List of top Geophysics Questions asked in CUET (PG)

The integral equation \[ y(x)=x+\int_0^3 \cos(x-t)y(t)\,dt \] is a:

For the asymptotes of an algebraic equation of degree \(n\), the value of \(m\) can be obtained by:
A. Putting \(y=mx\) in the highest degree term of equation,
B. Putting \(x=1,\ y=m\) in the highest degree term of equation,
C. Putting \(x=m,\ y=1\) in the lowest degree term of equation,
D. Putting \(x=1,\ y=m\) in the lowest degree term of equation.

The reduction formula for \(\int e^{ax}\cos bx\,dx\) is:

When a man jumps out of a boat, the boat moves backward because of:

Consider the following statements related to slopes and angles of lines:
A. The equation of a line which passes through the point \((x_1,y_1)\) and has the slope \(m\) is \(y-y_1=m(x-x_1)\),
B. The angle \(\theta\) between the lines having slopes \(m_1\) and \(m_2\) is given by \(\tan\theta=\pm\dfrac{m_2-m_1}{1+m_1m_2}\),
C. The acute angle \(\theta\) between two lines \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\) is given by \(\tan\theta=\left|\dfrac{a_2b_1-a_1b_2}{a_1a_2+b_1b_2}\right|\),
D. The equation of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(y-y_1=\left|\dfrac{y_2-y_1}{x_2-x_1}\right|(x-x_1)\).

The asymptotes parallel to \(x\)-axis of the curve \(y^3+x^2y+2xy^2-y+1=0\) is:

Match List-I with List-II. List-I:
A. \(\nabla\times\vec{r}\),
B. \(\operatorname{Div}(2x^2z\hat{i}-xy^2z\hat{j}+3yz^2\hat{k})\) at point \((1,1,1)\),
C. Curl of a vector is a,
D. Divergence of a vector is
A. List-II: I. Vector quantity, II. \(0\), III. Scalar quantity, IV. \(8\).

The equation of right circular cylinder of radius \(2\ \text{cm}\) whose axis passes through the point \((1,2,3)\) and has direction cosines proportional to \((2,-3,6)\) is:

Consider the following properties which are related to equations and their roots:
A. If \(1,\alpha,\beta,\gamma\) are roots of \(x^4-1=0\), then \((1-\alpha)(1-\beta)(1-\gamma)=0\),
B. If \(1,\alpha,\beta,\gamma\) are roots of \(x^4-1=0\), then \((1-\alpha)(1-\beta)(1-\gamma)=4\),
C. If \(\omega,\omega^2,\omega^3,\ldots,\omega^{n-1}\) are the imaginary roots of unity, then \((1-\omega)(1-\omega^2)\cdots(1-\omega^{n-1})=n-1\),
D. If \(\omega,\omega^2,\omega^3,\ldots,\omega^{n-1}\) are the imaginary roots of unity, then \((1-\omega)(1-\omega^2)\cdots(1-\omega^{n-1})=n\).

A non-homogeneous system of linear equation \(AX=B\) of \(n\) unknowns is called consistent if:

Which of the following are indeterminate forms?
A. \(0^0\),
B. \(1^\infty\),
C. \(\infty^0\),
D. \(0\times\infty\), E. \(1\cdot\infty\).

The equation of line passing through \((-3,5)\) and perpendicular to the line through the points \((2,5)\) and \((-3,6)\) is:

Given below are two statements:
Assertion (A): If a function \(f(x)\) is continuous in \([a,b]\) and differentiable in \((a,b)\), then there exists a point \(c\in(a,b)\) such that \(\dfrac{f(b)-f(a){b-a}=f'(c)\).
Reason (R): This is the statement of Cauchy's mean value theorem.}

Given below are two statements:
Assertion (A): Lyapunov direct method states that the equilibrium point of a system is asymptotically stable if there exists a positive definite function whose derivative is negative definite.
Reason (R): The equilibrium point of \(\dfrac{dx}{dt}=-y,\ \dfrac{dy}{dt}=x\) is asymptotically stable.

Which of the following quantity is not conserved in inelastic collision?

Evaluate \(\iint_S \vec{A}\cdot \hat{n}\,dS\), where \(\vec{A}=2y\hat{i}+yz\hat{j}+xz\hat{k}\) and \(S\) is the surface of the region bounded by \(x=0,\ y=0,\ z=0,\ y=3\) and \(x+2z=6\).

Consider the following differential equations which are obtained by successive differentiations. Choose the correct answer from the options given below.

The volume of the solid of revolution of the cardioid \(r=a(1+\cos\theta)\) about the initial line is:

Which motion is simple harmonic motion?

Given below are two statements:
Assertion (A): In photoelectric effect there is no time lag \((\sim10^{-9}s)\) between incidence of photon and emission of photoelectrons.
Reason (R): This is because electromagnetic wave energy is concentrated in photons and not spread out, so there should be no delay in the emission of electrons.

Calculate the entropy change in the following. Given latent heat of steam is \(540\ \text{cal/g}\), latent heat of ice is \(80\ \text{cal/g}\).
A. \(10g\) of water at \(100^\circ C\) converted to steam at same temperature,
B. \(20g\) of water at \(100^\circ C\) converted to steam at same temperature,
C. \(1g\) of ice at \(0^\circ C\) converted into water at \(0^\circ C\),
D. \(10g\) of ice at \(0^\circ C\) converted into water at \(0^\circ C\).

Which of the following is/are correct \(Tds\) equation?

Which of the following is correct in Compton effect?
A. X-ray photon strikes an electron which is at rest,
B. Maximum Compton shift is few metres,
C. Maximum Compton shift is \(0.0484\ \text{\AA}\),
D. An electron strikes on metal surface.

An iron furnace radiates \(42.5\) calories per second through an opening of cross-section \(1\ \text{cm}^2\). If the relative emittance of the furnace is \(0.80\), the temperature of furnace is given Stefan's constant \(\sigma=1.36\times10^{-8}\ \text{cal/m}^2\text{s K}^4\):

Which of the following is incorrect thermodynamical relation of Maxwell?