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3 votes
1 answer
2521
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 27
What is the middle term in the expansion of $\left(\frac{y\sqrt{x}}{2} - \frac{2}{x\sqrt{y}}\right)^{12}$. $924\left(\frac{y}{x}\right)^6$ $924\left(\frac{y}{x}\right)^3$ $2^{10}\left(\frac{y}{x}\right)^6$ None of the above
What is the middle term in the expansion of $$\left(\frac{y\sqrt{x}}{2} - \frac{2}{x\sqrt{y}}\right)^{12}$$.$924\left(\frac{y}{x}\right)^6$$924\left(\frac{y}{x}\right)^3$...
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4 votes
4 answers
2522
TIFR2010-Maths-A-8
Let $f(x)= |x|^{3/2}, x \in \mathbb{R}$. Then $f$ is uniformly continuous. $f$ is continuous, but not differentiable at $x=0$. $f$ is differentiable and $f ' $ is continuous. $f$ is differentiable, but $f ' $ is discontinuous at $x=0$.
Let $f(x)= |x|^{3/2}, x \in \mathbb{R}$. Then$f$ is uniformly continuous.$f$ is continuous, but not differentiable at $x=0$.$f$ is differentiable and $f ' $ is continuous...
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0 votes
1 answer
2523
Kenneth Rosen Edition 7 Exercise 6.5 Question 1 (Page No. 432)
In how many different ways can five elements be selected in order from a set with three elements when repetition is allowed?
In how many different ways can five elements be selected in order from a set with three elements when repetition is allowed?
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0 votes
1 answer
2525
Kenneth Rosen Edition 7 Exercise 6.5 Question 37 (Page No. 433)
A student has three mangos, two papayas, and two kiwi fruits. If the student eats one piece of fruit each day, and only the type of fruit matters, in how many different ways can these fruits be consumed?
A student has three mangos, two papayas, and two kiwi fruits. If the student eats one piece of fruit each day, and only the type of fruit matters, in how many different w...
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1 votes
1 answer
2526
GATE Overflow Test Series | Mixed Subjects | Test 1 | Question: 17
You are at a party with $8$ of your friends and you order a $16$-cut pizza ($16$ identical slices). How many distributions of pizza slices are there if each person gets at least one slice of pizza? $6435$ $6433$ $6437$ $6439$
You are at a party with $8$ of your friends and you order a $16$-cut pizza ($16$ identical slices). How many distributions of pizza slices are there if each person gets a...
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2 votes
1 answer
2528
GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 16
The solution to the recurrence relation $a_{n}=a_{n-1}+2^{n}$ with $a_{0}=1$ is ________ $a_{n} = 2^{n} - 1 $ $a_{n} = 2^{n+1} - 2 $ $a_{n} = 2^{n+1} - 1 $ $a_{n} = 2^{n-1} - 1 $
The solution to the recurrence relation $a_{n}=a_{n-1}+2^{n}$ with $a_{0}=1$ is ________$a_{n} = 2^{n} - 1 $$a_{n} = 2^{n+1} - 2 $$a_{n} = 2^{n+1} - 1 $$a_{n} = 2^{n-1} -...
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2 votes
1 answer
2529
GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 19
Let $G$ be a finite group on $243$ elements. The size of the largest possible proper subgroup of $G$ is ________
Let $G$ be a finite group on $243$ elements. The size of the largest possible proper subgroup of $G$ is ________
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0 votes
1 answer
2530
Kenneth Rosen Edition 7 Exercise 6.5 Question 21 (Page No. 432)
How many ways are there to distribute six indistinguishable balls into nine distinguishable bins?
How many ways are there to distribute six indistinguishable balls into nine distinguishable bins?
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1 votes
1 answer
2531
GATE Overflow Test Series | Mixed Subjects | Test 1 | Question: 12
How many triangles can be formed by $15$ points of which $6$ are collinear? $455$ $445$ $452$ $435$
How many triangles can be formed by $15$ points of which $6$ are collinear?$455$$445$$452$$435$
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1 votes
1 answer
2533
GATE Overflow Test Series | Mixed Subjects | Test 1 | Question: 8
The following propositional statement is a $\ \neg(\neg A \wedge B)\leftrightarrow (A\rightarrow B)$ Tautology Contradiction Contingent More than one of these
The following propositional statement is a$\ \neg(\neg A \wedge B)\leftrightarrow (A\rightarrow B)$TautologyContradictionContingentMore than one of these
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2 votes
1 answer
2535
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 1
The minimum number of people that must be in a room to ensure that at least three were born on the same day of the week is $\_\_\_\_\_$
The minimum number of people that must be in a room to ensure that at least three were born on the same day of the week is $\_\_\_\_\_$
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3 votes
1 answer
2536
GATE Overflow Test Series | Discrete Mathematics | Test 1 | Question: 23
Which of the following is/are bijection from $\mathbb{R}$ to $\mathbb{R}?$ (Mark all the appropriate choices) $2x+1$ $x^2+1$ $x^3$ $x$
Which of the following is/are bijection from $\mathbb{R}$ to $\mathbb{R}?$ (Mark all the appropriate choices)$2x+1$$x^2+1$$x^3$$x$
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14 votes
4 answers
2540
TIFR CSE 2011 | Part A | Question: 3
The probability of three consecutive heads in four tosses of a fair coin is $\left(\dfrac{1}{4}\right)$ $\left(\dfrac{1}{8}\right)$ $\left(\dfrac{1}{16}\right)$ $\left(\dfrac{3}{16}\right)$ None of the above
The probability of three consecutive heads in four tosses of a fair coin is$\left(\dfrac{1}{4}\right)$$\left(\dfrac{1}{8}\right)$$\left(\dfrac{1}{16}\right)$$\left(\dfrac...
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