If L = 2.331 cm, B = 2.1 cm, then L + B =?

1. 4.431 cm

2. 4.43 cm

3. 4.4 cm

4. 4 cm

If the length of rod A is 3.25 ± 0.01 cm and that of B is 4.19 ± 0.01 cm then the rod B is longer than rod A by 

1. 0.94 ± 0.00 cm

2. 0.94 ± 0.01 cm

3. 0.94 ± 0.02 cm

4. 0.94 ± 0.005 cm

A physical quantity is given by \(X=[M^aL^bT^c]\). The percentage error in measurement of \(M, L\) and \(T\) are \(𝛼 , 𝛽\) and \(𝛾\) respectively. Then maximum percentage error in the quantity \(X\) is:

1. \(\alpha\alpha+\beta\beta+c\gamma\)
2. \(\alpha\alpha+\beta\beta-c\gamma\)
3. \(\frac{\alpha}{\alpha}+\frac{\beta}{\beta}+\frac{c}{\gamma}\)
4. None of these

A physical quantity \(A\) is related to four observable quantities \(a\), \(b\), \(c\) and \(d\) as follows, \(A= \frac{a^2b^3}{c\sqrt{d}},\) the percentage errors of measurement in \(a\), \(b\), \(c\) and \(d\) are \(1\%\), \(3\%\), \(2\%\) and \(2\%\) respectively. The percentage error in quantity \(A\) will be: 
1. \(12\%\)
2. \(7\%\)
3. \(5\%\)
4. \(14\%\)

If the acceleration due to gravity is \(10\ \text{m/s}^{–2}\) and the units of length and time are changed in kilometer and hour respectively, the numerical value of the acceleration is:

1. \(360000\)

2. \(72,000\)

3. \(36,000\)

4. \(129600\)

If L, C and R represent inductance, capacitance and resistance respectively, then which of the following does not represent dimensions of frequency? [This question includes concepts from the 12th syllabus]

1. $\frac{1}{RC}$

2. $\frac{R}{L}$

3. $\frac{1}{\sqrt{LC}}$

4. $\frac{C}{L}$

The number of particles crossing a unit area perpendicular to the \(x\)-axis in unit time is given by $$\(n= -D\dfrac{n_2-n_1}{x_2-x_1}\), where \(n_1\) and \(n_2\) are the number of particles per unit volume for the value of \(x\) equal to \(x_1\) and \(x_2\) respectively. The dimensions of \(D,\) known as the diffusion constant, will be:
1. \(\left[M^0LT^{2}\right]\)
2. \(\left[M^0L^2T^{-4}\right]\)
3. \(\left[M^0LT^{-3}\right]\)
4. \(\left[M^0L^2T^{-1}\right]\)

With the usual notations, the following equation $S_t=u+\frac{1}{2}a(2t-1)$ is

1. Only numerically correct

2. Only dimensionally correct

3. Both numerically and dimensionally correct

4. Neither numerically nor dimensionally correct

If the dimensions of length are expressed as $G^x{c}^y{h}^z$; where G, c and h are the universal gravitational constant, speed of light and Planck's constant respectively, then  

1. $x=\frac{1}{2},y=\frac{1}{2}$

2. $x=\frac{1}{2},z=\frac{1}{2}$

3. $y=\frac{1}{2},z=\frac{3}{2}$

4. $y=-\frac{3}{2},z=-\frac{1}{2}$

A highly rigid cubical block A of small mass M and side L is fixed rigidly onto another cubical block B of the same dimensions and of low modulus of rigidity $\eta$ such that the lower face of A completely covers the upper face of B. The lower face of B is rigidly held on a horizontal surface. A small force F is applied perpendicular to one of the side faces of A. After the force is withdrawn block A executes small oscillations. The time period of which is given by 

1. $2\pi \sqrt{\frac{M\eta }{L}}$

2. $2\pi \sqrt{\frac{L}{M\eta }}$

3. $2\pi \sqrt{\frac{ML}{\eta }}$

4. $2\pi \sqrt{\frac{M}{\eta L}}$