On solving the inequalities 6x + y >18, x+4y>12, 2x+y<10  we get the following situation:

Solve x +2 < 4

If one root of a equation is 2+√𝟓 , then the quadratic equation is :

Ratio between 150 gm and 2 kg

a: b = c: d, then b: a = d: c

Find the value of x if 10/3: x = 5/2: 5/4

Find the third proportion to 2.4 kg, 9.6 kg.

On the average, experienced person does 5 units of work while fresh one 3 units work daily but the employer have to maintain the output to at least 30 units work per day. The situation can be expressed as

Find the value of k form (√𝟗)-7 x (√𝟑)-5 3k

Solve the absolute value inequality 2|𝟑𝒙 + 𝟗|<36

A sum of money is to be distributed among A, B, C and D in the proportion of
5: 2: 4: 3. If c gets Rs. 1000 more than D, what is B’s share?

Which of the following is correct?

I.    If b2-4ac = 0 the roots are real and equal;

II.  If b2-4ac > 0 then the roots are imaginary;

III.  If b2-4ac <0 then the roots are equal;

IV.  If b2-4ac is a perfect square (0) the roots are real, rational and unequal

V.   If b2-4ac>0 but not a perfect square the roots are real, irrational and unequal.

If both the roots of k (6x3 + 3) + rx + 2x2 – 1 = 0 and 6k (2x2 + 1) + px + 4x2 – 2 = 0 are common,then 2r – p is equal to

If a root of the equations x2 + px + q = 0 and x2 + αx +β = 0 is common then its

value will be (where p ≠ α and q ≠ β) Condition for common roots is 𝟏𝟐𝒌+𝟒/𝟔𝒌+𝟐   = 𝒑/ 𝒆

If the two equations x2 – cx +d = 0 and x2 –ax +b = 0 have one common root and the second has equal roots then 2 (b +d) =

How many three letters words can be formed using the letters of the word SQUARE?

A sum of money doubles itself in 10 years. The number of years it would triple itself is:

A company establishes a sinking fund to provide for the payment of 2, 00,000 debt maturing in 20 years. Contribution to the fund is to be made at the end of every year. Find the amount of each annual deposit if interest is 5% per annum.

In how many different ways can five persons stand a line for a group photograph?

A machine worth 4, 90,740 is depreciated at 15% on its opening value each year. When its value would reduce to 2, 00,000:

How many three letters words can be formed using the letters the word HEXAGON? 

A sum amount to 1,331 at a principal of 1,000 at 10% compounded annually; Find the time.

An examination paper with 10 questions consists of 6 questions in mathematics and 4 questions in statistic part. At least one question from each part is to be attempted in how many ways can this be done? 

The sum of the infinite G.P series 1 -𝟏/3+ 𝟏/9– 𝟏/27 …..

Find the 10th term of the A.P.: 2, 4, 6, ….

The 10th term of an A.P. is -15 and 31st term is -57, find the 15th term

Which term of the A.P.: 5, 11, 17 … is 119?

Is 600 a term of the A. P.: 2, 9, 16, ….?

The common difference of an A.P. is 3 and the 15th term is 37. Find the first term.

Geometric mean G between two numbers a and b id