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Questions by jjayantamahata

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21

ISI-2004-30
If the tangent at the point $P$ with co-ordinates $(h, k)$ on the curve $y^2 = 2x^3$ is perpendicular to the straight line $4x=3y$, then $(h, k) = (0,0)$ $(h, k) = (1/8, -1/16)$ $(h, k) = (0,0)$ or $(h, k) = (1/8, -1/16)$ no such point $(h, k)$ exists.

asked in Mathematical Logic Apr 16, 2018

204 views

0 votes

1 answer

22

ISI-2004-23
If $f(x) = x^2$ and $g(x)=x \sin x + \cos x$ then $f$ and $g$ agree at no points. $f$ and $g$ agree at exactly one point. $f$ and $g$ agree at exactly two points. $f$ and $g$ agree at more than two points.

asked in Mathematical Logic Apr 15, 2018

316 views

0 votes

1 answer

23

ISI-2004-16
For complex numbers $z_1 = x_1 + iy_1$ and $z_2 = x_2 + iy_2$, write $z_1 \preceq z_2$ if $x_1 \leq x_2$ and $y_1 \leq y_2$. Then for all complex numbers $z$ with $1 \preceq z, ( 1 \neq z)$. $\begin{vmatrix} \dfrac{1+z}{1-z} \end{vmatrix} \preceq 1$ $\dfrac{1+z}{1-z} \preceq 0$ $\dfrac{1-z}{1+z} \preceq 0$ none of these.

asked in Mathematical Logic Apr 15, 2018

193 views

0 votes

1 answer

24

ISI-2004-14
The inequality $\cfrac{2-gx-x^2}{1-x+x^2} \leq 3$ is true for all values of $x$ if and only if $1 \leq g \leq 7$ $-1 \leq g \leq 1$ $-6 \leq g \leq 7$ $-1 \leq g \leq 7$

asked in Mathematical Logic Apr 15, 2018

233 views

0 votes

1 answer

25

ISI-2004-10
The equation $P(x) = \alpha$ where $P(x) = x^4 + 4x^3 – 2x^2 – 12x$ has four distinct real roots if and only if $P(-3) < \alpha$ $P(-1) > \alpha$ $P(-1) < \alpha$ $P(-3) < \alpha < P(-1)$

asked in Mathematical Logic Apr 14, 2018

154 views

0 votes

1 answer

26

ISI-2004-11
If $a_1,a_2, \dots,a_n$ are positive real numbers, then $\frac{a_1}{a_2} + \frac{a_2}{a_3} + \cdots + \frac{a_{n-1}}{a_n}+\frac{a_n}{a_1}$ is always $\geq n$ $\leq n$ $\leq n^{1/n}$ none of the above.

asked in Mathematical Logic Apr 14, 2018

218 views

0 votes

1 answer

27

ISI-2004-8
If $\alpha _1, \alpha _2,\dots,\alpha _n$ be the roots of $x^n + 1 = 0$, then $(1-\alpha _1)(1-\alpha _2)\dots(1-\alpha _n)$ is equal to $1$ $0$ $n$ $2$

asked in Mathematical Logic Apr 14, 2018

195 views

0 votes

0 answers

28

ISI-2014-SAMPLE-25

asked in Mathematical Logic Apr 11, 2018

226 views

1 vote

0 answers

29

ISI-SAMPLE-2014-22

asked in Mathematical Logic Apr 11, 2018

148 views

0 votes

0 answers

30

ISI-SAMPLE-2014

asked in Mathematical Logic Apr 8, 2018

136 views

0 votes

2 answers

31

ISI-SAMPLE-2014

asked in Mathematical Logic Apr 8, 2018

184 views

0 votes

2 answers

32

ISI-2014-SAMPLE-18

asked in Mathematical Logic Apr 7, 2018

298 views

0 votes

0 answers

33

ISI-SAMPLE-2014-17

asked in Mathematical Logic Apr 7, 2018

212 views

0 votes

2 answers

34

ISI-SAMPLE-2014-15

asked in Mathematical Logic Apr 7, 2018

433 views

0 votes

1 answer

35

ISI-2016-05
Let $f(x,y) = \begin{cases} \dfrac{x^2y}{x^4+y^2}, & \text{ if } (x,y) \neq (0,0) \\ 0 & \text{ if } (x,y) = (0,0)\end{cases}$ Then $\displaystyle{\lim_{(x,y)\rightarrow(0,0)}}f (x,y)$ equals $0$ equals $1$ equals $2$ does not exist

asked in Calculus Mar 30, 2018

530 views

3 votes

4 answers

36

ISI-2016-04
If $a,b,c$ and $d$ satisfy the equations $a+7b+3c+5d =16$ $8a+4b+6c+2d = -16$ $2a+6b+4c+8d = 16$ $5a+3b+7c+d= -16$ Then $(a+d)(b+c)$ equals $-4$ $0$ $16$ $-16$

asked in Linear Algebra Mar 30, 2018

1.5k views

1 vote

3 answers

37

ISI-2016-02
How many complex numbers $z$ are there such that $\mid z+1 \mid = \mid z+i \mid$ and $\mid z \mid = 5$ ? $0$ $1$ $2$ $3$

asked in Mathematical Logic Mar 30, 2018

364 views

10 votes

8 answers

38

ISI2017-MMA-29
Suppose the rank of the matrix $\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$ is $2$ for some real numbers $a$ and $b$. Then $b$ equals $1$ $3$ $1/2$ $1/3$

asked in Linear Algebra Mar 29, 2018

2.7k views

1 vote

1 answer

39

ISI-2017-23
What is the smallest degree of a polynomial with real coefficients and having roots $2\omega, 2+3\omega, 2{\omega}^2, -1-3\omega \text{ and } 2-\omega-{\omega}^2$? [Here $\omega \neq 1$ is a cube root of unity.] $5$ $7$ $9$ $10$

asked in Mathematical Logic Mar 28, 2018

976 views

6 votes

5 answers

40

ISI2017-MMA-21
There are four machines and it is known that exactly two of them are faulty. They are tested one by one in a random order till both the faulty machines are identified. The probability that only two tests are required is $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{4}\right)$ $\left(\dfrac{1}{6}\right)$

asked in Probability Mar 28, 2018

2.9k views

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