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Subject - Wise Solutions to Your Questions

Trending Questions

Q:
If a random variable \( X \) has the probability distribution:
\[ P(X = x) = \begin{cases} k, & \text{if } x = 0 \\ 2k, & \text{if } x = 1 \text{ or } 2 \\ 0, & \text{otherwise} \end{cases} \] then the value of \( k \) is
View Solution
Q:
The slope of the normal to the curve \( y = \frac{x - 3}{x - 4} \) at \( x = 6 \) is
View Solution
Q:
If \( \left| \begin{array}{cc} 2x & 5 \\ 4 & x \end{array} \right| = \left| \begin{array}{cc} 3 & 5 \\ 4 & 6 \end{array} \right| \), then the value of \( x \) is:
View Solution
Q:
The inverse of matrix \( A = \begin{bmatrix} 4 & -1 \\ 2 & 1 \end{bmatrix} \) is
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Q:
If $a>b$ and $c<0$, then which of the following is true?
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Q:
Fit a straight-line trend by the method of least squares for the following data:
\begin{tabular}{lcccccc} Year: & 2011 & 2012 & 2013 & 2014 & 2015 & 2016
Production (in tons): & 210 & 225 & 275 & 220 & 240 & 235
\end{tabular}
View Solution
Q:
Using properties of determinants, prove that
\[ \Delta = (b+c)^2 & a^2 & a^2
b^2 & (c+a)^2 & b^2
c^2 & c^2 & (a+b)^2 = 2abc(a + b + c)^3 \]
View Solution
Q:
Solve the following linear programming problem graphically:
Maximize $z = 50x + 30y$
Subject to:
$2x + y \leq 18$
$3x + 2y \leq 34$
$x \geq 0$, $y \geq 0$
View Solution
Q:
A machinist is making engine parts with axle diameter of 0.7 cm. A random sample of 10 parts shows mean diameter 0.742 cm with a standard deviation of 0.04 cm. On the basis of this sample, find if you would say that the work is inferior.
(Given $t_9(0.05) = 2.262$)
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Q:
If the supply function is $p = 4 - 5x + x^2$, then find the producer’s surplus when price is 18.
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Q:
Compute the seasonal indices by 4-year moving averages from the given data of production of paper (in thousand tons):
\begin{tabular}{lcccccccccccc} Year: & 2001 & 2002 & 2003 & 2004 & 2005 & 2006 & 2007 & 2008 & 2009 & 2010
Index: & 2450 & 1470 & 2150 & 1800 & 1210 & 1950 & 2300 & 2500 & 2480 & 2680
\end{tabular}
View Solution
Q:
If $A = 2 & -3 & 5
3 & 2 & -4
1 & 1 & -2 $, find $A^{-1}$ and hence solve the system of equations:
$2x - 3y + 5z = 11$
$3x + 2y - 4z = -5$
$x + y - 2z = -3$
View Solution
Q:
Calculate EMI under Flat-Rate System for a loan of ₹ 5,00,000 with 7.5% annual interest rate for 5 years.
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Q:
The mortality rate for a certain disease is 0.007. Using Poisson distribution, calculate the probability for 2 deaths in a group of 400 people. [Use $e^{-2.8} = 0.0608$]
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Q:
If the mean and variance of a binomial distribution are $\dfrac{4}{3}$ and $\dfrac{8}{9}$ respectively, then find $P(X = 1)$.
View Solution
Q:
Given $A = 2 & 0 & 1
3 & 4 & 5
0 & 2 & 3 $ and $B = 1 & 1 & -5
-5 & 1 & -5
1 & -2 & 4 $, find $BA$.
View Solution
Q:
Given that the mean of a normal variate $X$ is 9 and standard deviation is 3, then find:
(i) the z-score of the data point 15
(ii) the data point if its z-score is 4
View Solution
Q:
There are two types of fertilizers $F_1$ and $F_2$. $F_1$ consists of 10% nitrogen and 6% phosphoric acid. $F_2$ consists of 5% nitrogen and 10% phosphoric acid.
After testing the soil conditions, a farmer finds that he needs at least 14 kg of nitrogen and 14 kg of phosphoric acid for his crop.
If $F_1$ costs ₹ 6 per kg and $F_2$ costs ₹ 5 per kg, how much of each type of fertilizer should be used so that the cost is minimum.
Formulate a linear programming problem.
View Solution

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