balls are transferred from A to B, then the number of balls in both the baskets become equal. If 20 balls had been transferred from B to A , then the number of balls in basket A would have been twice that of in B . Find the original number of balls in basket A .

6.A,B&C start a business in which A,s Investment is Rs. 20,000. If at the end of the year , in total profit of Rs. 2000 , A's share is Rs. 1000 and that of B's is Rs.600, Find the investment of C .

7. The cost of Nano car increases by 10% and that of Maruti car by 18% . The cost of an Nano car is thrice of Maruti car. Find the increase (in percentage) in  the cost of 10 Nano & 5 Maruti Car .

Graphs

HOW TO PLOT THE GRAPH OF CUBIC POLYNOMIALS?

LET  US  consider  a  general  3  degree  equation   F(x) -- ax³+bx²+cx+d , a >0

STEP -1) find f '(x) i.e.  3ax²+2bx+c,  if dicriminant of thif eqn. = D {=(2b)²-4(3a)(c) < o }, then only one real solution . and graph (of  F(x) ) is --- always inc.  from  -infinity to +infinit and cuitting x-axis at exactly one point .

STEP-2) if D =0 , then 3 real equal ruts . again cutting x-axis at only one point and graph ( of F(x) }  is from -infinity to +infinity. ( always increasing )

STEP-3) if D > 0 , then let two solutions of f ' (x)  be  a₁ &  a₂ .  SO, F(a₁)  will be minimum  and  F(a₂) will be maximum. and so, the graph of  f(x) will increase 4m  x= - infinity  to x= a₁ and decreases 4m x= a₁ to x-a_{2 .} again graph increases from x=a₂ to  =infinity

Logic

If in a coloney of sundervan there are 200 residents . The residents include only two types one who always tells the truth (99 % )in number & rest are those who always tells a lie.How many person who always tells the truth must leave the coloney so that the number of truth speaking reduces to (98%). 

L ogic

1) A Man was born in the first half of nineteenth century was x years old in the year x^2. He was born in

a) 1806         b) 1836            c) 1812               d) 1825

2)A three digit number has, from left to right , the digits h,t & u with h > u . When the number with the digits reversed is substracted from the original number , the unit's digit in the difference is 4. The next two digits , from the right to the left , are :
a) 5 & 9    b) 9 & 5    c) 5 & 4      d) 4 & 5

3) A merchant bought some goods at a discount of 20% of the list price . He wants to mark them at such a price that he can give a discount of 20% of the marked price and still make a profit of 20% of the  selling price. The percent of the list price of which he should mark them is :
a) 20       b) 100        c) 125          d) 80

4) A taxi travelling at a uniform speed . The driver sees a milestone showing a 2 - digit number. After travelling for an hour the driver sees another milestone with the same digits in the reverse order.After anothe hour the driver sees another milestone containing three digits and with the same two digits included .The average speed of the taxi is
a) 45km/hr   b) 36 km/hr  c) 54 km/hr   d) 42 km/hr

100

Start the sequence with non zero digits so that the result of desired arithmetic operation is zero.

12+3-4+5+67+8+9=100

123+4-5+67-89=100
other cases

1=148 / 296 + 35/70

100 = 33 X 3 +3/3


1+2+34-5+67+89-8+9=100

12+3-4+5+67+8+9=100

123-4-5-6-7+8-9=100

1+2.3-4+5+6.7+89=100
and many more

Paildrome Numbers / Calculations

Palindromes are very special kind of numbers.  A palindrome can be described as a number, word, sentence, etc. which reads same forward and backward. Specifically with regards to numbers, Palindromes are numbers which are symmetrical, i.e. they remain the same even when their digits are reversed. For example 14641 is a Palindrome. In fact all the single digit numbers and numbers with same digit repeated are palindromes. So all numbers like 1,2,3…8,9,11,22,99,111,etc. are palindromes.

Features of Palindrome Numbers

1)      Reverse a non-palindromic number and add it to the original number. We will get a palindromic number by repeating this process. We may even get a palindromic number in first go. For example, let the original number be 37 (non-palindromic). Add reverse of it 73 to 37, we get 110 (not a palindromic number). Therefore repeat the process. 110 + 011 = 121 (palindromic number). Another example, 16+61 = 77 (palindromic number).

Any number that never becomes palindromic in this way is known as Lychrel Number.

2)      A palindromic number in one base may or may not be palindromic in any other base.  For example, 1991 is palindromic in both decimal and hexadecimal (7C7)

3)      Certain powers of palindromes made up of digit 1,2 and at times 3 are mostly palindromes. For example,

11^2 = 121

22^2 = 484

101*101=10201
111*111=12321 121*121=14641
202*202=40804
212*212=44944

There are, however, an infinite number of cases as demonstrated here:

11^2 = 121, 101^2 = 10201, 1001^2 = 1002001, 10001^2 = 100020001, etc.

22^2 = 484, 202^2 = 40804, 2002^2 = 4008004, 20002^2 = 400080004, etc.

4)      All even digit palindromes are divisible by 11. There are many prime palindrome numbers also like 101, 131, 151, 181, and 191

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

Number Systen

                                   1
                           2       3     4
                    5     6      7      8      9
                ---------------------------
              ------------------------------
           ----------------------------------
       ---------------------------------------till the 10 th row.

Ques 1 . What is the sum of all the  numbers in the 10th row of the above pyramid.

Ques 2 .  What is the sum of all the  numbers on the side of the triangle formed by the 10th row  pyramid.

Ques 3. What is the sum of all the  numbers inside the triangle formed by the 10th row pyramid.


Ques 4. if      ( ab + cd ) ^ 2 =   abcd , where ab & cd are two digits number

a) How many values a can take if d = 1   ?

b) How many values b can take if c = 2  ?

c) How many values a can take if b = 1  ?

d) How many such numbers are possible ?