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1503
CMI-2019-DataScience-A: 1
Let $X=\{ x_1,x_2,\dots,x_n\}$ and $Y=\{y_1,y_2\}$. The number of surjective functions from $X$ to $Y$ equals $2^n$ $2^n-1$ $2^n-2$ $2^{n/2}$
Let $X=\{ x_1,x_2,\dots,x_n\}$ and $Y=\{y_1,y_2\}$. The number of surjective functions from $X$ to $Y$ equals$2^n$$2^n-1$$2^n-2$$2^{n/2}$
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1504
CMI-2019-DataScience-A: 2
If $P(A\cup B)=0.7$ and $P(A\cup B^c)=0.9$ then find $P(A).$
If $P(A\cup B)=0.7$ and $P(A\cup B^c)=0.9$ then find $P(A).$
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1505
CMI-2019-DataScience-A: 3
Which of the following statements are true for all $n\times n$ matrices $A,B:$ $(A^T)^T=A$ $|A^T|=|A|$ $(AB)^T=A^TB^T$ $(A+B)^T=A^T+B^T$
Which of the following statements are true for all $n\times n$ matrices $A,B:$$(A^T)^T=A$$|A^T|=|A|$$(AB)^T=A^TB^T$$(A+B)^T=A^T+B^T$
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1506
CMI-2019-DataScience-A: 4
Let $A=\begin{bmatrix} 1& 1& 1\\0&2&2\\0&0&3 \end{bmatrix}, B=\begin{bmatrix} 5&5&5\\0&10&10\\0&0&15\end{bmatrix}, C=\begin{bmatrix} 3&0&0\\3&6&0\\3&6&9 \end{bmatrix}$. Which of the following statements are true? $|A|=|B|$ $|B|=125|A|$ $|C|=27|A|$ $|C|=\frac{|A|}{3}$
Let $A=\begin{bmatrix} 1& 1& 1\\0&2&2\\0&0&3 \end{bmatrix}, B=\begin{bmatrix} 5&5&5\\0&10&10\\0&0&15\end{bmatrix}, C=\begin{bmatrix} 3&0&0\\3&6&0\\3&6&9 \end{bmatrix}$. W...
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1507
CMI-2019-DataScience-A: 5
Consider the polynomials $p(x)=(5x^2+6x+1)(x+1)(2x+3)$ and $q(x)=(5x^2-9x-2)(2x^2+5x+3)$. The set of common divisors of $p(x)$ and $q(x)$ is: $\{2x+3,\;x+1,\;5x+1\}$ $\{2x+3,\;x-1,\;5x+1\}$ $\{x+3,\;2x+1,\;x-2\}$ $\{2x-3,\;x+1,\;5x+1\}$
Consider the polynomials $p(x)=(5x^2+6x+1)(x+1)(2x+3)$ and $q(x)=(5x^2-9x-2)(2x^2+5x+3)$. The set of common divisors of $p(x)$ and $q(x)$ is:$\{2x+3,\;x+1,\;5x+1\}$$\{2x+...
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1510
CMI-2019-DataScience-A: 8
Consider the following Venn diagram. The universal set $U$ is the set of all natural numbers from $1$ to $1000.$ The sets $A,B,C$ contain integers in $U$ that are multiples of $6,7,8$ respectively. The number of elements in the shaded region is: $12$ $15$ $16$ $17$
Consider the following Venn diagram. The universal set $U$ is the set of all natural numbers from $1$ to $1000.$ The sets $A,B,C$ contain integers in $U$ that are multipl...
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1512
CMI-2019-DataScience-A: 10
$\text{Description for the following question:}$ The following table gives the budget allocation (in Rupees Crores) to $5$ ... percentage of total allocation, the maximum quarterly expenditure ( in any quarter) was shown by $D2$ $D5$ $D1$ $D3$
$\text{Description for the following question:}$The following table gives the budget allocation (in Rupees Crores) to $5$ different departments and their quarterly expend...
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1513
CMI-2019-DataScience-A: 11
$\text{Description for the following question:}$ The following table gives the budget allocation (in Rupees Crores) to $5$ ... quarter is concerned? $Q4<Q1<Q3<Q2$ $Q1<Q4<Q2<Q3$ $Q4<Q1<Q2<Q3$ $Q1<Q4<Q3<Q2$
$\text{Description for the following question:}$The following table gives the budget allocation (in Rupees Crores) to $5$ different departments and their quarterly expend...
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1517
CMI-2019-DataScience-A: 15
The sum of the diagonal elements of a matrix $A$ is called the trace of $A$ and is denoted by $tr(A)$. Which of the following statements about the trace are true? $\text{tr(A+B)=tr(A)+tr(B)}$ $\text{tr(2A)=2tr(A)}$ $\text{tr($A^T$)=tr(A)}$ $\text{tr($A^{-1}$)=tr(A)}$
The sum of the diagonal elements of a matrix $A$ is called the trace of $A$ and is denoted by $tr(A)$. Which of the following statements about the trace are true?$\text{t...
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