90372
For some integer m, every even integer is of the form:
1 )m
2 )m + 1
3 )2m
4 )2m + 1
Explanation:
Exp: C 2m We know that, even integers are 2, 4, 6, … So, it can be written in the form of 2m Where, m = Integer = Z [Since, integer is represented by Z] or m = …, -1, 0, 1, 2, 3, … 2m = …, -2, 0, 2, 4, 6, …
REAL NUMBERS
90373
Every positive even integer is of the form ________ for some integer ‘q’.
1 )2q + 1
2 )2q
3 )2q - 1
4 )None of these
Explanation:
Exp: B 2q Let a be any positive integer and b = 2 Then by applying Euclid’s Division Lemma, we have, a = 2q + r where \(0\leq\text{r}<2\text{ r}=0\text{ r}1\) Therefore, a = 2q or 2q + 1 Thus, it is clear that a = 2q i.e., a is an even integer in the form of 2q
REAL NUMBERS
90376
The sum of exponents of prime factors in the prime-factorisation of 196 is:
1 )3
2 )4
3 )5
4 )2
Explanation:
Exp: B 4 196 = 2 × 2 × 7 × 7 = 2\(^{2}\) × 7\(^{7}\) = 2 + 2 (exponent is the power of a number) = 4
REAL NUMBERS
90378
\(\sqrt2\) is:
1 )A rational number.
2 )An irrational number.
3 )A terminating decimal.
4 )A non-terminating repeating decimal.
Explanation:
Exp: B An irrational number. An irrational number is a number that is non-terminating and non-repeating. \(\sqrt2=1.4142135\dots\) which is neither terminating nor repeating, and hence is an irrational number. Never Active
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REAL NUMBERS
90372
For some integer m, every even integer is of the form:
1 )m
2 )m + 1
3 )2m
4 )2m + 1
Explanation:
Exp: C 2m We know that, even integers are 2, 4, 6, … So, it can be written in the form of 2m Where, m = Integer = Z [Since, integer is represented by Z] or m = …, -1, 0, 1, 2, 3, … 2m = …, -2, 0, 2, 4, 6, …
REAL NUMBERS
90373
Every positive even integer is of the form ________ for some integer ‘q’.
1 )2q + 1
2 )2q
3 )2q - 1
4 )None of these
Explanation:
Exp: B 2q Let a be any positive integer and b = 2 Then by applying Euclid’s Division Lemma, we have, a = 2q + r where \(0\leq\text{r}<2\text{ r}=0\text{ r}1\) Therefore, a = 2q or 2q + 1 Thus, it is clear that a = 2q i.e., a is an even integer in the form of 2q
REAL NUMBERS
90376
The sum of exponents of prime factors in the prime-factorisation of 196 is:
1 )3
2 )4
3 )5
4 )2
Explanation:
Exp: B 4 196 = 2 × 2 × 7 × 7 = 2\(^{2}\) × 7\(^{7}\) = 2 + 2 (exponent is the power of a number) = 4
REAL NUMBERS
90378
\(\sqrt2\) is:
1 )A rational number.
2 )An irrational number.
3 )A terminating decimal.
4 )A non-terminating repeating decimal.
Explanation:
Exp: B An irrational number. An irrational number is a number that is non-terminating and non-repeating. \(\sqrt2=1.4142135\dots\) which is neither terminating nor repeating, and hence is an irrational number. Never Active
90372
For some integer m, every even integer is of the form:
1 )m
2 )m + 1
3 )2m
4 )2m + 1
Explanation:
Exp: C 2m We know that, even integers are 2, 4, 6, … So, it can be written in the form of 2m Where, m = Integer = Z [Since, integer is represented by Z] or m = …, -1, 0, 1, 2, 3, … 2m = …, -2, 0, 2, 4, 6, …
REAL NUMBERS
90373
Every positive even integer is of the form ________ for some integer ‘q’.
1 )2q + 1
2 )2q
3 )2q - 1
4 )None of these
Explanation:
Exp: B 2q Let a be any positive integer and b = 2 Then by applying Euclid’s Division Lemma, we have, a = 2q + r where \(0\leq\text{r}<2\text{ r}=0\text{ r}1\) Therefore, a = 2q or 2q + 1 Thus, it is clear that a = 2q i.e., a is an even integer in the form of 2q
REAL NUMBERS
90376
The sum of exponents of prime factors in the prime-factorisation of 196 is:
1 )3
2 )4
3 )5
4 )2
Explanation:
Exp: B 4 196 = 2 × 2 × 7 × 7 = 2\(^{2}\) × 7\(^{7}\) = 2 + 2 (exponent is the power of a number) = 4
REAL NUMBERS
90378
\(\sqrt2\) is:
1 )A rational number.
2 )An irrational number.
3 )A terminating decimal.
4 )A non-terminating repeating decimal.
Explanation:
Exp: B An irrational number. An irrational number is a number that is non-terminating and non-repeating. \(\sqrt2=1.4142135\dots\) which is neither terminating nor repeating, and hence is an irrational number. Never Active
90372
For some integer m, every even integer is of the form:
1 )m
2 )m + 1
3 )2m
4 )2m + 1
Explanation:
Exp: C 2m We know that, even integers are 2, 4, 6, … So, it can be written in the form of 2m Where, m = Integer = Z [Since, integer is represented by Z] or m = …, -1, 0, 1, 2, 3, … 2m = …, -2, 0, 2, 4, 6, …
REAL NUMBERS
90373
Every positive even integer is of the form ________ for some integer ‘q’.
1 )2q + 1
2 )2q
3 )2q - 1
4 )None of these
Explanation:
Exp: B 2q Let a be any positive integer and b = 2 Then by applying Euclid’s Division Lemma, we have, a = 2q + r where \(0\leq\text{r}<2\text{ r}=0\text{ r}1\) Therefore, a = 2q or 2q + 1 Thus, it is clear that a = 2q i.e., a is an even integer in the form of 2q
REAL NUMBERS
90376
The sum of exponents of prime factors in the prime-factorisation of 196 is:
1 )3
2 )4
3 )5
4 )2
Explanation:
Exp: B 4 196 = 2 × 2 × 7 × 7 = 2\(^{2}\) × 7\(^{7}\) = 2 + 2 (exponent is the power of a number) = 4
REAL NUMBERS
90378
\(\sqrt2\) is:
1 )A rational number.
2 )An irrational number.
3 )A terminating decimal.
4 )A non-terminating repeating decimal.
Explanation:
Exp: B An irrational number. An irrational number is a number that is non-terminating and non-repeating. \(\sqrt2=1.4142135\dots\) which is neither terminating nor repeating, and hence is an irrational number. Never Active
