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Syllabus

A manufacturer has 600 L of a 12% solution of acid. How many litres of a 30% acid solution must be added to it so that the acid content in the resulting mixture will be more than 15% but less than 18%?

➩ mod (x) - 1 ÷ mod (x) - 2 is greater than or equal to 0.

{Please explain the whole sum in detail}

Sir, these types of sums are not in our ncert booklet. But I found the same in RD sharma. So, tell me that whether it is right to concentrate in this type of sums or not.

a polygon has 44 diagonals.find the no. of its sides.

an object dropped from cliff falls with a constant acceleration of 10m/s2 find its speed after 2s after it was dropprd

1. First quadrant

2.That half of xy plane which lies above the line 2x+y+6=0

➩ mod(x - 2) is greater then or equal to 5.

How to do the last step, please explain sir.

if

^{22}P_{r}+1^{:20p}_{r}+2 = 11:52 find rQ. Solve graphically:- 3y-2x<4, x+3y>3, x+y<equals 5.

a scooter covers 20km/h at a uniform speed of 30km/h what should be its speed for the next 40 km if the average speed is 60km/h

if log

_{0.3}(x-1) < log_{0.09}(x-1), then x lies in the interval....Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23.

Illustration: The quadratic polynomial p(x) has the following properties :

p(x) can be positive or zero for all real numbers

p(1) = 0 and p(2) = 2

Then find the quadratic polynomial.

Sol: p(x) is positive or zero for all real numbers.

Also p(1) = 0

Then we have p(x) = k(x-1)

^{2}, where k > 0Now p(2) = 2

$\Rightarrow $ k=2

∴ p(x) = 2(x-1)

^{2}if

^{n-1}c_{r}:^{n}c_{r}:^{n+1}c_{r}=6:9:13 find n and rshow graphically that the solution set of the following system of inequalities is empty

x-2y greater than = 0, 2x-y less than = -2 ,x greater than = 0, y greater than = 0

an object moves along a straight line with an acceleration of 2m/s2 if its initial speed is 10m/s what will be its speed 5s later

if the products of the roots of the equation x

^{2}-3kx+2e^{2logk}-1=0 is 7, then the roots are real for k=..........if all permutations of the letters of the word INDIA are arranged as in a dictionary what is the 60

^{th}word?how to solve modulus (2x - 1/x - 1)>2?

A plumber can be paid under 2 schemes as given below:-

I : $600 and $ 50 per hour.

II: $ 170 per hour .

If the job takes n hours, what values of n does Scheme I give the plumber better wages?

a) half of XOY plane which lies below x-axis

b) half of XOY-plane which lies above Xaxis

c) half of XOY - plane whichlies below x axis including the points on the x axis

d) none of theese.

correct answer is a)

but i am confused that why we can't take c) ??????????

While drilling a hole in the earth, it was found that the temperature (TC) at x km below the surface of the earth was given by

T = 30 + 25(x - 3), when 3 ≤ x ≤ 15.

Between which depths will the temperature be between 200C and 300C?

2x + 19<_ 6x+47 and represent the solution in number line.

a milk of 80% conc. is diluted at home by the seller by adding some water to it so that milk conc. is reduced btw 65% to 70% . if 640 l of milk of 80% conc. is available how much water has been added??

|x-1|+|x-2|+|x-3|>=6

marks obtained by her in the second and third

examinations are more than 5 and 10 respectively

than in the first examination. If her average mark

is at least 80 find the minimum mark that she

should get in the first examination?

1) to realize a profit

2) to realize a profit of more than Rs. 100000

3) to realize a profit of more than Rs. 150000

The longest side of a triangle is 3 times the shortest side and the third side

A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second?

[Hint: If

xis the length of the shortest board, thenx, (x+ 3) and 2xare the lengths of the second and third piece, respectively. Thus,x= (x+ 3) + 2x≤ 91 and 2x≥ (x+ 3) + 5]_{a}x,log_{b}x log_{c}x are in A.P. where x not equal to 1, show that c^{2}= (ac)^{log}_{a}^{b }How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

Draw the graph of the following system of inequalities and mark the solution.

2x + y – 3 ≥ 0

x - 2y ≤ 0

y ≤ 3

in the first four paper each of 100 marks, rishi got 95,72,73,83 marks. if he wants an average of greater than or equal to75 marks and less than 80 marks , find the range of marks he should score in the fifth paper.

sir i dont understand this line ......

however when both inequalities are multiplied opr divided by a negative number then the sign of the inequality is reserved .. ????

in how many ways can the letters of the word FRACTION be arranged so that no two vowels are together.

IQ of a person is given by the formula

IQ = (MA/CA)*100,

where MA is the mental age & CA is the chronological age. If 80≤IQ≤140 for a group of 12 yr children, find the range of their mental age.

What is the sign scheme method.Can you explain it briefly?

what is wavy curve method?

A company manufactures cassettes. Its cost and revenue functions are C(x)=26000+30xand R(x)=43x, respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realise some profit?

1) find all pairs of consecutive odd positive integers,both of which are smaller than 18,such that their sum is more than 20.

in this why you took x+ 2 not only x please tell me

exactly do we use open and closed brackets...??

PLEASE SHOW ME THE FOLLOWING GRAPHS WITH THE SHADED PORTION :1) x=0 [ x is greater than or equal to zero ]

2) y=0 [ y is greater than or equal to zero ]

3) x=0 , y=0 [x is greater than or equal to zero , y is greater than or equal to zero]

The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.

if t and k are (+)ve integers above and tk, find the value of t

(SAT ques; expert help required)

solve the system of inequalities x+2y>= 20 and 3x+y<=15

A point moves such that the sum of its distances from the point (ae,0) and (-ae,0) is 2a. Show that the locus of this point is x

^{2}/a^{2}+ y^{2}/a^{2}(1-e^{2}) = 1find the real values of the parameter a such that (2a +1)x

^{2 }- a(x-1) =2 has one root greater than 1 while the other less than 1 ?^{2}Solve:

2x/ 2x

^{2}+5x+2 > 1/x+1A company manufactures cassettes and its cost equation for a week is ( C = 300 + 1.5 x ), while its revenue equation is (R= 2x ) , where x is the number of cassettes sold. How many cassettes must be sold by the company to get some profit?

Write the number of integral solutions of x+2/x

^{2}+1 1/2.solve the polynomial inequality

(1) x

^{4 }- 5x^{2 }+ 4 < 0(2) x

^{4}- 2x^{2 }- 63 < or = 0A milk of 80% concentration is diluted at home by the seller by adding some water to it so that milk concentration is reduced between 65% to 70%. If 640 litres of milk of 80% concentration is available, how much water has been added? Which value system the seller is lacking.

Fill in the blanks with correct inequality signs...

1. a less than b and c less than 0

so a divided by b ......?...... b divided by c.

How will i come to know that which sign i have to write down?

IF 1/8! + 1/9! = x/10! . Then find the value of x .

15x less than 73, where (i)x belongs to N and (ii) Z.

solve the inequation and represent the solution set on the number line.

Hi

Solve the equation for x and y: (x - iy) (2 + 3i) = x+2i / 1-i

Solve the following inequations in R.

1. 1/x-1≤2

2. 5x+8/4-x<2

3. x/x-5>1/2

4. 0<-x/2<3

5. |3x-4/2|≤5/12

6. |x-2|/x-2>0

7. |x+2|-x/x<2

8. |2x-1/x-1|>2

9. |x-1|+|x-2|+|x-3|≥6

10. The marks scored by rohit in two tests were 65 and 70. Find the minimum marks he should score in third test to have an average of at least 65 marks.

11. The longest side of a triangle is three times the shortest side and the third side is 2 cm shorter than the longest side if the perimeter of the triangle at least 61cm, find the minimum length of the shortest-side.

12. How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

13. A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If there are 640 litres of the 8% solution, how many litres of 2% solution will have to be added?

14. The water acidity in a pool is considered normal when he average pH reading of three daily measurements is between 7.2 and 7.8. If the first two pH reading are 7.48 and 7.85, find the range of pH value for the third reading that will result in the acidity level being normal.

15. Show that the solution set of the following linear inequations is empty set:

15.1) x-2y ≥0, 2x-y ≤-2,x ≥0, y ≥0

15.2) x+2y≤3, 3x+4y ≥12, y ≥1, x ≥0, y ≥0

x/2 less than or equal to (5x-2)/3 - (7x-3)/5.

If a+b=1, then prove that, (a+1/a)

^{2}+(b+1/b)^{2}>25/2 [ where a is not equal to b]Solve the following system of inequalities graphically

2x +y ≤ 24 ,

x +y ≤ 11 ,

2x + 5y ≤ 40 ,

x ≥0 , y ≥ 0

2x -3 / 3x -7 0. solve this inequality..!!

How can we understand which region we have to shade? answer meas soon as possible.