10-question readiness test

The function  \(f(x)=x^2-6x+1,\)  satisfies the condition  of  Lagrange's  mean value theorem. The co-ordinates of the point at which the tangent is parallel to the chord joining  \(A(1,-4) \)  and  \(B=(3,-8) \)  are : 

The expression  \(n^3+3n^2+5n+3,n\in N\)  is divisible by : 

Spontaneous adsorption of a gas on solid surface is an exothermic process, because

Two spheres of the same material have radii 1 m and 4 m, temperature 4000 K and 2000 K respectively. The energy radiated per second by the first sphere(E1) and second spehere(E2) is

Let  \(\theta\in(0,\frac \pi 4 )\)  and  \(t_1= (tan\theta) ^{tan\theta},t_2=(tan \theta)^{cot \theta},t_3=(cot\theta)^{tan\theta}\)  and  \(t_4=(cot\theta)^{cot\theta},\)  then 

A vessel contains 1 mole of  \(O_2\)  gas (molar mass 32) at a temperature T. The pressure of the gas is  \(P\) . An identical vessel containing one mole of the gas (molar mass 4) at a temperature  \(2T\) has a pressure of  

The molarity of a solution obtained by mixing 750 mL of 0.5 M HCl with 250 mL of 2 M HCl will be 

The trajectory of a projectile in a vertical plane is  \(y = ax - bx^2\) , where  \(a, b\)  are constants and  \(x\)   and  \(y\)  are horizontal and vertical distances respectively of the projectile from the point of projection. The maximum height attained is 

\(Me_2SiCl_2 \)  in hydrolysis will produce 

Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block in the directio  of the lighter block. The velocity of the centre of mass is