Algebra test - STD VIII and STD IX

miscellaneous equations,

Solve for x:

3x² - 4√(3x² – 4x + 1) = 4x – 4 

irrational numbers

Evaluate:

√[6 + √{6 + √(6 +.........)}

IIT 73 

miscellaneous equations

solve for x:

√x + √{x - √(1 – x)} = 1

miscellaneous equations

Find the real values of x, y and z for the equations
x + y = 2
xy - z²  = 1

IIT 72

miscellaneous equations

Solve for x, y and z

xy + x + y = 23
xz + z + x = 41
yz + y + z = 27

IIT 

miscellaneous equations

Solve for x, y and z

x + y - 4xy = 0
y + z - 6yz = 0
z + x - 8zx = 0

IIT 73

Questions on Brackets for STD V

Questions on Brackets for STD V

JMO, indices, number

In the sum 23¹⁵ + 19¹⁷ + 27³⁵, find the digit in the unit place.

JMO STD V and STD VI

numbers -- JMO std. V and VI

 Find the total number of digits in the number
123456789101112..........20102011

JMO STD V and STD VI

series summation - JMO

Pages of a book are numbered from one onwards. A boy has torn one page of the book. If sum of page numbers of remaining pages of the book is 1620.
Then (1) find page number of torn page and
(2) How many pages the book had ?

JMO ---- STD V and VI

distance and time --- JMO V and VI

If I travel at 30 km/hr I reach  my destination at 10 O clock.
If I travel a 20 km/hr I reach my destination at 4 O' Clock.
How far is the destination from my house

JMO STD V VI

JMO VII and VIII -- series problems

If 

3! = 3 x 2 x 1;

4! = 4 x 3 x 2 x 1,

5! = 5 x 4 x 3 x 2 x 1

Then, find the value of 

1.1 ! + 2.2! + 3.3! + 4.4! + …… + 99.99!               

 JMO VII and VIII

JMO -- DIvisibility

Which are the two numbers less than 260 that exactly divides

 2³² – 1?

JMO – VII and VIII

series problems for STD V and STD VI

Questions on the application of the formulae:

For S = 1 + 2 + 3 + .....n terms = i.e. sum of natural numbers from 1 to n.
S = n (n+1)/2

1. S = ( 1 + 3 + 5 + ... 25 terms) + ( 2 + 4 + 6 ..... 25 terms)
2. S = (3 + 6 + 9 ...... 25 terms)
3. S = ( 2 + 4 + 6 + ...... 25 terms)
4. S = (1 - 1/5) + (1 - 2/5) + (1 - 3/5) + (1 - 4/5) + ..... 25 terms
5. S = (1 - 1/n) + (1 - 2/n) + (1 - 3/n) +........ n terms
6. S = (2a - 3b) + (4a - 6b) + (6a - 9b) +.......... 25 terms, given a = 5 and b = 2

simple equations --- STD V

algebraic expressions -- STD V

writing algebraic expressions --- STD V

compound interest

The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is --------------------

compound interest

The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is...................................