List of top Questions asked in GATE GG, GATE EY

Let $f(x)$ be a real-valued function such that $f'(x_0)=0$ for some $x_0 \in (0,1)$, and $f''(x) > 0$ for all $x \in (0,1)$. Then $f(x)$ has

The dimension of the sub-matrix $M$ in the Newton-Raphson Jacobian is $\underline{\hspace{2cm}}$.

Two discrete-time linear time-invariant systems with impulse responses $h_1[n] = \delta[n-1] + \delta[n+1]$ and $h_2[n] = \delta[n] + \delta[n-1]$ are connected in cascade. The impulse response of the cascaded system is

Let $p(z) = z^3 + (1 + j)z^2 + (2 + j)z + 3$, where $z$ is a complex number. Which one of the following is true?

A satellite orbits the Earth at an altitude of 700 km on the equatorial plane of the earth and it revolves in the same direction as the direction of rotation of the earth. Considering the radius of a spherical earth as 6300 km and the acceleration due to gravity as 10 m/s², the tangential velocity of the satellite in the orbit is $\underline{\hspace{1cm}}$ km/s. (round off to 2 decimal places)

A rock formed at time $ t_0 $ with number of $ ^{14}C $ atoms = $ 10^5 $. The number of $ ^{14}C $ atoms (in log10) after a time of $ 8 \times 10^3 $ years is $\underline{\hspace{1cm}}$ (round off to 3 decimal places). (Use a decay constant of $ 1.25 \times 10^{-4} \, \text{yr}^{-1} $)

The grade of copper (in wt%) of an ore body determined at locations 1, 2 and 3 are indicated (in parentheses) below. The grade of copper at an unknown location x calculated using Inverse-Square Distance Weighting (IDW) is $\underline{\hspace{1cm}}$ wt %. (round off to 2 decimal places)

The sketch shows a triangular rock mass (ABC) resting on a joint plane (AC) inclined at 35° with the horizontal. A rockbolt having an inclination of 25° with the horizontal is used to stabilize the slope. If the bolt tension (T) is 110 kN, the absolute value of shear force along the joint plane induced by the bolt tension is $\underline{\hspace{1cm}}$ kN.

In a zone of active normal faulting, the maximum and minimum in situ principal stresses (compressive in nature) are 30 MPa ($ \sigma_1 $) and 10 MPa ($ \sigma_3 $), respectively. The fault plane striking N-S has a dip amount of 60° towards E. Considering Anderson theory of faulting and using the given information, the calculated normal stress on the fault plane is $\underline{\hspace{1cm}}$ MPa. (in integer)

A circular tunnel is being excavated in a blocky rock mass by drilling and blasting. An excavation disturbed zone (EDZ) around the tunnel extends 0.70 m into the rock from the excavation surface. Considering the unit weight of the rock as 25 kN/m³, the support pressure required at the crown of the tunnel to stabilize the loose blocks of the EDZ is $\underline{\hspace{1cm}}$ kPa. (round off to one decimal place)

The mole percentages of $SiO_2$, $Al_2O_3$, and $K_2O$ in a granitic rock are 84.21, 7.89 and 7.89, respectively. The molar proportion (in %) of K-feldspar in the rock is $\underline{\hspace{1cm}}$ . (round off to one decimal place)

A mantle source rock melts at a time to giving rise to melt (M) and residue (R). Which of the following statements is CORRECT about evolution of the $( ^{143}Nd/^{144}Nd )$ and $( ^{87}Sr/^{86}Sr )$ isotope ratio in M (that crystallized to form a rock) and R?

Match the rock types in Group-I with their most likely corresponding lithospheric / tectonic settings of formation in Group-II
\[\begin{array}{|c|c|} \hline \textbf{Group I} & \textbf{Group II} \\ \hline \text{P. Boninite} & \text{1. Continental anorogenic} \\ \hline \text{Q. Lamproite} & \text{2. Island-arc} \\ \hline \text{R. Phonolite} & \text{3. Continental collision} \\ \hline \text{S. Leucogranite} & \text{4. Intraplate oceanic} \\ \hline \end{array}\]

The symmetry elements of a point group are: 3 crystallographic axes of 2-fold symmetry and 3 mirror planes perpendicular to the crystallographic axes. The Hermann – Mauguin notation of the point group is:

Match the items in Group-I with corresponding appropriate items in Group-II.
Group-I Group-II
P. Cs 1. Siderophile
Q. Au 2. Chalophile
R. Cd 3. Atmophile
S. Rn 4. Lithophile

With regard to the occurrence of groundwater in an area, which of the given statements is CORRECT?

The given outcrop pattern of a bed (shaded in grey) with respect to contours (dashed lines) indicates that the bed

With regard to superposed folding, the stereographic projection represents a geometry of:

Match the items in Group-I with appropriate items in Group-II

Match the following structures in Group I with the corresponding environment of deposition in Group II:

Match the following invertebrate genera in Group I with their corresponding Class/Phylum in Group II:
Group I Group II
P. Mytilus    1. Brachiopoda
Q. Planorbis 2. Cephalopoda
R. Productus    3. Gastropoda
S. Acanthoceras    4. Pelecypoda

Which one of the following equid genera was a one-toed grazer?

Based on the three statements given below, choose the CORRECT option:

Statement I: Gunderdehi Formation is a stratigraphic unit of the Chhattisgarh Supergroup.
Statement II: Raniganj Formation is a coal-bearing Triassic unit of the Gondwana Supergroup.
Statement III: Pitepani Volcanics is a stratigraphic unit of the Dongargarh Supergroup.

In the given reaction, \[ 2Fe^{2+} + 3H_2O \rightarrow Fe_2O_3 + 6H^+ + 2e^- \] consider ideal condition, take concentration of $ Fe^{2+} $ as $ 10^{-5} $ molal, $ E^0 = 0.98 \, \text{V} $ and pH = 6. The value of $ (2.303 \times R \times T / F) = 0.059 $ (where $ F $ is the Faraday constant). The value of $ E_h $ on the $ Fe^{2+} / $ hematite boundary at 25°C is $\underline{\hspace{1cm}}$ V (round off to 2 decimal places).

The first and second dissociation constants of $ \text{H}_2\text{CO}_3 $ are $ 6.761 \times 10^{-7} $ and $ 4.68 \times 10^{-11} $, respectively. If the concentration of $ \text{H}_2\text{CO}_3 $ is 1 molal and pH = 6, the $ \sum \text{CO}_2 $ in the solution (assuming ideal condition) is $\underline{\hspace{0cm}}$ molal. (round off to 3 decimal places)