Most Important XAT Algebra Questions PDF, Download Now

Find z, if it is known that:
a: $$-y^2 + x^2 = 20$$
b: $$y^3 - 2x^2 - 4z \geq -12$$ and
c: x, y and z are all positive integers

Consider the real-valued function $$f(x)=\frac{\log{(3x-7)}}{\sqrt{2x^{2}-7x+6}}$$ Find the domain of f(x).

A chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of same size. The number of boxes to be sent is 96 of brand A, 240 of brand B and 336 of brand C. These boxes are to be packed in cartons of same size containing equal number of boxes. Each carton should contain boxes of same brand of chocolates. What could be the minimum number of cartons that the dealer has to send?

The Guava club has won 40% of their football matches in the Apple Cup that they have played so far. If they play another n matches and win all of them, their winning percentage will improve to 50. Further, if they play 15 more matches and win all of them, their winning percentage will improve from 50 to 60. How many matches has the Guava club played in the Apple Cup so far? In the Apple Cup matches, there are only two possible outcomes, win or loss; draw is not possible.

A polynomial y=$$ax^{3} + bx^{2 }+ cx + d$$ intersects x-axis at 1 and -1, and y-axis at 2. The value of b is:

Consider the system of two linear equations as follows: $$3x + 21y + p = 0$$; and $$qx + ry - 7 = 0$$, where p, q, and r are real numbers.
Which of the following statements DEFINITELY CONTRADICTS the fact that the lines represented by the two equations are coinciding?

p, q and r are three non-negative integers such that p + q + r = 10. The maximum value of pq + qr + pr + pqr is

For a positive integer x, define f(x) such that f(x + a) = f(a × x), where a is an integer and f(1) = 4. If the value of f(1003) = k, then the value of ‘k’ will be:

Consider the expression $$\frac{(a^2+a+1)(b^2+b+1)(c^2+c+1)(d^2+d+1)(e^2+e+1)}{abcde}$$, where a,b,c,d and e are positive numbers. The minimum value of the expression is

Let x and y be two positive integers and p be a prime number. If x (x - p) - y (y + p) = 7p, what will be the minimum value of x - y?

The sum of the possible values of X in the equation |X + 7| + |X - 8| = 16 is:

Let $$f(x) = \frac{x^2 + 1}{x^2 - 1}$$ if $$x \neq 1, -1,$$ and 1 if x = 1, -1. Let $$g(x) = \frac{x + 1}{x - 1}$$ if $$x \neq 1,$$ and 3 if x = 1.
What is the minimum possible values of $$\frac{f(x)}{g(x)}$$ ?

If $$x^2 + x + 1 = 0$$, then $$x^{2018} + x^{2019}$$ equals which of the following:

If f(x) = ax + b, a and b are positive real numbers and if f(f(x)) = 9x + 8, then the value of a + b is:

The mean of six positive integers is 15. The median is 18, and the only mode of the integers is less than 18. The maximum possible value of the largest of the six integers is

The number of point(s) satisfying the above mentioned characteristics and not in the first quadrant is/are

Given $$A = |x + 3| + | x - 2 | - | 2x -8|$$. The maximum value of $$|A|$$ is:

The operation ( x ) is defined by
(i) (1) = 2
(ii)(x  + y) = (x).(y)

for all positive integers x and y.
If $$\sum_{x=1}^n(x)$$ = 1022 then n =

If $$x=(9+4\sqrt{5})^{48} = [x] +f$$, where [x] is defined as integral part of x and f is a fraction, then x (1 - f) equals

The roots of the polynomial $$P(x) = 2x^3 - 11x^2 + 17x - 6$$ are the radii of three concentric circles.
The ratio of their area, when arranged from the largest to the smallest, is:

Find the equation of the graph shown below.

a, b, c are integers, |a| ≠ |b| ≠|c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc - (a + b + c)]?

If $$2 \leq |x - 1| \times  |y + 3| \leq 5$$ and both $$x$$ and $$y$$ are negative integers, find the number of possible combinations of $$x$$ and $$y$$.

The sum of the cubes of two numbers is 128, while the sum of the reciprocals of their cubes is 2.

What is the product of the squares of the numbers?

Determine the value(s) of “a” for which the point $$(a, a^{2})$$ lies inside the triangle formed by the lines: 2x+ 3y= 1, x+ 2y=3 and 5x-6y= 1

Given that a and b are integers and that $$5x+2\sqrt{7}$$ is a root of the polynomial $$x^2 - ax + b + 2\sqrt{7}$$ in $$x$$, what is the value of b?

If $$\log_4m + \log_4n = \log_2(m + n)$$ where m and n are positive real numbers, then which of the following must be true?

Consider the equation $$\log_5(x - 2) = 2 \log_{25}(2x - 4)$$, where x is a real number.
For how many different values of x does the given equation hold?

If $$f(x^2 - 1) = x^4 - 7x^2 + k_1$$ and $$f(x^3 - 2) = x^6 - 9x^3 +k_2$$ then the value of $$(k_2 - k_1)$$ is

For how many distinct real values of $$x$$ does the equation below hold true? (Consider $$a$$ > 0.)
$$\dfrac{x^2 \log_a(16)}{\log_a(32)} - \dfrac{\log_a(64)}{\log_a(32)} - x = 0 $$

If $$x$$ and $$y$$ are real numbers, the least possible value of the expression $$4(x - 2)^{2} + 4(y - 3)^{2} - 2(x - 3)^{2}$$ is :

For a positive integer x, define f(x) such that f(x + a) = f(a × x), where a is an integer and f(1) = 4. If the value of f(1003) = k, then the value of ‘k’ will be:

The figure below shows the graph of a function f(x). How many solutions does the equation f(f(x)) = 15 have?

The domain of the function $$f(x) =log_{7}({ log_{3}(log_{5}(20x-x^{2}-91 )))}$$ is:

Consider the function f(x) = (x + 4)(x + 6)(x + 8) ⋯ (x + 98). The number of integers x for which f(x) < 0 is:

The y - ordinates of $$A_8$$ is

The value of the expression: $$\sum_{i=2}^{100}\frac{1}{log_{i}100!}$$ is:

Consider the four variables A, B, C and D and a function Z of these variables, $$Z = 15A^2 - 3B^4 + C + 0.5D$$ It is given that A, B, C and D must be non-negative integers and thatall of the following relationships must hold:
i) $$2A + B \leq 2$$
ii) $$4A + 2B + C \leq 12$$
iii) $$3A + 4B + D \leq 15$$
If Z needs to be maximised, then what value must D take?

$$\frac{log (97-56\sqrt{3})}{log \sqrt{7+4\sqrt{3}}}$$ equals which of the following?

Two different quadratic equations have a common root. Let the three unique roots of the two equations be A, B and C - all of them are positive integers. If (A + B + C) = 41 and the product of the roots of one of the equations is 35, which of the following options is definitely correct?

Rahul has just made a $$3 \times 3$$ magic square, in which, the sum of the cells along any row, column or diagonal, is the same number N. The entries in the cells are given as expressions in x, y, and Z. Find N?

Consider the quadratic function $$f(x) = ax^2 + bx + a$$ having two irrational roots, with a and b being two positive integers, such that $$a, b \leq 9$$.
If all such permissible pairs (a, b) are equally likely, what is the probability that a + b is greater than 9?

Aman decides to buy only onion, in whatever maximum quantity possible (in positive integer kilogram), with the money he has come to the market with. How much money will he be left with after the purchase?

f is a function for which f(1)= 1 and f(x) = 2x + f(x - 1) for each natural number x$$\geq$$2. Find f(31)

The number of point(s) satisfying the above mentioned characteristics and not in the first quadrant is/are

The Guava club has won 40% of their football matches in the Apple Cup that they have played so far. If they play another n matches and win all of them, their winning percentage will improve to 50. Further, if they play 15 more matches and win all of them, their winning percentage will improve from 50 to 60. How many matches has the Guava club played in the Apple Cup so far? In the Apple Cup matches, there are only two possible outcomes, win or loss; draw is not possible.

Find the equation of the graph shown below.