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1
The ratio of boys to girls in a class is $7$ to $3$. Among the options below, an acceptable value for the total number of students in the class is $21$ $37$ $50$ $73$
answered Jun 27 in Numerical Ability Sharanam 140 points
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2
Some people suggest anti-obesity measures $\text{(AOM)}$ such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality. Which one of the following statements summarizes the ... $\text{AOM}$ are addressing the problem superficially
recategorized Apr 11 in Verbal Ability Lakshman Patel RJIT 100 points
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3
If the area of a triangle with the vertices $(k,0), (2,0)$ and $(0, -2)$ is $2$ square units, the value of $k$ is _________
recategorized Apr 11 in Calculus Lakshman Patel RJIT 100 points
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4
The value of $\underset{x \to 0} \lim \left [ \dfrac{x- \sin 2x}{x-\sin 5x} \right]$ (rounded off to two decimal places) is __________
recategorized Apr 11 in Calculus Lakshman Patel RJIT 100 points
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5
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6
$\dfrac{d}{dx} \left [ \ln (2x) \right ]$ is equal to $1/2x \\$ $1/x \\$ $1 /2 \\$ $x$
recategorized Apr 11 in Calculus Lakshman Patel RJIT 100 points
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7
The Cartesian coordinates $(x,y)$ of a point $A$ with polar coordinates $\left ( 4, \pi/4 \right)$ is $ \left( \sqrt{3}, 2 \sqrt{2} \right ) \\$ $ \left( 2, 2 \sqrt{3} \right ) \\$ $ \left( 2\sqrt{2}, \sqrt{3} \right ) \\$ $ \left( 2 \sqrt{2}, 2 \sqrt{2} \right )$
recategorized Apr 11 in Calculus Lakshman Patel RJIT 100 points
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8
Given below are two statements $1$ and $2$, and two conclusions $I$ and $II$. $\text{Statement 1}$: All bacteria are microorganisms. $\text{Statement 2}$: All pathogens are microorganisms. $\text{Conclusion I}$: Some pathogens are bacteria. $\text{Conclusion II}$: All ... is correct Either conclusion $\text{I}$ or $\text{II}$ is correct Neither conclusion $\text{I}$ nor $\text{II}$ is correct
recategorized Apr 11 in Analytical Aptitude Lakshman Patel RJIT 100 points
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9
A circular sheet of paper is folded along the lines in the direction shown. The paper, after being punched in the final folded state as shown and unfolded in the reverse order of folding, will look like ________.
recategorized Apr 11 in Spatial Aptitude Lakshman Patel RJIT 100 points
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10
There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability that at least two chocolates are identical is _________ $0.3024$ $0.4235$ $0.6976$ $0.8125$
recategorized Apr 11 in Numerical Ability Lakshman Patel RJIT 100 points
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11
Consider the following sentences: Everybody in the class is prepared for the exam. Babu invited Danish to his home because he enjoys playing chess. Which of the following is the $\text{CORRECT}$ observation about the above two sentences? $\text{(i)}$ is grammatically correct and ... correct and $\text{(ii)}$ is ambiguous $\text{(i)}$ is grammatically incorrect and $\text{(ii)}$ is ambiguous
recategorized Apr 11 in Verbal Ability Lakshman Patel RJIT 100 points
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12
A polygon is convex if, for every pair of points, $P$ and $Q$ belonging to the polygon, the line segment $PQ$ lies completely inside or on the polygon. Which one of the following is $\underline {\text{NOT}}$ a convex polygon?
recategorized Apr 11 in Spatial Aptitude Lakshman Patel RJIT 100 points
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13
____________ is to $\textit{surgery}$ as $\textit{writer}$ is to __________ Which one of the following options maintains a similar logical relation in the above sentence? Plan, outline Hospital, library Doctor, book Medicine, grammar
recategorized Apr 11 in Verbal Ability Lakshman Patel RJIT 100 points
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14
We have $2$ rectangular sheets of paper, $M$ and $N$, of dimensions $6$ cm $\times$ $1$ cm each. Sheet $M$ is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet $N$ is cut into equal square patches and assembled to form the largest possible closed cube. ... to that of the cube is _____________ $\frac{\pi}{2}\\$ $\frac{3}{\pi} \\$ $\frac{9}{\pi} \\$ $3 \pi$
recategorized Apr 11 in Numerical Ability Lakshman Patel RJIT 100 points
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15
$\begin{array}{|c|c|c|c|} \hline \textbf{Items} & \textbf{Cost} & \textbf{Profit} \% & \textbf{Marked Price} \\ & (₹) && (₹) \\ \hline P & 5,400 & \dots & 5,860 \\ \hline Q & \dots & 25 & 10,000 \\ \hline \end{array}$ ... $Q$, as a percentage of its marked price, is ___________ $25$ $12.5$ $10$ $5$
recategorized Apr 11 in Numerical Ability Lakshman Patel RJIT 100 points
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16
If the values of two random variables $(X,Y)$ are $(121, 360)$, $(242, 364)$ and $(363, 362)$, the value of correlation coefficient between $X$ and $Y$ (rounded off to one decimal place) is ________.
recategorized Apr 11 in Probability and Statistics Lakshman Patel RJIT 100 points
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17
The determinant of matrix $A = \begin{pmatrix} 1 & 1& 1 & 1 \\ -1 & 1 & 1 & 1 \\ -1 & -1 & 1 & 1 \\ 1 & 1 & 1 & 3 \end{pmatrix}$ is __________.
recategorized Apr 11 in Linear Algebra Lakshman Patel RJIT 100 points
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18
Calculate the following integral $\int \limits_0^{\pi^2/4} \sin \sqrt{x} dx =$____________.
recategorized Apr 11 in Calculus Lakshman Patel RJIT 100 points
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19
A system consists of two reactors, connected by a valve. The first reactor $(R1)$ contains an ideal gas $A$ of volume $5\: L$ and the second reactor $(R2)$ has an ideal gas $B$ of volume $10\: L$. Initially, the valve is closed and ... equilibrium. If the temperature $T$ of both the reactors is maintained constant, the final equilibrium pressure in $\textit{atm}$ of the system is _____________
answer reshown Apr 9 in Others prateeksinha 140 points
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20
Under standard temperature $(T)$ and pressure $(P)$ conditions, $128 \: g$ of an ideal has molecule $A$ occupies a volume of $1 \: L$. The gas molecule $A$ obeys the relationship $\text{RT=0.25 PV}$. $R$ and $V$ are universal gas constant and ideal gas volume, respectively. The molecule $A$ is $\text{CO}_2$ $\text{H}_2$ $\text{N}_2$ $\text{O}_2$
retagged Mar 18 in Others Lakshman Patel RJIT 100 points
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21
The largest eigenvalue of the matrix $\begin{bmatrix} 4 &1 \\ -2& 1 \end{bmatrix}$ is ______________.
recategorized Mar 18 in Linear Algebra Lakshman Patel RJIT 100 points
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22
A normal random variable has mean equal to $0$, and standard deviation equal to $3$. The probability that on a random draw the value of this random variable is greater than $0$ is __________ (round off to $2$ decimal places).
recategorized Mar 18 in Probability and Statistics Lakshman Patel RJIT 100 points
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23
The system of linear equations $cx+y=5$ $3x+3y=6$ has no solution when $c$ is equal to _______________________.
recategorized Mar 18 in Linear Algebra Lakshman Patel RJIT 100 points
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24
A function $f$ is given as : $f(X)=4X-X^{2}$ The function $f$ is maximized when $X$ is equal to _________________.
recategorized Mar 18 in Calculus Lakshman Patel RJIT 100 points
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25
An infinite series $S$ is given as: $S=1+2/3+3/9+4/27+5/81+\:.\dots$ (to infinity) The value of $S$ is ______________________ (round off to $2$ decimal places).
recategorized Mar 18 in Calculus Lakshman Patel RJIT 100 points
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26
A function $f$ is as follows: $f(x) = \begin{cases} 15 & \text{if }x<1 \\ cx& \text{if } x\geq 1 \end{cases}$ The function $f$ is a continuous function when $c$ is equal to ____________________ (answer in an integer).
recategorized Mar 18 in Calculus Lakshman Patel RJIT 100 points
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27
A variable $Y$ is a function of $t$. Given that $Y\left ( t=0 \right )=1$ and $Y\left ( t=1 \right )=2,\dfrac{dY}{dt}$ in the interval $t=\left [ 0,1 \right ]$ can be approximated as _________________.
retagged Mar 18 in Others Lakshman Patel RJIT 100 points
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28
If $1+r + r^2+ r^3 +\dots \infty = 1.5$, then, $1 + 2r + 3r^2 + 4r^3 + \dots \infty = $ (up to two dcimal places) ________
retagged Mar 18 in Calculus Lakshman Patel RJIT 100 points
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29
Consider the following infinite series: $1+ r+r^2 +r^3+ \dots \dots \infty$ If $r = 0.3$, then the sum of this infinite series is ____________
retagged Mar 18 in Calculus Lakshman Patel RJIT 100 points
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30
Which of the following are geometric series? $1,\:6,\:11,\:16,\:21,\:26,\:\dots$ $9,\:6,\:3,\:0,\:-3,\:-6,\:\dots$ $1,\:3,\:9,\:27,\:81,\:\dots$ $4,\:-8,\:16,\:-32,\:64,\:\dots$ $P$ and $Q$ only $R$ and $S$ only $Q$ and $S$ only $P, Q$ and $R$ only
retagged Mar 18 in Calculus Lakshman Patel RJIT 100 points
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31
Given that $Z=X^{2}+Y^{2}$, the value of $\dfrac{\partial Z}{\partial X}$ for $X=1$ and $Y=0$ is ________________ (answer is an integer).
retagged Mar 18 in Others Lakshman Patel RJIT 100 points
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32
The solution of $ \underset{x\rightarrow 8 }\lim\left ( \dfrac{x^{2}-64}{x-8} \right )$ is _____________.
recategorized Mar 18 in Calculus Lakshman Patel RJIT 100 points
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33
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34
$\int _{-1}^{1}\:f\left ( x \right )dx$ calculated using trapezoidal rule for the values given in the table is ______ (rounded off to $2$ ...
recategorized Mar 18 in Numerical Methods Lakshman Patel RJIT 100 points
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35
Matrix $A=\begin{bmatrix} 0&6 \\ p&0 \end{bmatrix}$ will be skew-symmetric when $p$= ____.
recategorized Mar 18 in Linear Algebra Lakshman Patel RJIT 100 points
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36
The Laplace transform of the function $f\left ( t \right )=t^{2}+2t+1$ is $\dfrac{1}{s^{3}}+\dfrac{3}{s^{2}}+\dfrac{1}{s} \\$ $\dfrac{4}{s^{3}}+\dfrac{4}{s^{2}}+\dfrac{1}{s} \\$ $\dfrac{1}{s^{3}}+\dfrac{2}{s^{2}}+\dfrac{1}{s} \\$ $\dfrac{2}{s^{3}}+\dfrac{2}{s^{2}}+\dfrac{1}{s}$
retagged Mar 18 in Others Lakshman Patel RJIT 100 points
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37
What is the solution of the differential equation $\dfrac{\mathrm{dy} }{\mathrm{d} x}=\dfrac{x}{y}$, with the initial condition, at $x=0, y=1?$ $x^{2}=y^{2}+1$ $y^{2}=x^{2}+1$ $y^{2}=2x^{2}+1$ $x^{2}-y^{2}=0$
retagged Mar 18 in Others Lakshman Patel RJIT 100 points
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38
Which one of the following equations represents a one-dimensional wave equation? $\dfrac{\partial u}{\partial t}=C^{2}\dfrac{\partial ^{2}u}{\partial x^{2}} \\$ $\dfrac{\partial ^{2}u}{\partial t^{2}}=C^{2}\dfrac{\partial ^{2}u}{\partial x^{2}} \\$ ... $\dfrac{\partial ^{2}u}{\partial t^{2}}+\dfrac{\partial ^{2}u}{\partial x^{2}}=0$
retagged Mar 18 in Others Lakshman Patel RJIT 100 points
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39
The variable $z$ has a standard normal distribution. If $P(0 \leq z \leq 1)= 0.34$ then $P(z^2 > 1)$ is equal to (up to two decimal places) ____________
recategorized Mar 18 in Probability and Statistics Lakshman Patel RJIT 100 points
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40
The determinant of the matrix $\begin{pmatrix} 4 & -6 \\ -3 & 2 \end{pmatrix}$ is _________
recategorized Mar 18 in Linear Algebra Lakshman Patel RJIT 100 points
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