A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction between tyres and road is 0.34. [Take g = 10 ms\(^{-2}\) ]

• (a) 3.4 ms\(^{-1}\)
• (b) 22.4 ms\(^{-1}\)
• (C) 13 ms\(^{-1}\)
• (d) 17 ms\(^{-1}\)

An electron moving along the x-axis has a position given by \(x = 20te^{-t}\) m, where \(t\) is in second. How far is the electron from the origin when it momentarily stop?

• (a) 20 m
• (b) 20 em
• (c) \(\frac{20}{e}\) m
• (d) zero

The ranges and heights for two projectiles projected with the same initial velocity at angles 42\(^\circ\) and 48\(^\circ\) with the horizontal are R\(_1\), R\(_2\) and H\(_1\), H\(_2\) respectively. Choose the correct option :

• (a) R\(_1\) > R\(_2\) and H\(_1\) = H\(_2\)
• (b) R\(_1\) = R\(_2\) and H\(_1\) < H\(_2\)
• (c) R\(_1\) < R\(_2\) and H\(_1\) < H\(_2\)
• (d) R\(_1\) = R\(_2\) and H\(_1\) = H\(_2\)

A particle moves under the effect of a force \(F = Cx\) from \(x = 0\) to \(x = x_1\). The work done in the process is

• (a) \(Cx_1^2\)
• (b) \(\frac{1}{2} Cx_1^2\)
• (C) \(Cx_1\)
• (d) Zero

Three-point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right-angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The center of mass of the system is at a point:

• (a) 0.6 cm right and 2.0 cm above 1 kg mass
• (b) 1.5 cm right and 1.2 cm above 1 kg mass
• (c) 2.0 cm right and 0.9 cm above 1 kg mass
• (d) 0.9 cm right and 2.0 cm above 1 kg mass

The number of valence electrons present in the metal among Cr, Co, Fe and Ni which has the lowest enthalpy of atomisation is

• (a) 8
• (b) 9
• (c) 6
• (d) 10

The Zeta potential is related to which property of colloids"

• (a) Colour
• (b) Tyndall effect
• (c) Charge on the surface of colloidal particles
• (d) Brownian movement

Based on the data given below:
\(E^0_{Cr_2O_7^{2-}/Cr^{3+}} = 1.33 V \quad E^0_{Cl_2/Cl^-} = 1.36 V\)
\(E^0_{MnO_4^-/Mn^{2+}} = 1.51 V \quad E^0_{Cr^{3+}/Cr} = -0.74 V\)

the strongest reducing agent is:

• (a) \(Mn^{2+}\)
• (b) \(Cr\)
• (c) \(MnO_4^-\)
• (d) \(Cl^-\)

An evacuated glass vessel weighs 40.0 g when empty, 135.0 g when filled with a liquid of density \(0.95 g mL^{-1}\) and 40.5 g when filled with an ideal gas at 0.82 atm at 250 K. The molar mass of the gas in \(g mol^{-1}\) is:

(Given: \(R = 0.082 L atm K^{-1} mol^{-1}\))

• (a) 35
• (b) 50
• (c) 75
• (d) 125

Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas? (Assume non-expansion work is zero)

• (a) Cyclic process: \(q = -w\)
• (b) Adiabatic process: \(\Delta U = -w\)
• (c) Isochoric process: \(\Delta U = q\)
• (d) Isothermal process: \(q = -w\)

If \( |z_1| = 2, |z_2| = 3, |z_3| = 4 \) and \( |2z_1 + 3z_2 + 4z_3| = 4 \), then absolute value of \( 8z_2z_3 + 27z_3z_1 + 64z_1z_2 \) equals

• (A) 24
• (B) 48
• (C) 72
• (D) 96

If \( a > 0, b > 0, c > 0 \) and \( a, b, c \) are distinct, then \( (a + b)(b + c)(c + a) \) is greater than

• (A) \( 2(a + b + c) \)
• (B) \( 3(a + b + c) \)
• (C) \( 6 abc \)
• (D) \( 8 abc \)

If \( A = 1 + r^a + r^{2a} + r^{3a} + \cdots \infty \) and \( B = 1 + r^b + r^{2b} + r^{3b} + \cdots \infty \), then \( a/b \) is equal to

• (A) \( \log_B(A) \)
• (B) \( \log_{1-B}(1-A) \)
• (C) \( \log_{\frac{B-1}{B}} \left( \frac{A-1}{A} \right) \)
• (D) None of these

If the \( 17^{th} \) and the \( 18^{th} \) terms in the expansion of \( (2 + a)^{50} \) are equal, then the coefficient of \( x^{35} \) in the expansion of \( (a + x)^{-2} \) is

• (A) -35
• (B) 3
• (C) 36
• (D) -36

Number of solutions of equations \( \sin 9\theta = \sin \theta \) in the interval \( [0, 2\pi] \) is

• (A) 16
• (B) 17
• (C) 18
• (D) 15