1
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The foot of the perpendicular from $$(2,4,-1)$$ to the line $$x+5=\frac{1}{4}(y+3)=-\frac{1}{9}(z-6)$$ is

A
$$(-4,-1,-3)$$
B
$$(4,-1,-3)$$
C
$$(-4,-1,3)$$
D
$$(-4,1,-3)$$
2
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

In how many ways can the word "CHRISTMAS" be arranged so that the letters '$$\mathrm{C}$$' and '$$\mathrm{M}$$' are never adjacent?

A
$$8!\times \frac{9}{2}$$
B
$$8!\times \frac{7}{2}$$
C
$$7!\times \frac{9}{2}$$
D
$$9!\times \frac{7}{2}$$
3
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\lim _\limits{x \rightarrow 0} \frac{\sqrt{a+x}-\sqrt{a}}{x \sqrt{a(a+x)}}$$ equals to

A
$$a^{-\frac{3}{2}}$$
B
$$\frac{1}{2 a^{\frac{3}{2}}}$$
C
$$\frac{1}{2}$$
D
$$2 a^{-\frac{3}{2}}$$
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

A and B each have a calculator which can generate a single digit random number from the set $$\{1,2,3,4,5,6,7,8\}$$. They can generate a random number on their calculator. Given that the sum of the two numbers is 12 , then the probability that the two numbers are equal is

A
$$\frac{5}{64}$$
B
$$\frac{1}{5}$$
C
$$\frac{1}{16}$$
D
$$\frac{1}{8}$$
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