30 Questions
What is the magnitude of acceleration of point A of the solid cylinder?
88ω0 R
What is the angular velocity of the solid cylinder about its own axis?
10ω0
In the scenario described, what is the magnitude of acceleration of point B of the solid cylinder with respect to the contact surface of the hollow cylinder?
112ω0 R
What is the radius of curvature of point A at the given instant?
32R
When a hollow tube containing a ball is accelerated horizontally and the ball is slightly displaced from point 'A', what represents the approximate nature of N1 and N2?
|N1| > |N2|
In the scenario described with the hollow tube and a ball, what relationship between N1 and N2 can be observed?
|N1| < |N2|
In which of the following cases, if plate A and C are earthed, the charge on the left surface of plate B is 4Q/3?
(II), (iii), (Q)
If plate B is earthed, in which of the following cases does the sum of the charges on plates A and C equal 2Q?
(III), (iv), (P)
What is the single digit integer answer to the question involving the surface mass density of a semi-circular disc with a given force applied for translational motion?
5
If a box with attached plates AB and CD is released on an inclined plane, what is the angle of inclination of the plane?
45 degrees
For the situation involving a semi-circular disc, what does the parameter 'h' represent?
Height
Given the information about the force applied to the semi-circular disc, what does the constant 'k' represent?
Pi
Which reagent from the table is capable of converting benzene into a mixture of two carboxylic acids?
Ac2O / AlCl3
Which compound from the first column reacts with Mg / Et2O and then with CO2 to give effervescence?
Conc.HNO3
Which reagent in the table is more acidic than water?
Conc.HNO3 / Conc.H2SO4
Which reagent gives off H2 gas on reaction with sodium metal?
Pr opene, H3PO4
Which compound from the first column reacts with K2Cr2O7 / Conc.H2SO4 to produce H3O+ ions?
Pr opene, H3PO4
Which reagent from the table reacts with Br2 / NaOH and then with Fe to form CO2 and H3O+?
HeCl / AlCl3
What is the correct integral representation for $I(\alpha)$ in Column 1?
$\int\limits_{0}^{1} \frac{x^2}{1 - x^2} \tan^{-1}(\alpha x) dx$
If $\alpha = 1$, which combination of integrals and options in Column 2 is correct?
III, (iv), Q
For $\alpha^2 = 4$, which set of integrals and options in Column 1 is true?
$II, (iii), R$
Which integral expression in Column 1 corresponds to the natural logarithm of $\frac{5+1}{2}$?
$\int\limits_{0}^{1} \ln\left(\frac{17+4}{4}\right) dx$
If $\alpha = \frac{1}{2}$, which combination of integrals and options in Column 2 is correct?
I, (ii), S
When $\alpha^2 = 9$, which set of integrals and options in Column 1 is accurate?
$IV, (ii), S$
What is the product of the roots of the equation $x^5 + x^2 + 1 = 0$?
-1
What is the value of $n$ in the equation $3^{n-1} + 3^{n-2} + 3^{n-3} = a$?
$1$
If $g(x) = x^2 - 2$, what is the value of $g(x_1) \cdot g(x_2) \cdot g(x_3) \cdot g(x_4) \cdot g(x_5) - 30g(x_1x_2x_3x_4x_5)$?
$-30$
What is the equation of the curve obtained by reflecting the ellipse $\frac{(x-4)^2}{16} + \frac{(y-3)^2}{9} = 1$ about the line $x - y - 2 = 0$?
$16x + 9y - 36 = 0$
In the context of vectors, if $d = \sin(x)(a \times b) + \cos(y)(b \times c) + 2(c \times b)$, what is the minimum value of $x^2 + y^2$?
$2\pi^2$
If $a, b, c$ are non-coplanar vectors and $d = \sin(x)(a \times b) + \cos(y)(b \times c) + 2(c \times b)$, what is the sum of $a$ and $b$ when $x^2 + y^2 = \pi^2$, given that $a$ and $b$ are coprime?
$2\pi$
Explore the dynamics of a solid cylinder rolling without slipping inside a hollow cylinder. Calculate the angular velocity, magnitude of acceleration at different points, and understand the motion of the cylinder system.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
