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:

A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was f 1,500 after 4 years of service and 1,800 after 10 years of service, what was his starting salary and what is the annual increment in rupees?

The value of k for which the points (k, 1), (5,5) and (10,7 ) may be collinear is:

A man went to the Reserve Bank of India with – 1,000. He asked the cashier to give him Rs.5 and 10 notes only in return. The man got 175 notes in all. Find how many notes of 5 and f 10 did he receive?

The length of the rectangle is 5 cm more than its breadth if the perimeter of the rectangle is 40 cm find the area of rectangle

A straight line of x = 15 is

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

If thrice of A’s age 6 years ago be subtracted from twice his present age, the result would be equal to his present ages. Find A’s present age.

 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.

The age of a man three times the sum of the ages of his two sons and 5 years hence his age will be double the sum of their ages. Find the present age of the man?

Examine the nature of the roots of the following equations x2 – 8x +16 = 0

Find the roots of the quadratic equation: x2 + 2x – 15 = 0?

The sum of the squares of two consecutive positive integers exceeds their product by 91. Find the integers?

A number is equal to 4 times this number less 75. What is the number?

If √𝟑 − 𝟐𝒙 + √𝟕 + 𝟐𝒙 = 4, then find the positive value of x?

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

A simple equation in one unknown x is in form ax + b = 0. Is true or not?

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

Solve the equation: x3 +10 = 2x x3+10 = 2x.

2(3x – 7) + 4(3x+2) = 6(5x+9)

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