List of top Mathematics Questions on Equations

In the equation \(y_i = β_0+β_1.X_1+ε_1, \ β_0\) stands for

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): Equation 5x-7y+z=11, 6x-8y-z=15 and 3x+2y-6z=7, then the system is consistent and has infinitely many solutions.
Reasons (R): If D=0 then the 3 linear equations is consistent and has infinitely many solutions if D₁ = D₂ = D₃=0.
In the light of the above Statements, choose the correct answer from the options given below :

If α and β are the roots of a quadratic equation x²+αx + β=0 where β≠0, then what is the value of α + β?

The joint equation of the straight line x + y =1 and x-y = 4 is

Fresh grapes contain 80 per cent water while dry grapes contain 10 per cent water. If the weight of dry grapes is 250 kg what was its total weight when it was fresh ?

A mixture (40 litres) contains tonic and water in the ratio 3 : 1 to make the ratio 2 : 1, how much additional amount of water is required?

If m and n are natural numbers such that 2^m − 2ⁿ = 960 what is value of m

A's age is \(\frac{1}{6}\)^th of B's age. B's age will be twice of C's age after 10 years. If C's eighth birthday was celebrated two years ago, then the present age of A must be

Two passengers boarding a flight were found to have between them 34.5 kg of luggage. As per the excess luggage policy of the flight operator, the two passengers were made to pay Rs. 3.75 and Rs. 6.00 for the excess weight of their luggage. Later they found out that if the same luggage were to belong to just one person, then the excess luggage fee would have been Rs. 13.50. How much free luggage is allowed for each passenger?

If a and b are the roots of the equation x² - 6x + 6=0, then the value of a² + b² is

What is the value of \(\frac{P + Q}{P - Q}\) if \(\frac{P}{Q} = 7\) ?

What is the value of the following expression?
(1 + x) (1 + x²) (1 + x⁴) (1 + x⁸) (1 - x)

Which of the following equations has real roots?

What is missing figure in the expression given below ?
\(\frac{16}{7}×\frac{16}{7}-\frac{*}{7}×\frac{9}{7}+\frac{9}{7}×\frac{9}{7} = 1\)

If \(\frac{5a + 3b}{2a - 3b} = \frac{23}{5}\), then the value of a: b is

Father's age is 4 times that of his son. 5 years back, it was 7 times. His age now is

You have to find out what will come in place of the question mark
2154.832 ÷ 16.1514 = ?

You have to find out what will come in place of the question mark
0.7 x 0.5 = ?

You have to find out what will come in place of the question mark
\(\sqrt{486}\)++ 21% of 32 =?

You have to find out what will come in place of the question mark
42 + 73 + 137 = ?

You have to find out what will come in place of the question mark
20 x \(\frac{1}{2}\)