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1 votes
1 answer
3541
ISI2018-PCB-A1
Consider a $n \times n$ matrix $A=I_n-\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alpha=1$.Show that $A^2=A$.
Consider a $n \times n$ matrix $A=I_n-\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alp...
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2 votes
1 answer
3543
ISI2018-MMA-29
Let $f$ be a continuous function with $f(1) = 1$. Define $F(t)=\int_{t}^{t^2}f(x)dx$. The value of $F’(1)$ is $-2$ $-1$ $1$ $2$
Let $f$ be a continuous function with $f(1) = 1$. Define $$F(t)=\int_{t}^{t^2}f(x)dx$$.The value of $F’(1)$ is$-2$$-1$$1$$2$
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0 votes
1 answer
3546
ISI2018-MMA-14
Let $A$ be a $3× 3$ real matrix with all diagonal entries equal to $0$. If $1 + i$ is an eigenvalue of $A$, the determinant of $A$ equals $-4$ $-2$ $2$ $4$
Let $A$ be a $3× 3$ real matrix with all diagonal entries equal to $0$. If $1 + i$ is an eigenvalue of $A$, the determinant of $A$ equals$-4$$-2$$2$$4$
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0 votes
1 answer
3549
self doubt consistency and satisfiability
how can we link consistency and satisfiability ? are they bidirectional? plz help
how can we link consistency and satisfiability ?are they bidirectional? plz help
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1 votes
1 answer
3550
A first course in probability by Sheldon Ross
What are the relevant chapter of probability by sheldon ross to study for gate? I think whole syllabus is within chapter 5,Should i study everything upto chapter 5 or there are some topics that can be skipped.
What are the relevant chapter of probability by sheldon ross to study for gate?I think whole syllabus is within chapter 5,Should i study everything upto chapter 5 or ther...
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1 votes
1 answer
3553
ISI2019-MMA-28
Consider the functions $f,g:[0,1] \rightarrow [0,1]$ given by $f(x)=\frac{1}{2}x(x+1) \text{ and } g(x)=\frac{1}{2}x^2(x+1).$ Then the area enclosed between the graphs of $f^{-1}$ and $g^{-1}$ is $1/4$ $1/6$ $1/8$ $1/24$
Consider the functions $f,g:[0,1] \rightarrow [0,1]$ given by$$f(x)=\frac{1}{2}x(x+1) \text{ and } g(x)=\frac{1}{2}x^2(x+1).$$Then the area enclosed between the graphs of...
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2 votes
1 answer
3556
ISI2019-MMA-14
If the system of equations $\begin{array} \\ax +y+z= 0 \\ x+by +z = 0 \\ x+y + cz = 0 \end{array}$ with $a,b,c \neq 1$ has a non trivial solutions, the value of $\frac{1}{1-a} + \frac{1}{1-b} + \frac{1}{1-c}$ is $1$ $-1$ $3$ $-3$
If the system of equations$\begin{array} \\ax +y+z= 0 \\ x+by +z = 0 \\ x+y + cz = 0 \end{array}$with $a,b,c \neq 1$ has a non trivial solutions, the value of $$\frac{1}{...
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0 votes
1 answer
3559
ISI2019-MMA-5
If $f(a)=2, \: f’(a) = 1, \: g(a) =-1$ and $g’(a) =2$, then the value of $\lim _{x\rightarrow a}\frac{g(x) f(a) – f(x) g(a)}{x-a}$ is $-5$ $-3$ $3$ $5$
If $f(a)=2, \: f’(a) = 1, \: g(a) =-1$ and $g’(a) =2$, then the value of $$\lim _{x\rightarrow a}\frac{g(x) f(a) – f(x) g(a)}{x-...
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1 votes
1 answer
3560
ISI2019-MMA-4
Suppose that $6$-digit numbers are formed using each of the digits $1, 2, 3, 7, 8, 9$ exactly once. The number of such $6$-digit numbers that are divisible by $6$ but not divisible by $9$ is equal to $120$ $180$ $240$ $360$
Suppose that $6$-digit numbers are formed using each of the digits $1, 2, 3, 7, 8, 9$ exactly once. The number of such $6$-digit numbers that are divisible by $6$ but not...
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