List of practice Questions

Which school of philosophy emphasizes that knowledge comes primarily from sensory experience?

The concept of separation of powers is most closely associated with:

The minimum number of satellites required to determine a 3D position using GPS is:

Which data model represents geographic features using points, lines, and polygons?

If \( A = \{1,2,3,4,5,6\} \) and \( B = \{1,2,3,\ldots,9\} \), then the number of strictly increasing functions \( f : A \to B \) such that \( f(i) \neq i \) for all \( i = 1,2,3,4,5,6 \) is:

A conducting rod of mass \( m \) and length \( l \) is moving on an infinite pair of conducting rails as shown. Conducting rails are connected to a resistance \( R \) at one end. Motion is in the vertical plane and horizontal magnetic field in the region is \( B \). Find the terminal speed of the rod.

If the end points of chord of parabola \(y^2 = 12x\) are \((x_1, y_1)\) and \((x_2, y_2)\) and it subtend \(90^\circ\) at the vertex of parabola then \((x_1x_2 - y_1y_2)\) equals :

After release, the blocks moves 81 cm in 9 seconds. Find moment of inertia of the pulley :
(Given $m_{1} = 400$ gm, $m_{2} = 350$ gm, R = 2 cm, g = 10 m/s$^2$)

If $f(a)$ is the area bounded in the first quadrant by $x=0$, $x=1$, $y=x^2$ and $y=|ax-5|-|1-ax|+ax^2$, then find $f(0)+f(1)$.

There is a weak base 'B' having $\text{pK}_b = 5.691$ of molarity 0.02M. When 0.02M HCl solution has been added, then pH of resultant buffer solution has been found to be 9. Take total volume of resultant buffer solution to be 100 ml. Find the value of 'x' & 'y', where 'x' is volume of HCl solution in ml & 'y' is volume of 'B' solution in ml. Given $\log(5) = 0.691$

Which of the following graph is correct between log P$_{CO_2}$ vs log X$_{CO_2}$? [given P$_{CO_2}$ = Partial Pressure of CO$_2$, X$_{CO_2}$ = Mole fraction of CO$_2$ in solution]

The coefficient of \( x^{48} \) in the expansion of \[ 1 + (1+x) + 2(1+x)^2 + 3(1+x)^3 + \dots + 100(1+x)^{100} \] is

In the binomial expansion of \( (ax^2 + bx + c)(1 - 2x)^{26} \), the coefficients of \( x, x^2 \), and \( x^3 \) are -56, 0, and 0 respectively. Then, the value of \( (a + b + c) \) is

If in the expansion of \( (1 + x^2)^2(1 + x)^n \), the coefficients of \( x \), \( x^2 \), and \( x^3 \) are in arithmetic progression, then the sum of all possible values of \( n \) (where \( n \geq 3 \)) is:

If three vectors are given as shown. If the angle between vectors \( \mathbf{p} \) and \( \mathbf{q} \) is \( \theta \) where \( \cos \theta = \frac{1}{\sqrt{3}} \), \( |\mathbf{p}| = 2 \), and \( |\mathbf{q}| = 2 \), then the value of \( |\mathbf{p} \times (\mathbf{q} - 3\mathbf{r})|^2 - 3|\mathbf{r}|^2 \) is:

For given vectors \( \mathbf{a} = -\hat{i} + \hat{j} + 2\hat{k} \) and \( \mathbf{b} = 2\hat{i} - \hat{j} + \hat{k} \), where \( \mathbf{c} = \mathbf{a} \times \mathbf{b} \) and \( \mathbf{d} = \mathbf{c} \times \mathbf{b} \), then the value of \( (\mathbf{a} - \mathbf{b}) \cdot \mathbf{d} \) is:

Let the lines \[ L_1:\ \vec r=(\hat i+2\hat j+3\hat k)+\lambda(2\hat i+3\hat j+4\hat k),\ \lambda\in\mathbb R \] \[ L_2:\ \vec r=(4\hat i+\hat j)+\mu(5\hat i+2\hat j+\hat k),\ \mu\in\mathbb R \] intersect at the point $R$. Let $P$ and $Q$ be the points lying on the lines $L_1$ and $L_2$ respectively, such that \[ |PR|=\sqrt{29}\quad \text{and}\quad |PQ|=\sqrt{\frac{47}{3}}. \] If the point $P$ lies in the first octant, then find $27(QR)^2$.