1
GATE CSE 2025 Set 1
MCQ (More than One Correct Answer)
+1
-0

Consider the given system of linear equations for variables $x$ and $y$, where $k$ is a realvalued constant. Which of the following option(s) is/are CORRECT?

$$\begin{aligned} & x+k y=1 \\ & k x+y=-1 \end{aligned}$$

A
There is exactly one value of $k$ for which the above system of equations has no solution.
B
There exist an infinite number of values of $k$ for which the system of equations has no solution.
C
There exists exactly one value of $k$ for which the system of equations has exactly one solution.
D
There exists exactly one value of $k$ for which the system of equations has an infinite number of solutions.
2
GATE CSE 2025 Set 1
Numerical
+1
-0

Let $S$ be the set of all ternary strings defined over the alphabet $\{a, b, c\}$. Consider all strings in $S$ that contain at least one occurrence of two consecutive symbols, that is, "aa", "bb" or "cc". The number of such strings of length 5 that are possible is __________ (Answer in integer)

Your input ____
3
GATE CSE 2025 Set 1
Numerical
+1
-0

Consider the given function $f(x)$.

$$f(x)=\left\{\begin{array}{cc} a x+b & \text { for } x<1 \\ x^3+x^2+1 & \text { for } x \geq 1 \end{array}\right.$$

If the function is differentiable everywhere, the value of $b$ must be _________ (Rounded off to one decimal place)

Your input ____
4
GATE CSE 2025 Set 1
Numerical
+1
-0

A box contains 5 coins: 4 regular coins and 1 fake coin. When a regular coin is tossed, the probability $P($ head $)=0.5$ and for a fake coin, $P($ head $)=1$. You pick a coin at random and toss it twice, and get two heads. The probability that the coin you have chosen is the fake coin is ________ . (Rounded off to two decimal places)

Your input ____
EXAM MAP