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4 votes
3 answers
993
GATE2010 TF: GA-7
Consider the series $\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{8}+\frac{1}{9}-\frac{1}{16}+\frac{1}{32}+\frac{1}{27}-\frac{1}{64}+\ldots.$ The sum of the infinite series above is$:$ $\infty$ $\frac{5}{6}$ $\frac{1}{2}$ $0$
Consider the series $\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{8}+\frac{1}{9}-\frac{1}{16}+\frac{1}{32}+\frac{1}{27}-\frac{1}{64}+\ldots.$ The sum of the infinite seri...
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8 votes
3 answers
995
GATE2010 TF: GA-5
Consider the function $f(x)=\max(7-x,x+3).$ In which range does $f$ take its minimum value$?$ $-6\leq x<-2$ $-2\leq x<2$ $2\leq x<6$ $6\leq x<10$
Consider the function $f(x)=\max(7-x,x+3).$ In which range does $f$ take its minimum value$?$ $-6\leq x<-2$ $-2\leq x<2$ $2\leq x<6$$6\leq x<10$
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1 votes
1 answer
998
GATE2010 TF: GA-2
The question below consists of a pair of related words followed by four pairs of words. Select the pair the best expresses the relation in the original pair$.$ Erudition : Scholar steadfast $:$ mercurial competence $:$ strict skill $:$ craftsman nurse $:$ doctor
The question below consists of a pair of related words followed by four pairs of words. Select the pair the best expresses the relation in the original pair$.$Erudition :...
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2 votes
1 answer
999
GATE2010 TF: GA-1
Which of the following options is the closest in meaning to the word below$:$ Ephemeral effeminate ghostlike soft short-lived
Which of the following options is the closest in meaning to the word below$:$Ephemeraleffeminateghostlikesoftshort-lived
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3 votes
1 answer
1002
GATE2010 MN: GA-8
Consider the set of integers $\{1,2,3,\ldots,5000\}.$ The number of integers that is divisible by neither $3$ nor $4$ is $:$ $1668$ $2084$ $2500$ $2916$
Consider the set of integers $\{1,2,3,\ldots,5000\}.$ The number of integers that is divisible by neither $3$ nor $4$ is $:$$1668$$2084$$2500$$2916$
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5 votes
2 answers
1003
GATE2010 MN: GA-7
Given the sequence $A,B,B,C,C,C,D,D,D,D,\ldots$ etc$.,$ that is one $A,$ two $B’s,$ three $C’s,$ four $D’s,$ five $E’s$ and so on, the $240^{th}$ latter in the sequence will be $:$ $V$ $U$ $T$ $W$
Given the sequence $A,B,B,C,C,C,D,D,D,D,\ldots$ etc$.,$ that is one $A,$ two $B’s,$ three $C’s,$ four $D’s,$ five $E’s$ and so on, the $240^{th}$ latter in the se...
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1 votes
1 answer
1007
GATE2010 MN: GA-3
Choose the most appropriate word from the options given below to complete the following sentence$:$ The committee wrote a _______ report$,$ extolling only the strengths of the proposal$.$ reasonable supportive biased fragmented
Choose the most appropriate word from the options given below to complete the following sentence$:$The committee wrote a _______ report$,$ extolling only the strengths of...
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1 votes
1 answer
1008
GATE2010 MN: GA-2
The question below consists of a pair of related words followed by four pairs of words$.$ Select the pair that best expresses the relation in the original pair$.$ Preamble : Constitution amendment $:$ law prologue $:$ play episode $:$ serial plot $:$ story
The question below consists of a pair of related words followed by four pairs of words$.$ Select the pair that best expresses the relation in the original pair$.$Preamble...
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3 votes
1 answer
1009
GATE2010 MN: GA-1
Which of the following options is the closest in meaning to the word below$:$ Exhort urge condemn restrain scold
Which of the following options is the closest in meaning to the word below$:$Exhort urgecondemnrestrainscold
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1 votes
0 answers
1010
ISI2018-PCB-A3
Let $n,r\ $and$\ s$ be positive integers, each greater than $2$.Prove that $n^r-1$ divides $n^s-1$ if and only if $r$ divides $s$.
Let $n,r\ $and$\ s$ be positive integers, each greater than $2$.Prove that $n^r-1$ divides $n^s-1$ if and only if $r$ divides $s$.
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