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

The equation of a line which is perpendicular to 5x – 2y = 7 and passes through the mid – point of line joining (2, 7) and (-4, 1) is:

Find the positive value of k for which the equations: x2 + kx +64 = 0 and x2–8x + k

= 0 will have real roots:

The point of intersection of the lines 2x – 5y = 6 and x + y = 3

Find the equation of the line passing through the point (1, 1) and parallel to the line 3x +5y+17=0

If one root of the equation x2-3x+k=0 is 2, then value of k will be:

If |𝒙 − 𝟐|+|𝒙 − 𝟑| = 7 then, ‘x’ will be equal to

 For a certain commodity the demand ‘d’ in kg, for a price ‘p’ in rupees per kg, is d

= 100(10 – p ). The supply equation giving the supply s in kg. for a price p in rupees per kg . is s 75(p - 3). The market price is such at which demand equals supply. Find the market price and quantity that will be bought and sold.

Solve 2x +5 y = 9 and 3x – y = 5.

I . a2 + 11a +30 = 0

II.b2+6b +5 = 0 to solve both the equations to find the values of a and b?

A number is equal to 7 times itself minus 18. Which is the number?

If a and b are the roots of the equations x2 – 9x +20 = 0, find the value of a2 + b2 + ab

If a + b = 29, b +c = 45, a +c = 44. Find a+ b + c?

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) =

If the equation x2 + px + q = 0 and x2 + qx + p = 0, have a common root, then p + q+1

If x2 + αx + 10 = 0 and x2 + bx -10 = 0 have a common root, then, a2 – b2 is equal to

x2 – 11x + a and x2 – 14x + 2a will have a common factor, if a = 42

2(3x – 7) + 4(3x+2) = 6(5x+9)

Find the solution x to the equations x3-x4=2×3-x4=2.                                 

A number, multiplied by 5, equals itself minus 48. Which is the number

An examination paper consists of 12 questions divided into parts A and B Part A contains 7 questions and part B contains 5 questions. A candidate is required to attempt 8 questions selecting at least 3 from each part. In how many maximum ways can the candidate select the question? 

Find 5!, 4! And 6!

Find 𝟗! ÷ 𝟔! ; 𝟏𝟎! ÷ 𝟕!

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

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

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? 

A student has three books on computer, three books on Economics and five books on Commerce. If these books are to be arranged subject wise, then these can be placed on a shelf in the number of ways: 

How many number of seven digit numbers which can be formed for the digits 3,4,5,6,7,8,9 no digits being repeated are not divisible by 5?