List of practice Questions

A block of mass 5 kg is released as shown in the figure. Surface CD is rough with = 0.5, rest of all the surfaces are smooth. Find the maximum compression in the spring (initially spring is in its natural length.)

Directions: The following question has four choices, out of which one or more are correct.Let $\alpha =a\hat{i}+b\hat{j}+c\hat{k},\beta =b\hat{i}+c\hat{j}+a\hat{k}$ and $y=c\hat{i}+a\hat{j}+b\hat{k}$ be three co-planar vectors with $a\ne b$ and$v=\hat{i}+\hat{j}+\hat{k},$ Then $v$ is perpendicular to

Directions: The following question has four choices, out of which one or more are correct.The internal bisector of $\mathrm{\angle }A$ of a triangle $ABC$ meets side $BC$ at $D$. A line drawn through $D$ perpendicular to $AD$ intersects the side $AC$ at $E$ and side $AB$ at $F$. If $a,b$ and $c$ represent the sides of $\mathrm{\Delta }ABC$, then

The two ends of a train moving with constant acceleration pass a certain point with velocities u and v. The velocity with which the middle point of the train passes the same point is

Which of the following properties are associative law ?

Suppose $\sin 2\theta =\cos 3\theta$, here $0<\theta <\frac{\pi }{2}$ then what is the value of $\cos 2\theta ?$

The nucleus of which of the following atoms whose atomic mass numbers '$A$' are given in the options would have the highest binding energy per nucleon?

Electrolysis of dilute aqueous $NaCl$ solution was carried out by passing $10$ milli ampere current. The time required to liberate $0.01$ mol of $H_2$ gas at the cathode is: ($1$ Faraday $=96500Cmo{l}^{-1}$)

$\overrightarrow{A}\times \overrightarrow{B}=\frac{1}{2}AB,$ what is the angle between $A$ and $B?$

If A = {1, 2, 3, 4}, B = {2, 3, 5, 6} and C = {3, 4, 6, 7}, then

The question given below consists of a question and two statements numbered I and II. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both statements and answer accordingly.
What is the product of x and y?
Statement I. Both x and y are consecutive even multiples of 32.
Statement II. The LCM of x and y is 3584.

Let f(x) = 4(x2+x), g(x)= √x+1, h(x) = g(f(x)). Find the domain and range of h(x).

In a family of 5 sisters, the average weight of the 4 sisters weighing the least is 50 kg, and the average weight of the 4 sisters weighing the most is 55 kg. What is the difference between the maximum and minimum possible overall average weight?

If ‘n’ and ‘a’ are positive integers such that nn = 3324 and n3 + 3n is an integral multiple of 3a, then find the largest possible value of a.

A square is inscribed in an equilateral triangle such that one of the sides of the square completely lies on one of the sides of the equilateral triangle. Find the ratio of the perimeters of the square and equilateral triangle.

In the figure below, AB and AC are two tangents of the circle from the same external point A touching at points B and C, respectively. If ∠BAC = 2z° and ∠BDC = 5z°, then find the value of ∠BOC + ∠BAC in degrees.

The correct order of ionisation enthalpy for Li, Na, Cl, F is:

The letter ?$D$? in $D$-carbohydrates represents

Complexes formed in the cyanide process are:

A solution of colourless unknown salt (X) on boiling with excess of NaOH produces non-flammable gas. The gas evolution ceases after some time. Upon addition of Zn dust to the same solution, the gas evolution restarts. The colourless salt (X) is (are)

If $f \left(z\right)=\frac{1-z^{3}}{1-z} ,$ where $z=x+iy$ with $z\ne1,$ then $Re\left\{\overline{f \left(z\right)}\right\}=0$ reduces to

Which of the drawings (a) to (d) show : 
\((a)\)

\((b)\)

\((c)\)

\((d)\)

(i) 2 × \(\frac{1}{5}\)
(ii) 2 × \(\frac{1}{2}\)
(iii) 3 × \(\frac{2}{3}\)
(iv) 3 × \(\frac{1}{4}\)

The vapour pressure of water at room temperature is 23.8 mm Hg. The vapour pressure of an aqueous solution of sucrose with mole fraction 0.1 is equal to

The area of the region bounded by the curve $y=x^2$ and the line $y=16$ is:

The solution of the differential equation $\frac{dy}{dx}=\sec \left(\frac{y}{x}\right)+\frac{y}{x}$ is: