List of top Mathematics Questions on Algebra asked in NATA

If a²-b² = 8 and a*b = 2, find a⁴+b⁴.

Find the value of log_y(x⁴) if log_x(y³) = 2

How many terms are in the Arithmetic Progression 20, 25, 30,..., 135, 140?

A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole workalone?

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

Sarthak bought 7 new trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 31 cards left. How many cards did Sarthak start with ?

Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220. If the second term in it is 12, then its 4th term is :

The sum of odd integers from 1 to 2001 is:

The function given by: x^myⁿ = (x + y)^m+n is:

The average age of 20 students in a class is 15 years. If the teacher’s age is including, the average increases by 1. What is the teacher’s age?

Let the following system of equations kx + y + z =1x + ky + z = kx + y + kz=k2Has no solution. Find

The system of linear equations -2x+y+2=a, x-2y+z=b, x+y-2z=c have infinitely many solutions if

If \( a, b, c \) are non-zero, then the number of solutions of \[\frac{2x^2}{a^2} - \frac{y^2}{b^2} - \frac{z^2}{c^2} = 0,\]\[-\frac{x^2}{a^2} + \frac{2y^2}{b^2} - \frac{z^2}{c^2} = 0\]is: