List of top Questions asked in Karnataka Common Entrance Test- 2024

An electric bulb of 60 W, 120 V is to be connected to a 220 V source. What resistance should be connected in series with the bulb, so that the bulb glows properly?

The ratio of molar specific heats of oxygen is

Gold sol is not a:

Identify the incorrect statement:

The area of the region bounded by the line $y = x$ and the curve $y = x^3$ is:

The upper level of valence band and lower level of conduction band overlap in the case of

In an experiment to determine the temperature coefficient of resistance of a conductor, a coil of wire X is immersed in a liquid. It is heated by an external agent. A meter bridge set up is used to determine resistance of the coil X at different temperatures. The balancing points measured at temperatures \( t_1 = 0^\circ \text{C} \) and \( t_2 = 100^\circ \text{C} \) are 50 cm and 60 cm respectively. If the standard resistance taken out is \( S = 4 \, \Omega \) in both trials, the temperature coefficient of the coil is

Three polaroid sheets are co-axially placed as indicated in the diagram. Pass axes of the polaroids 2 and 3 make 30° and 90° with pass axes of polaroid sheet 1. If \( I_1 \) is the intensity of the incident unpolarised light entering sheet 1, the intensity of the emergent light through sheet 3 is

The energy associated with the first orbit of He+ is:

In an LCR series circuit, the value of only capacitance \( C \) is varied. The resulting variation of resonance frequency \( f_0 \) as a function of \( C \) can be represented as

In the following scheme of reaction.

X, Y and Z respectively are:

The vectors $\overrightarrow{AB} = 3\hat{i} + 4\hat{k}$ and $\overrightarrow{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$ are the sides of a $\triangle ABC$. The length of the median through $A$ is:

If lines $\frac{x - 1}{-3} = \frac{y - 2}{2k} = \frac{z - 3}{2}$ and $\frac{x - 1}{3k} = \frac{y - 5}{1} = \frac{z - 6}{-5}$ are mutually perpendicular, then $k$ is equal to:

8.8 g of monohydric alcohol reacts with ethyl magnesium iodide, releasing 2240 $cm^3$ of ethane at STP. This monohydric alcohol forms a carbonyl compound that answers Tollen’s test. The alcohol is:

Let $\vec{a}$ and $\vec{b}$ be two unit vectors and $\theta$ is the angle between them. Then $\vec{a} + \vec{b}$ is a unit vector if:

The solution of $e^{\frac{dy}{dx}} = x + 1, \, y(0) = 3$ is:

The family of curves whose $x$ and $y$ intercepts of a tangent at any point are respectively double the $x$ and $y$ coordinates of that point is:

The volume of the parallelepiped whose co-terminous edges are $\hat{i} + \hat{j}, \hat{i} + \hat{k}, \hat{i} + \hat{j}$ is:

If $\vec{a}, \vec{b}, \vec{c}$ are three non-coplanar vectors and $\vec{p}, \vec{q}, \vec{r}$ are vectors defined by:}\\ \[ \vec{p} = \frac{\vec{a} \times \vec{c}}{[\vec{a} \, \vec{b} \, \vec{c}]}, \quad \vec{q} = \frac{\vec{c} \times \vec{b}}{[\vec{a} \, \vec{b} \, \vec{c}]}, \quad \vec{r} = \frac{\vec{b} \times \vec{a}}{[\vec{a} \, \vec{b} \, \vec{c}]}, \] then $(\vec{i} + \vec{b}) \cdot \vec{p} + (\vec{b} + \vec{c}) \cdot \vec{q} + (\vec{c} + \vec{a}) \cdot \vec{r}$ is:

The distance between the two planes $2x + 3y + 4z = 4$ and $4x + 6y + 8z = 12$ is:

The equation $xy = 0$ in three-dimensional space represents:

The plane containing the point $(3, 2, 0)$ and the line $\frac{x - 3}{1} = \frac{y - 6}{5} = \frac{z - 4}{4}$ is

Corner points of the feasible region for an LPP are $(0, 2), (3, 0), (6, 0), (6, 8)$ and $(0, 5)$. Let $z = 4x + 6y$ be the objective function. The minimum value of $z$ occurs at:

A die is thrown 10 times. The probability that an odd number will come up at least once is: