XAT Algebra Practice Questions With Solutions

Find the value of
$\frac{\sin^{6}15^{\circ} + \sin^{6}75^{\circ} + 6\sin^{2}15^{\circ}\sin^{2}75^{\circ}}{\sin^{4}15^{\circ} + \sin^{4}75^{\circ} + 5\sin^{2}15^{\circ}\sin^{2}75^{\circ}}$

Ramesh and Reena are playing with triangle ABC. Ramesh draws a line that bisects $\angle BAC$; this line cuts BC at D. Reena then extends AD to a point P. In response, Ramesh joins B and P. Reena then announces that BD bisects $\angle PBA$, hat a surprise! Together, Ramesh and Reena find that BD= 6 cm, AC= 9 cm, DC= 5 cm, BP=8 cm, and DP = 5 cm.

Fatima found that the profit earned by the Bala dosa stall today is a three-digit number. She also noticed that the middle digit is half of the leftmost digit, while the rightmost digit is three times the middle digit. She then randomly interchanged the digits and obtained a different number. This number was more than the original number by 198.

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?

An encryption system operates as follows:

Step 2. For each word, swap the first k letters from the front with the last k letters from the end in reverse order. If a word contains less than 2k letters, write the entire word in reverse order.

Example: k = 2: zebra --> arbez --> ctdgb.

Two circles P and Q, each of radius 2 cm, pass through each other’s centres. They intersect at points A and B. A circle R is drawn with diameter AB. What is the area of overlap (in square cm) between the circles R and P?

An article is marked x% above the cost price. A discount of $\frac{2}{3}$x% is given on the marked price. If the profit is 4% of the cost price and the value of x lies between 25 and 50, then the value of 50% of x is?

Let ABC be an isosceles triangle. Suppose that the sides AB and AC are equal and let the length of AB be x cm. Let b denote the angle ∠ABC and sin b = 3/5. If the area of the triangle ABC is M square cm, then which of the following is true about M?

An antique store has a collection of eight clocks. At a particular moment, the displayed times on seven of the eight clocks were as follows: 1:55 pm, 2:03 pm, 2:11 pm, 2:24 pm, 2:45 pm, 3:19 pm and 4:14 pm. If the displayed times of all eight clocks form a mathematical series, then what was the displayed time on the remaining clock?

A cone of radius 4 cm with a slant height of 12 cm was sliced horizontally, resulting into a smaller cone (upper portion) and a frustum (lower portion). If the ratio of the curved surface area of the upper smaller cone and the lower frustum is 1:2, what will be the slant height of the frustum?