List of practice Questions

Identify which of the given plan views (nets) can be folded to make the 3D object shown (a short cylinder with a tall, thin rectangular slab attached on its circular top and extending upward). 

Shown below is an image made from line segments. Identify the element, from the options at right, which is NOT part of the image.

A triangular prism is cut into two parts, P and Q, as shown. Which option represents part P? 

Choose the set of colours which is present in this painting.

Identify which net can be folded to make the shown 3D object. 

Three objects are given — one cube and two right-angled prisms. They can be merged to form one 3D object. From the options, choose the possible object(s) formed by this merging. 

The image below shows a 3D object. Only one option shows the same object from a different view. Identify it.

Kepler's third law states that square of period of revolution (T) of a planet around the sun, is proportional to third power of average distance r between sun and planet i.e. $T^2 = Kr^3$ here K is constant. If the masses of sun and planet are M and m respectively then as per Newton's law of gravitation force of attraction between them is $F = \frac {GMm}{r^2}$, here G is gravitational constant. The relation between G and K is described as
Acid catalysed hydration of alkene is an example for
Find the missing number: -1, 0, 0, ____, 8
The antibiotics have no effect on viruses because
The frequency of a sonometer wire is $100\, Hz$. When the weights producing the tensions are completely immersed in water, the frequency becomes $80\, Hz$ and on immersing the weights in a certain liquid, the frequency becomes $60\, Hz$. The specific gravity of the liquid is
A thin rod of length $4l$, mass $4\, m$ is bent at the points as shown in figure. What is the moment of inertia of the rod about the axis passing point $O$ and perpendicular to the plane of the paper?
A charged particle moving in a uniform magnetic field and losses $4\%$ of its kinetic energy. The radius of curvature of its path changes by
A person is standing at a distance of 1800 meters facing a giant clock at the top of a tower. At 5.00 p.m., he can see the tip of the minute hand of the clock at 30 degree elevation from his eye level. Immediately, the person starts walking towards the tower. At 5.10 p.m., the person noticed that the tip of the minute hand made an angle of 60 degrees with respect to his eye-level. Using three-dimensional vision, find the speed at which the person is walking. The length of the minute hand is \( \frac{200}{\sqrt{3}} \) meters (where \( \sqrt{3} = 1.732 \)).
The mean square deviation of a set of $n$ observation $x_{1}, x_{2},... x_{n}$ about a point $c$ is defined as $\frac{1}{n} \displaystyle\sum_{i=1}^{n}\left(x_{i}-c\right)^{2}$.The mean square deviations about $- 2$ and $2$ are $18$ and $10$ respectively, the standard deviation of this set of observations is
Let $M$ be a $3 \times 3$ non-singular matrix with $det(M)=\alpha$. If $\left[M^{-1} adj(adj(M)]=K I\right.$, then the value of $K$ is
The number of real roots of the equation $e^{x-1} + x - 2 = 0$ is
The arithmetic mean of the data $0,1,2, \ldots \ldots, n$ with frequencies $1,{ }^{n} C_{1},{ }^{n} C_{2}, \ldots,{ }^{n} C_{n}$ is
A bag contains $3$ red and $3$ white balls. Two balls are drawn one by one. The probability that they are of different colours is.
Let $S$ be the focus of the parabola $y ^{2}=8 x$ and let $PQ$ be the common chord of the circle $x^{2}+y^{2}-2 x-4 y=0$ and the given parabola. The area of the $\Delta PQS$ is
If a function $f(x)$ is given by $f(x)=\frac{x}{1+x}+\frac{x}{(x+1)(2 x+1)}+\frac{x}{(2 x+1)(3 x+1)}+\ldots \infty$ then at $x =0$, $f(x)$

Observe the following sequence of figures and choose the correct figure to continue the sequence. 
Problem Figure: 

Observe the following sequence of figures and choose the correct figure to continue the sequence. 
Problem Figure: 

Observe the following sequence of figures and choose the correct figure to continue the sequence.