List of practice Questions

Solution of 12 g of non-electrolyte (A) prepared by dissolving it in 1000 mL of water exerts the same osmotic pressure as that of 0.05 M glucose solution at the same temperature. The empirical formula of A is CH₂O. The molecular mass of A is ____ g. (Nearest integer)

25.0 mL of 0.050 M Ba(NO₃)₂ is mixed with 25.0 mL of 0.020 M NaF. K_sp of BaF₂ is 0.5 x 10^-6 at 298 K. The ratio of [Ba2+] [F^-]² and K_sp is__ (Nearest integer)

A metal surface of 100 cm2 area has to be coated with nickel layer of thickness 0.001mm. A current of 2A was passed through a solution of Ni (NO₃)₂ for 'x' seconds to coat the desired layer. The value of x is_____ (Nearest integer)
 (P_Ni (density of Nickel) is 10 gmL^-1, Molar mass of Nickel is 60 gmol^-1 F = 96500 C mol^-1)

For the given reaction

The total number of possible products formed by tertiary carbocation of A is____.

20 mL of calcium hydroxide was consumed when it was reacted with 10 mL of unknown solution of H₂SO4. Also 20 mL standard solution of 0.5 M HCI containing 2 drops of phenolphthalein was titrated with calcium hydroxide the mixture showed pink colour when burette displayed the value of 35.5 mL whereas the burette showed 25.5 mL initially. The concentration of H₂SO₄ is_____M (Nearest integer)

Let A = {1, 2, 3, 4,.....10} and B = {0, 1, 2, 3, 4}. The number of elements in the relation R = {(a, b) ∈ A × A: 2(a – b)2 + 3(a – b) ∈ B} is______.

Let the point (p, p+1) lie inside the region \(E = \{(x,y):3-x≤y≤\sqrt{9-x^2}, 0 ≤ x ≤ 3\} \)If the set of all values of p is the interval (a,b). then b2 + b - a2 is equal to_____

Let a∈ Z and [t] be the greatest integer t. Then the number of points, where the function f(x)=[a+13 sin x], x ∈ (0, π) is not differentiable, is ____

If the area of the region \( S={(x,y) : 2y-y^2 ≤ x^2 ≤ 2y, x ≥ y}\) is equal to \(\frac{ n+2}{n+1}−\frac{π}{n−1}\), then the natural number n is equal to _____.

Let the tangent to the curve x² + 2x – 4y + 9 = 0 at the point P(1, 3) on it meet the y-axis at A. Let the line passing through P and parallel to the line x – 3y = 6 meet the parabola y² = 4x at B. If B lies on the line 2x – 3y = 8. then (AB)² is equal to___

Let y = y(x) be a solution of the differential equation (x cos x)dy +(xy sin x + y cos x – l)dx = 0, 0 < x < \(\frac{π}{2}\). If\(\frac{π}{3}y(\frac{π}{3})=\sqrt3\), then \(| \frac{π}{6 }y“( \frac{π}{6})+2 y'( \frac{π}{6})| \) is equal to______.

Why did Gandhi consider the salt tax more oppressive than other taxes? (A) It revealed the most oppressive side of the colonial rule.
(B) Salt was consumed by rich and poor alike.
(C) It earned profit twenty times more than its value.
(D) It was a national property, so needed to be destroyed.

Consider the graph of Gibbs free energy G vs Extent of reaction. The number of statement/s from the following which are true with respect to points (a), (b) and (c) is…

A. Reaction is spontaneous at (a) and (b)  
B. Reaction is at equilibrium at point (b) and nonspontaneous at point (c)  
C. Reaction is spontaneous at (a) and nonspontaneous at (c)  
D. Reaction is non-spontaneous at (a) and (b)

For the adsorption of hydrogen on platinum, the activation energy is 30 kJ mol^-1 and for the adsorption of hydrogen on nickel, the activation energy is 41.4 kJ mol^-1 . The logarithm of the ratio of the rates of chemisorption on equal areas of the metals at 300 K is ……… (Nearest integer) Given: ln 10 = 2. 3  R = 8.3 JK^-1 mol^-1

The number of relations, on the set {1,2,3} containing (1,2) and (2,3), which are reflexive and transitive but not symmetric, is______

Let D_k=\(\begin{vmatrix} 1 & 2k & 2k-1\\ n & n^2+n+2 & n^2 \\ n & n^2+n & n^2+n+2 \end{vmatrix} \) If \(∑^n_{k=1} D_k=96,\) The n is equal to

Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?

Let [x] be the greatest integer ≤ x. Then the number of points in the interval (-2,1), where the function f(x)=|[x]|+√x−[x] is discontinuous is _____.

Let I(x) = \(∫√\frac{x+7}{x} dx\) and I (9) = 12 + 7 loge 7. If I (1) = α + 7 loge (1 + 2√2), then α4 is equal to_____.

Let the plane x+3y–2z+6=0 meet the co-ordinate axes at the points A,B,C. If the orthocentre of the triangle ABC is\( (α,β,\frac{6 }{7} ), \) then 98(α + β)² is equal to___.

A fair n (n>1) faces die is rolled repeatedly until a number less than n appears. If the mean of the number of tosses required is \(\frac{n}{9}\), then n is equal to_____.

A compass needle of oscillation magnetometer oscillates 20 times per minute at a place P of dip 30°. The number of oscillations per minute become 10 at another place Q of 60° dip. The ratio of the total magnetic field at the two places respectively is \(\frac{4}{√x}\) The value of x is 

To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be ____KJ. [The coefficient of friction between tyre of bus and road is 0.04].

For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is \(\frac{x}{5}\). The value of x is____.

Glycerine of density 1.25 × 10³ kg m^-3 is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends is 10 cm2 and 5 cm2 and pressure drop across its length is 3 Nm^-2. The rate of flow of glycerine through the pipe is x x10^-5 m3 s^-1. The value of x is____.