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Answers by NastyBall
0
votes
1
ISI2019-MMA-19
Let $G =\{a_1,a_2, \dots ,a_{12}\}$ be an Abelian group of order $12$ . Then the order of the element $ ( \prod_{i=1}^{12} a_i)$ is $1$ $2$ $6$ $12$
Let $G =\{a_1,a_2, \dots ,a_{12}\}$ be an Abelian group of order $12$ . Then the order of the element $ ( \prod_{i=1}^{12} a_i)$ is$1$$2$$6$$12$
2.1k
views
answered
Jul 9, 2021
Set Theory & Algebra
isi2019-mma
engineering-mathematics
discrete-mathematics
set-theory&algebra
group-theory
+
–
0
votes
2
ISI2019-MMA-20
Suppose that the number plate of a vehicle contains two vowels followed by four digits. However, to avoid confusion, the letter $‘O’$ and the digit $‘0’$ are not used in the same number plate. How many such number plates can be formed? $164025$ $190951$ $194976$ $219049$
Suppose that the number plate of a vehicle contains two vowels followed by four digits. However, to avoid confusion, the letter $‘O’$ and the digit $‘0’$ are not ...
2.5k
views
answered
Jul 9, 2021
Combinatory
isi2019-mma
engineering-mathematics
discrete-mathematics
combinatory
+
–
0
votes
3
ISI2018-MMA-21
The angle between the tangents drawn from the point $(1, 4)$ to the parabola $y^2 = 4x$ is $\pi /2$ $\pi /3$ $\pi /4$ $\pi /6$
The angle between the tangents drawn from the point $(1, 4)$ to the parabola $y^2 = 4x$ is$\pi /2$$\pi /3$$\pi /4$$\pi /6$
758
views
answered
Jul 9, 2021
Quantitative Aptitude
isi2018-mma
general-aptitude
quantitative-aptitude
+
–
0
votes
4
ISI2015-MMA-84
For positive real numbers $a_1, a_2, \cdots, a_{100}$, let $p=\sum_{i=1}^{100} a_i \text{ and } q=\sum_{1 \leq i < j \leq 100} a_ia_j.$ Then $q=\frac{p^2}{2}$ $q^2 \geq \frac{p^2}{2}$ $q< \frac{p^2}{2}$ none of the above
For positive real numbers $a_1, a_2, \cdots, a_{100}$, let $$p=\sum_{i=1}^{100} a_i \text{ and } q=\sum_{1 \leq i < j \leq 100} a_ia_j.$$ Then $q=\frac{p^2}{2}$$q^2 \geq ...
435
views
answered
Jun 20, 2021
Others
isi2015-mma
summation
non-gate
+
–
0
votes
5
ISI2015-MMA-83
If $\alpha, \beta$ are complex numbers then the maximum value of $\dfrac{\alpha \overline{\beta}+\overline{\alpha}\beta}{\mid \alpha \beta \mid}$ is $2$ $1$ the expression may not always be a real number and hence maximum does not make sense none of the above
If $\alpha, \beta$ are complex numbers then the maximum value of $\dfrac{\alpha \overline{\beta}+\overline{\alpha}\beta}{\mid \alpha \beta \mid}$ is$2$$1$the expression m...
427
views
answered
Jun 20, 2021
Others
isi2015-mma
complex-number
non-gate
+
–
0
votes
6
ISI2015-MMA-76
Given that $\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$, the value of $ \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} e^{-(x^2+xy+y^2)} dxdy$ is $\sqrt{\pi/3}$ $\pi/\sqrt{3}$ $\sqrt{2 \pi/3}$ $2 \pi / \sqrt{3}$
Given that $\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$, the value of $$ \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} e^{-(x^2+xy+y^2)} dxdy$$ is$\sqrt{\pi/3}$$...
454
views
answered
Jun 20, 2021
Calculus
isi2015-mma
calculus
definite-integral
non-gate
+
–
0
votes
7
ISI2015-MMA-75
The length of the curve $x=t^3$, $y=3t^2$ from $t=0$ to $t=4$ is $5 \sqrt{5}+1$ $8(5 \sqrt{5}+1)$ $5 \sqrt{5}-1$ $8(5 \sqrt{5}-1)$
The length of the curve $x=t^3$, $y=3t^2$ from $t=0$ to $t=4$ is$5 \sqrt{5}+1$$8(5 \sqrt{5}+1)$$5 \sqrt{5}-1$$8(5 \sqrt{5}-1)$
499
views
answered
Jun 20, 2021
Geometry
isi2015-mma
curves
non-gate
+
–
0
votes
8
ISI2015-MMA-74
Let $f$ and $g$ be two differentiable functions such that $f’(x)\leq g’(x)$for all $x<1$ and $f’(x) \geq g’(x)$ for all $x>1$. Then if $f(1) \geq g(1)$, then $f(x) \geq g(x)$ for all $x$ if $f(1) \leq g(1)$, then $f(x) \leq g(x)$ for all $x$ $f(1) \leq g(1)$ $f(1) \geq g(1)$
Let $f$ and $g$ be two differentiable functions such that $f’(x)\leq g’(x)$for all $x<1$ and $f’(x) \geq g’(x)$ for all $x>1$. Thenif $f(1) \geq g(1)$, then $f(x)...
427
views
answered
Jun 20, 2021
Calculus
isi2015-mma
calculus
differentiation
+
–
0
votes
9
ISI2015-MMA-71
Let $f(x,y) = \begin{cases} 1, & \text{ if } xy=0, \\ xy, & \text{ if } xy \neq 0. \end{cases}$ Then $f$ is continuous at $(0,0)$ and $\frac{\partial f}{\partial x}(0,0)$ exists $f$ is not continuous at $(0,0)$ ... $f$ is not continuous at $(0,0)$ and $\frac{\partial f}{\partial x}(0,0)$ does not exist
Let $$f(x,y) = \begin{cases} 1, & \text{ if } xy=0, \\ xy, & \text{ if } xy \neq 0. \end{cases}$$ Then$f$ is continuous at $(0,0)$ and $\frac{\partial f}{\partial x}(0,0)...
408
views
answered
Jun 20, 2021
Others
isi2015-mma
continuity
partial-derivatives
non-gate
+
–
0
votes
10
ISI2015-MMA-31
Consider the sets defined by the real solutions of the inequalities $A = \{(x,y):x^2+y^4 \leq 1 \} \:\:\:\:\:\:\:\: B = \{ (x,y):x^4+y^6 \leq 1\}$ Then $B \subseteq A$ $A \subseteq B$ Each of the sets $A – B, \: B – A$ and $A \cap B$ is non-empty none of the above
Consider the sets defined by the real solutions of the inequalities$$A = \{(x,y):x^2+y^4 \leq 1 \} \:\:\:\:\:\:\:\: B = \{ (x,y):x^4+y^6 \leq 1\}$$Then$B \subseteq A$$A \...
536
views
answered
Jun 17, 2021
Set Theory & Algebra
isi2015-mma
set-theory
non-gate
+
–
1
votes
11
ISI2015-MMA-27
Let $\cos ^6 \theta = a_6 \cos 6 \theta + a_5 \cos 5 \theta + a_4 \cos 4 \theta + a_3 \cos 3 \theta + a_2 \cos 2 \theta + a_1 \cos \theta +a_0$. Then $a_0$ is $0$ $1/32$ $15/32$ $10/32$
Let $\cos ^6 \theta = a_6 \cos 6 \theta + a_5 \cos 5 \theta + a_4 \cos 4 \theta + a_3 \cos 3 \theta + a_2 \cos 2 \theta + a_1 \cos \theta +a_0$. Then $a_0$ is$0$$1/32$$...
628
views
answered
Jun 17, 2021
Quantitative Aptitude
isi2015-mma
quantitative-aptitude
trigonometry
non-gate
+
–
1
votes
12
ISI2015-MMA-26
$\displaystyle{}\underset{n \to \infty}{\lim} \frac{1}{n} \bigg( \frac{n}{n+1} + \frac{n}{n+2} + \cdots + \frac{n}{2n} \bigg)$ is equal to $\infty$ $0$ $\log_e 2$ $1$
$\displaystyle{}\underset{n \to \infty}{\lim} \frac{1}{n} \bigg( \frac{n}{n+1} + \frac{n}{n+2} + \cdots + \frac{n}{2n} \bigg)$ is equal to$\infty$$0$$\log_e 2$$1$
741
views
answered
Jun 17, 2021
Calculus
isi2015-mma
calculus
limits
non-gate
+
–
0
votes
13
ISI2015-MMA-23
Let $X$ be a nonempty set and let $\mathcal{P}(X)$ denote the collection of all subsets of $X$. Define $f: X \times \mathcal{P}(X) \to \mathbb{R}$ by $f(x,A)=\begin{cases} 1 & \text{ if } x \in A \\ 0 & \text{ if } x \notin A \end{cases}$ Then $f(x, A \cup B)$ ... $f(x,A)+f(x,B)\: - f(x,A) \cdot f(x,B)$ $f(x,A)\:+ \mid f(x,A)\: - f(x,B) \mid $
Let $X$ be a nonempty set and let $\mathcal{P}(X)$ denote the collection of all subsets of $X$. Define $f: X \times \mathcal{P}(X) \to \mathbb{R}$ by$$f(x,A)=\begin{cases...
759
views
answered
Jun 17, 2021
Set Theory & Algebra
isi2015-mma
set-theory
functions
non-gate
+
–
0
votes
14
ISI2015-MMA-20
The limit $\underset{n \to \infty}{\lim} \left( 1- \frac{1}{n^2} \right) ^n$ equals $e^{-1}$ $e^{-1/2}$ $e^{-2}$ $1$
The limit $\underset{n \to \infty}{\lim} \left( 1- \frac{1}{n^2} \right) ^n$ equals$e^{-1}$$e^{-1/2}$$e^{-2}$$1$
701
views
answered
Jun 17, 2021
Calculus
isi2015-mma
calculus
limits
non-gate
+
–
0
votes
15
ISI2015-MMA-19
The limit $\:\:\:\underset{n \to \infty}{\lim} \Sigma_{k=1}^n \begin{vmatrix} e^{\frac{2 \pi i k }{n}} – e^{\frac{2 \pi i (k-1) }{n}} \end{vmatrix}\:\:\:$ is $2$ $2e$ $2 \pi$ $2i$
The limit $\:\:\:\underset{n \to \infty}{\lim} \Sigma_{k=1}^n \begin{vmatrix} e^{\frac{2 \pi i k }{n}} – e^{\frac{2 \pi i (k-1) }{n}} \end{vmatrix}\:\:\:$ is$2$$2e$$2 ...
939
views
answered
Jun 17, 2021
Calculus
isi2015-mma
calculus
limits
non-gate
+
–
0
votes
16
ISI2015-MMA-11
The number of positive integers which are less than or equal to $1000$ and are divisible by none of $17$, $19$ and $23$ equals $854$ $153$ $160$ none of the above
The number of positive integers which are less than or equal to $1000$ and are divisible by none of $17$, $19$ and $23$ equals$854$$153$$160$none of the above
1.1k
views
answered
Jun 17, 2021
Quantitative Aptitude
isi2015-mma
quantitative-aptitude
number-system
remainder-theorem
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–
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