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GATE2019 CE1: 1
Which one of the following is correct? $\lim_{x\rightarrow 0} ( \frac{sin4x}{sin2x})=2 $ and $\lim_{x\rightarrow 0} ( \frac{tanx}{x})=1$ $\lim_{x\rightarrow 0} ( \frac{sin4x}{sin2x})=1$ and $\lim_{x\rightarrow 0} ( \frac{tanx}{x})=1$ ... $\lim_{x\rightarrow 0} ( \frac{sin4x}{sin2x})=2$ and $\lim_{x\rightarrow 0} ( \frac{tanx}{x})= \infty$
answered
3 days
ago
in
Calculus
by
Kushagra गुप्ता
(
140
points)
gate2019ce1
calculus
limit
0
votes
0
answers
2
2015 gate mcq true or false type
State true statement for degree of disturbance of collected soil sample
asked
Dec 19, 2019
in
Soil Mechanics
by
Pratikshanere
(
120
points)
0
votes
0
answers
3
GATE2015255
Two Pegs A and B were fixed on opposite banks of a $50$ m wide river. The level was set up at A and the staff readings on Pegs A and B were observed as $1.350$ m and $1.550$ m, respectively. Thereafter the instrument was shifted and set up at B. The staff reading on Pegs B and ... m and $0.550$ m, respectively. If the R.L. of Peg A is $100.200$ m, the R.L. (in m) of Peg B is _______.
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Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
4
GATE2015251
The relation between speed $u$ (in km/h) and density $k$ (number of vehicles/km) for a traffic stream on a road is $u=700.7k$. The capacity on this road is _________ vph (vehicles/hour).
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Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
5
GATE2015250
In a wastewater treatment plant, primary sedimentation tank (PST) designed at an overflow rate of $32.5 \: m^3/day/m^2$ is $32.5$ m long, $8.0$ m wide and liquid depth of $2.25$ m. If the length of the weir is $75$ m, the weir loading rate (in $m^3/day/m$) is ______.
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Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
6
GATE2015248
A water treatment plant of capacity, $1 \: m^3/s$ has filter boxed of dimensions $6 \; m \times 10 \: m$. Loading rate to the filters is $120 \: m^3/day/m^2$. When two of the filters are out of service for back washing, the loading rate (in $m^3/day/m^2$) is _________.
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Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
7
GATE2015247
A landfill is to be designed to serve a population of $200000$ for a period of $25$ years. The solid waste (SW) generation is $2$ kg/person/day. The density of the uncompacted SW is $100 \: kg/m^3$ and a compaction ratio of $4$ is suggested. The ratio of compacted fill (i.e., SW+cover) to compacted SW is $1.5$. The landfill volume (in $million \: m^3$) required is _________.
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Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
8
GATE2015246
A pipe of $0.7$ m diameter has a length of $6$ km and connects two reservoirs A and B. The water level in reservoir A is at an elevation $30$ m above the water level in reservoir B. Halfway along the pipe line, there is a branch through which water can be supplied ... to gravity as $9.81 \: m/s^2$ and neglecting minor losses, the discharge (in $m^3/s$) into the reservoir B is _______.
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Nov 29, 2019
in
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by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
9
GATE2015243
A triangular gate with a base width of $2$ m and a height of $1.5$ m lies in a vertical plane. The top vertex of the gate is $1.5$ m below the surface of a tank which contains oil of specific gravity $0.8$. Considering the density of water and acceleration due ... $9.81 m/s^2$ respectively, the hydrostatic force (in kN) exerted by the oil on the gate is _________.
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Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
10
GATE2015242
A field channel has cultivable commanded are of $2000$ hectares. The intensities of irrigation for gram and wheat are $30 \%$ and $50\%$ respectively. Gram has a kor period of $18$ days, kor depth of $12$ cm, while wheat has a kor period of $18$ ... cm. The discharge (in $m^3/s$) required in the filed channel to supply water to the commanded area during the kor period is ________.
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Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
11
GATE2015239
A pile of diameter $0.4$ m is fully embedded in a clay stratum having $5$ layers, each $5$ m thick as shown in the figure below. Assume a constant unit weight of soil as $18 \: kN/m^3$ for all the layers. Using $\lambda$method. ($ \lambda = 0.15$ for $25$ m embedment length) and neglecting the end bearing component the ultimate pile capacity (in kN) is ___________.
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Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
12
GATE2015238
A $4$ m thick layer of normally consolidated clay has an average void ratio of $1.30$. Its compression index is $0.6$ and coefficient of consolidation is $1 \: m^2/yr$. If the increase in vertical pressure due to foundation load on the clay layer is equal to the existing effective overburden pressure, the change in the thickness of the clay layer is _______ mm.
retagged
Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
13
GATE2015237
A $588 \: cm^3$ volume of moist sand weighs $1010$ gm. Its dry weight is $918$ gm and specific gravity of solids, $G$ is $2.67$. Assuming density of water as $1 \: gm/cm^3$, the void ratio is _________.
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Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
14
GATE2015234
According to the concept of Limit State Design as per $IS \: 456:2000$, the probability of failure of a structure is ______.
retagged
Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
15
GATE2015233
A simply supported beam AB of span, $L=24$ m is subjected to two wheel loads acting at a distance, $d=5$ m apart as shown in the figure below. Each wheel transmits a load, $P=3$ kN and may occupy any position along the beam. If the beam is an $I$section having section modulus, $S=16.2 \:cm^3$, the maximum bending stress (in GPa) due to the wheel loads is _______.
edited
Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
16
GATE2015232
A steel strip of length $L=200$ mm is fixed at end $A$ and rests at $B$ on a vertical spring of stiffness, $k=2 \: N/mm$. The steel strip is $5$ mm wide and $10$ mm thick. A vertical load, $P=50$ N is applied at $B$, as shown in the figure. Considering $E=200$ GPa, the force (in N) developed in the spring is ________.
edited
Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
17
GATE2015231
A simply supported reinforced concrete beam of length $10$ m sags while undergoing shrinkage. Assuming a uniform curvature of $0.004 m^{1}$ along the span, the maximum deflection (in m) of the beam at midspan is __________.
retagged
Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
18
GATE2015229
For stepsize, $\Delta x =0.4$, the value of following integral using Simpson’s $1/3$ rule is _______. $\int_0^{0.8} (0.2 + 25 x – 200 x^2 + 675 x^3 – 900 x^4 +400 x^5) dx$
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Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
19
GATE2015227
Consider the following second order linear differential equation $\dfrac{d^2y}{dx^2} = 12x^2 +24 x – 20$ The boundary conditions are: at $x=0, \: y=5$ and at $x=2, \: y=21$. The value of $y$ at $x=1$ is _________.
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Nov 29, 2019
in
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by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
20
GATE2015226
The probability density function of a random variable, $x$ is $\begin{array} \text{f(x)} & \text{=} & \dfrac{x}{4} ( 4x^2) & \text{ for } 0 \leq x \leq 2 \\ {} & = & 0 & \text{ otherwise} \end{array}$ The mean $\mu _x$ of the random variable is ______.
retagged
Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
21
GATE2015224
In a leveling work, sum of the Back Sight (B.S.) and Force Sight (F.S.) have been found to be $3.085$ m and $5.645$ m respectively. If the Reduced Level (R.L.) of the starting station is $100.000$ m, the R.L. (in m) of the last station is ________.
retagged
Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
22
GATE2015220
A groundwater sample was found to contain $500$ mg/L total dissolved solids (TDS). TDS (in %) present in the sample is ________.
retagged
Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
23
GATE2015217
A nozzle is so shaped that the average flow velocity changes linearly from $1.5$ m/s at the beginning to $15$ m/s at its end in a distance of $0.375$m. The magnitude of the convective acceleration (in $m/s^2$ ) at the end of the nozzle is ________.
retagged
Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
24
GATE201522
In newtonRaphson iterative method, the initial guess value $(x_{\text{ini}})$ is considered as zero while finding the roots of the equation: $f(x) = 2+6x4x^2+0.5x^3$. The correction, $\Delta x$, to be added to $x_{\text{ini}}$ in the first iteration is _________
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Nov 29, 2019
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by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
25
GATE20152GA8
How many four digit numbers can be formed with the $10$ digits $0,1,2,…,9$ if no number can start with $0$ and if repetitions are not allowed?
retagged
Nov 29, 2019
in
Numerical Ability
by
jothee
(
100
points)
gate2015ce2
numericalanswers
0
votes
0
answers
26
GATE2015155
In a region with magnetic declination of $2^{\circ}E$, the magnetic Fore bearing (FB) of a line $AB$ was measured as $N79^{\circ}50'E$. There was local attraction at $A$. To determine the correct magnetic bearing of the line, a point $O$ was selected at which there was no local ... true $FB$ of line $AB?$ $N81^{\circ}50'E$ $N82^{\circ}10'E$ $N84^{\circ}10'E$ $N77^{\circ}50'E$
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jothee
(
100
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gate2015ce1
0
votes
0
answers
27
GATE2015152
On a circular curve, the rate of superelevation is $e$. While negotiating the curve a vehicle comes to a stop. It is seen that the stopped vehicle does not slide inwards (in the radial direction). The coefficient of side friction is $f$. Which of the following is true: $e \leq f$ $f < e < 2f$ $e \geq 2f$ none of the above
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Nov 29, 2019
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by
jothee
(
100
points)
gate2015ce1
0
votes
0
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28
GATE2015148
The $4$hr unit hydrograph for a catchment is given in the table below. What would be the maximum ordinate of the S  curve (in $m^3/s$ ...
retagged
Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce1
numericalanswers
0
votes
0
answers
29
GATE2015146
The drag force, $F_D$, on a sphere kept in a uniform flow field, depends on the diameter of the sphere $D$; flow velocity, $V$, fluid density, $\rho$; and dynamic viscosity, $\mu$. Which of the following options represents the nondimensional parameters which could be used to analyze this problem ... $\frac{_{\rho}VD}{\mu}$ $\frac{F_D}{_{\rho}V^3D^3}$ and $\frac{\mu}{_{\rho}VD}$
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Nov 29, 2019
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by
jothee
(
100
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gate2015ce1
0
votes
0
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30
GATE2015139
A water tank is to be constructed on the soil deposit shown in the figure below. A circular footing of diameter $3$ m and depth of embedment $1$ ... the load dispersion pattern as $2V:1H$. The expected settlement of the tank due to primary consolidation of the clay layer is _________ mm.
edited
Nov 29, 2019
in
Others
by
jothee
(
100
points)
gate2015ce1
numericalanswers
0
votes
0
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31
GATE2015136
Two beams are connected by a linear spring as shown in the following figure. For a load $P$ as shown in the figure, the percentage of the applied load $P$ carried by the spring is _________.
edited
Nov 29, 2019
in
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by
jothee
(
100
points)
gate2015ce1
numericalanswers
0
votes
0
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32
GATE2015135
A tapered circular rod of diameter varying from $20$ mm to $10$ mm is connected to another uniform circular rod of diameter $10$ mm as shown in the following figure. Both bars are made of same material with the modulus of elasticity, $E=2 \times 10^5$ MPa. When subjected to a load $P=30 \pi$ kN, the deflection at point $A$ is ______ mm.
edited
Nov 29, 2019
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jothee
(
100
points)
gate2015ce1
numericalanswers
0
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0
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33
GATE2015134
For formation of $\textit{collapse mechanism}$ in the following figure, the minimum value of $P_u$ is $cM_p/L$. $M_p$ and $3M_p$ denote the plastic moment capacities of beam sections as shown in this figure. The value of $c$ is ________.
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jothee
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100
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gate2015ce1
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0
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34
GATE2015133
Consider the singly reinforced beam section given below (left figure). The stress block parameters for the crosssection from $IS:4562000$ are also given below (right figure). The moment of resistance for the given section by the limit state method is _______ kNm
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100
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gate2015ce1
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35
GATE2015131
The composition of an airentrained concrete is given below: ... gravity of OPC, sand and coarse aggregate to be $3.14$, $2.67$, and $2.74$, respectively. The air content is ______ $liters/m^3$.
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gate2015ce1
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36
GATE2015130
The directional derivative of the field $u(x,y,z) = x^23yz$ in the direction of the vector $(\hat{i}+\hat{j}2 \hat{k})$ at point $(2, 1, 4)$ is _________.
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37
GATE2015127
The quadratic equation $x^2 – 4x +4 =0$ is to be solved numerically, starting with the initial guess $x_0=3$. The NewtonRaphson method is applied once to get a new estimate and then the Secant method is applied once using the initial guess and this new estimate. The estimated value of the root after the application of the Secant method is _________.
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100
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gate2015ce1
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38
GATE2015123
Which of the following statements CANNOT be used to describe free flow speed $(u_f)$ of a traffic stream? $(u_f)$ is the speed when flow is negligible $(u_f)$ is the speed when density is negligible $(u_f)$ is affected by geometry and surface conditions of the road $(u_f)$ is the speed at which flow is maximum and density is optimum
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(
100
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gate2015ce1
0
votes
0
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39
GATE2015122
The penetration value of a bitumen sample tested at $25^{\circ}C$ is $80$. When this sample is heated to $60^{\circ}C$ and tested again, the needle of the penetration test apparatus penetrates the bitumen sample by $d$ mm. The value of $d$ CANNOT be less than ______ mm.
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100
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gate2015ce1
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0
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40
GATE2015120
Total Kjeldahl Nitrogen (TKN) concentration (mg/L as N) in domestic sewage is the sum of the concentrations of organic and inorganic nitrogen in sewage organic nitrogen and nitrate in sewage organic nitrogen and ammonia in sewage ammnia and nitrate in sewage
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100
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gate2015ce1
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41
GATE2015119
The two columns below show some parameters and their possible values. ...  IV, R  I, S  V P  I, Q  V, R  VI, S  II P  III, Q  II, R  V, S  IV
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42
GATE2015118
A circular pipe has a diameter of $1$ m, bed slope of $1$ in $1000$, and Manning's roughness coefficient equal to $0.01$. It may be treated as an open channel flow when it is flowing just full, i.e., the water level just touches the crest. The discharge in this condition is denoted ... by $Q_{\text{half}}$. The ratio $Q_{\text{full}} / Q_{\text{half}}$ is $1$ $\sqrt{2}$ $2$ $4$
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100
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gate2015ce1
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43
GATE2015113
Which of the following statements is TRUE for degree of disturbance of collected soil sample? Thinner the sampler wall, lower the degree of disturbance of collected soil sample Thicker the sampler wall, lower the degree of disturbance of collected soil ... sample are unrelated The degree of disturbance of collected soil sample is proportional to the inner diameter of the sampling tube
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44
GATE2015111
A finegrained soil has $60 \%$ (by weight) slit content. The soil behaves as $\textit{semisolid}$ when water content is between $15 \%$ and $28 \%$. The soil behaves $\textit{fluidlike}$ when the water content is more than $40 \%$. The $’\textit{Activity}\:’$ of the soil is $3.33$ $0.42$ $0.30$ $0.20$
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45
GATE2015110
Two triangular wedges are glued together as shown in the following figure. The stress acting normal to the interface, $\sigma_n$ is _______ MPa.
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100
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gate2015ce1
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46
GATE201519
For the beam shown below, the value of the support moment $M$ is _____ $kNm$.
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100
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gate2015ce1
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47
GATE201513
Consider the following probability mass function (p.m.f) of a random variable $X:$ $p(x,q) = \begin{cases} q & \text{ if } X=0 \\ 1 – q & \text{ if } X=1 \\ 0 & \text{otherwise} \end{cases} $ If $q=0.4$, the variance of $X$ is _________
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48
GATE201511
For what value of $p$ the following set of equations will have no solution? $2x+3y=5$ $3x+py=10$
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49
GATE20151GA8
The exports and imports (in crores of Rs.) of a country from the year $2000$ to $2007$ are given in the following bar chart. In which year is the combined percentage increase in imports and exports the highest?
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Nov 29, 2019
in
Numerical Ability
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100
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gate2015ce1
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50
GATE2015154
In a survey work, three independent angles $X, Y$ and $Z$ were observed with weights $W_X, W_Y, W_Z$,respectively. The weight of the sum of angles $X, Y$ and $Z$ is given by: $1/ \big( \frac{1}{W_X} + \frac{1}{W_Y} + \frac{1}{W_Z} \big)$ $\big( \frac{1}{W_X} + \frac{1}{W_Y} + \frac{1}{W_Z} \big)$ $W_X +W_Y+W_Z$ $W_X^2 +W_Y^2+W_Z^2$
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