The slope of the tangent drawn on a position-time graph at any instant is equal to the instantaneous ______.

• (A) acceleration
• (B) force
• (C) velocity
• (D) momentum
• (E) impulse

The dimensions for the gravitational constant \(G\) are _____.

• (A) \(M^{-1}L^{2}T^{-2}\)
• (B) \(M^{0}L^{0}T^{0}\)
• (C) \(MT^{-2}\)
• (D) \(ML^{2}T^{-2}\)
• (E) \(M^{-1}L^{3}T^{-2}\)

The de Broglie wavelength associated with an electron accelerated by a potential of 64 V is _____.

• (A) 1.227 nm
• (B) 0.613 nm
• (C) 0.302 nm
• (D) 0.153 nm
• (E) 2.454 nm

The horizontal range of a projectile is maximum when the angle of projection is _____.

• (A) \(0^{\circ}\)
• (B) \(30^{\circ}\)
• (C) \(45^{\circ}\)
• (D) \(60^{\circ}\)
• (E) \(90^{\circ}\)

The graph between displacement and time for a particle moving with uniform acceleration is a _____.

• (A) straight line with a positive slope
• (B) parabola
• (C) ellipse
• (D) straight line parallel to time axis
• (E) straight line perpendicular to time axis

Zr (Z = 40) and Hf (Z = 72) have similar atomic and ionic radii because of:

• (A) Diagonal relationship
• (B) Lanthanoid contraction
• (C) Having similar chemical properties
• (D) Belonging to same group

The reagent 'R' in the given sequence of chemical reaction is:

• (A) \(CH_3CH_2OH\)
• (B) \(HI\)
• (C) \(CuCN/KCN\)
• (D) \(H_2O\)

Reaction of butanone with methylmagnesium bromide followed by hydrolysis gives:

• (A) 2-methyl-2-butanol
• (B) 2-butanol
• (C) 3-methyl-2-butanol
• (D) 2,2-dimethyl-1-butanol
• (E) 2-pentanol

X and Y in the below reaction are _____ and _____ respectively
\[ C_6H_5-CO_2H + X \xrightarrow{Heat} C_6H_5-COCl \xrightarrow{H_2/Pd/BaSO_4, Quinoline} Y \]

• (A) \(SOCl_2\) and \(C_6H_5CHO\)
• (B) \((COCl)_2\) and \(C_6H_5CH_3\)
• (C) \(SOCl_2\) and \(C_6H_5CH_3\)
• (D) \((COCl)_2\) and \(C_6H_5CH_2OH\)
• (E) \(SOCl_2\) and \(C_6H_5CH_2Cl\)

The correct increasing order of the acid strength of benzoic acid (I), 4-nitrobenzoic acid (II), 3,4-dinitrobenzoic acid (III) and 4-methoxybenzoic acid (IV) is

• (A) I \(<\) II \(<\) III \(<\) IV
• (B) II \(<\) I \(<\) IV \(<\) III
• (C) IV \(<\) I \(<\) II \(<\) III
• (D) IV \(<\) II \(<\) I \(<\) III
• (E) I \(<\) IV \(<\) II \(<\) III

The value of the integral \(\int_{0}^{\pi} \frac{\cos x}{1+\sin^2 x} dx\) is

• (A) \(0\)
• (B) \(1\)
• (C) \(\frac{\pi}{2}\)
• (D) \(\pi\)
• (E) \(2\pi\)

The value of \(k\), if the circles \(2x^2+2y^2-4x+6y=3\) and \(x^2+y^2+kx+y=0\) cut orthogonally is

• (A) \(2\)
• (B) \(3\)
• (C) \(4\)
• (D) \(5\)
• (E) \(1\)

The axis of the parabola \(x^2+6x+4y+5=0\) is

• (A) \(x=0\)
• (B) \(y=1\)
• (C) \(x+3=0\)
• (D) \(y=4\)
• (E) \(y+2=0\)

The distance between the foci of the ellipse \(\frac{(x+2)^2}{9} + \frac{(y-1)^2}{4} = 1\) is

• (A) \(\sqrt{5}\)
• (B) \(2\sqrt{5}\)
• (C) \(3\sqrt{5}\)
• (D) \(9\sqrt{5}\)
• (E) \(7\sqrt{5}\)

The circle passing through the point \((1, -2)\) and touching the x-axis at \((3,0)\) also passes through the point

• (A) \((2, -5)\)
• (B) \((-5, -2)\)
• (C) \((-2, 5)\)
• (D) \((-5, 2)\)
• (E) \((5, -2)\)