Integrating (1/(1-cosx)) -(1/(1+cosx)) w.r.t x.

 

The altitude of a right triangle is 7 cm less than its base. If the Hypotenuse is 13 cm, find the other two sides. [ncert 10th]

Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan's present age. [ncert 10th]

 

Find the two Numbers, whose sum is 27 and product is 182. [ncert 10th]

Find two consecutive positive integers, sum of whose squares is 365. [ncert 10th.]

Let the two consecutive positive integers

are  x and x+1.

Given that x²+(x+1)² = 365

Using (a+b)=a²+b²+2ab, we get,

=> x²+x²+1+2x=365.  

 => 2x²+2x+1-365=0

=> 2x²+2x-364=0

Dividing both sides by 2 (non zero), we get,

=> x²+x-182=0

=> x²+14x-13x-182=0

=> (x²+14x)-(13x+182)=0

=> x(x+14)-13(x+14)=0

=> (x+14)(x-13)=0

=> Either x+14=0 or x-13=0

=> Either x= -14 , 13

But we have to find positive integer, so -14 must be rejected.

So x= 13 is the required positive integer.

Now two consecutive positive integers shall be x, x+1 

=> 13 and 13+1=14

So 13 and. 14 are the required positive consecutive integers. Ans.

If A=[(1,3),(3,4)], B=[(-2,1),(-3,2)] and A²-5B²=5C. Find matrix C where C is a 2 by 2 matrix. [icse2017].

What must be subtracted from 16x ^ 3 - 8x ^ 2 + 4x + 7 that the resulting expression has (2x + 1) as a factor? [icse2017]

If (x+2) and (x+3) are factors of x^3+ax+b, find the values of 'a' and 'b'. [icse 2018]

 

If A=[(3,x),(0,1)] and B=[(9,16), (0,-y)], find x and y, when A²=B. [icse 2015]

 

Solve the following inequation and write down the solution set. 11x-4 < 15x+4 <= 13x+14 ; xεW. Represent the solution on a number line. [icse 2019]

 Here solution set will contain only Whole   numbers.

Solve the following inequation and represent the solution set on a number line.(-8*1/2)< -1/2 -4x<=7*1/2 ; x€I [icse 2017]

 

Use the remainder theorem to factorise the following expression: 2x^3+x^2-13x+6. [icse 2010]

 

Rules for solving Inequations

Find the value of x, which satisfy the inequation - 2*5/6 less than1/2 -2x/3 less than aur equal to 2 and x€W and represent the solution on the numbe line.[icse 10th 2014]

Solve the following inequation, write the solution set and represent on the number line. x+1 -3(x - 7) ≥ 15 - 7x > X€R [icse 2016]