problem archive
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The product of two consecutive positive integers is 306. We need to find the integers. -
Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present ag... -
A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same di... -
Find the roots of the equation 2x^2 - 5x + 3 = 0, by factorisation. -
Find the roots of the quadratic equation $6x^2 - x - 2 = 0$ -
Find the roots of the quadratic equation $3x^2 - 2\sqrt{6}x + 2 = 0$ -
Find the roots of the following quadratic equations by factorisation: (i) x^2 - 3x - 10 = 0 (ii) 2x^2 + x - 6 = 0 (iii) sqrt(2)x^2 + 7 + 5sqrt(2) = 0 ... -
Find the discriminant of the quadratic equation \(2x^2 - 4x + 3 = 0\), and hence find the nature of its roots. -
A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from ... -
Find the discriminant of the equation \(3x^2 - 2x + \frac{1}{3} = 0\) and hence find the nature of its roots. Find them, if they are real. -
Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: (i) $2x^2 - 3x + 5 = 0$ (ii) $3x^2 - 4\sqrt{3}x... -
Find the values of $k$ for each of the following quadratic equations, so that they have two equal roots. (i) $2x^2 + kx + 3 = 0$ (ii) $kx(x - 2) + 6 =... -
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is $800 m^2$? If so, find its length and breadth. -
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product ... -
Is it possible to design a rectangular park of perimeter $80 m$ and area $400 m^2$? If so, find its length and breadth. -
Reena applied for a job and got selected. She has been offered a job with a starting monthly salary of ₹ 8000, with an annual increment of ₹ 500 in he... -
The lengths of the rungs of a ladder decrease uniformly by 2 cm from bottom to top (see Fig. 5.1). The bottom rung is 45 cm in length. The lengths (in... -
In a savings scheme, the amount becomes \(\frac{5}{4}\) times of itself after every 3 years. The maturity amount (in ₹) of an investment of ₹ 8000 aft... -
The number of unit squares in squares with side 1, 2, 3, ... units (see Fig. 5.2) are, respectively 1^2, 2^2, 3^2, ... -
Shakila puts ₹100 into her daughter’s money box when she was one year old and increased the amount by ₹50 every year. The amounts of money (in ₹) in t...