Coachify CAT Club
The $(x, y)$ coordinates of vertices $P$, $Q$ and $R$ of a parallelogram $PQRS$ are $(-3, -2)$, $(1, -5)$ and $(9, 1)$, respectively. If the diagonal $SQ$ intersects the $x$-axis at $(a, 0)$, then the value of $a$ is:
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which $\{(a_1)^1 \times (a_2)^2 \times \ldots \times (a_{20})^{20}\} $ < $ \{a_{21} \times a_{22} \times \ldots \times a_{(20+m)}\}$ is.
In a 3-digit number $N$, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, the number of factors of the minimum possible value of $N$ is:
In a circle with centre $C$ and radius $6\sqrt{2}$ cm, $PQ$ and $SR$ are two parallel chords perpendicular to one of the diameters. $\angle PQC = 45^{\circ}$, and the ratio of the perpendicular distances of $PQ$ and $SR$ from $C$ is $3:2$. Then, the area, in sq. cm, of the quadrilateral $PQRS$ is:
A cafeteria offers 5 types of sandwiches. Moreover, for each type of sandwich, a customer can choose one of 4 breads and opt for either small or large sized sandwich. Optionally, the customer may also add up to 2 out of 6 available sauces. The number of different ways in which an order can be placed for a sandwich, is:
Stocks A, B and C are priced at rupees 120, 90 and 150 per share, respectively. A trader holds a portfolio consisting of 10 shares of stock A, and 20 shares of stocks B and C put together. If the total value of her portfolio is rupees 3300, then the number of shares of stock B that she holds, is:
In the set of consecutive odd numbers $\{1, 3, 5, \dots, 57\}$, there is a number $k$ such that the sum of all the numbers less than $k$ is equal to the sum of all the numbers greater than $k$. Then, $k$ equals:
Let $3 \leq x \leq 6$ and $[x^2] = [x]^2$, where $[x]$ is the greatest integer not exceeding $x$. If set $S$ represents all feasible values of $x$, then a possible subset of $S$ is .
If $a - 6b + 6c = 4$ and $6a + 3b - 3c = 50$, where $a$, $b$ and $c$ are real numbers, the value of $2a + 3b - 3c$ is.
A shopkeeper offers a discount of 22% on the marked price of each chair, and gives 13 chairs to a customer for the discounted price of 12 chairs to earn a profit of 26% on the transaction. If the cost price of each chair is Rs 100, then the marked price, in rupees, of each chair is: