List of practice Questions

Let f(x) = $\displaystyle\sum_{k=1}^{10} kx^k$ , x ∈ R. If 2f(2) + f(2) = 190(2)ⁿ + 1 then n is equal to____.

A boy presented with a fever and chills. Rapid test was positive for specific antigen HRP-2. Which of the following species of Plasmodium is the most likely causative agent?

Arrange the following in increasing order of their boiling points:
1-chloropropane, 2-chloropropane, 1-chlorobutane
(A) 2-chloropropane $<$ 1-chloropropane $<$ 1-chlorobutane

The figure shows a square pyramid that will be cut into multiple solids by extending the purple and red shapes. Select the solids that will result from the cuts.

Which option represents the front view of the object shown below?

A sheet of paper is folded as shown. Then the word ‘MAKER’ is written on the folded paper. Which option correctly represents the unfolded paper?

‘श्रवणकुमार’ खण्डकाव्य की कथावस्तु पर विचार कीजिए।

If the x-intercept of a focal chord of the parabola $y^2=8 x+4 y+4$ is 3 , then the length of this chord is equal to ___

What are the functions of Leydig cells?

The essence of management is:

Assertion (A): Phenol gives 2,4,6-trinitrophenol on treatment with concentrated $ HNO_3 $ and concentrated $ H_2SO_4 $.
Reason (R): –OH group in phenol is $ m $-directing.

A triangular pyramid with equal sides can be flipped on its edges without slipping or sliding as shown on the left. What is the minimum number of flips needed for the pyramid to reach the finishing line if the starting position is as shown on the right?

A tourist is shooting photographs of an ancient building from four locations A, B, C and D marked by x. The tourist is using only one camera without changing its magnification. Identify the location(s) in the floor plan which will result in the given photograph.

Which of the pieces could be used four times individually to form a square? The pieces can be rotated and flipped but should not be overlapped.

Which option, when folded, will result in the solid shown?

Shown below is a 3D block. Four such blocks are interlocked in a square form. What will be the top view of the blocks after interlocking?

Shown in the top row are 4 pieces of building blocks. Which of the option(s) is/are made using all four pieces?

Shown on the left are all the 6 faces of a cube. Which option can be folded into this cube?

The total number of monobromo derivatives formed by the alkanes with molecular formula $C _5 H _{12}$ is (excluding stereo isomers) _______

Let f : $\R^2 → \R$ be the function defined as follows :
$f(x,y)=\begin{cases} (x^2-1)^2\cos^2(\frac{y^2}{(x^2-1)^2}) & \text{if }x \ne ±1 \\ 0 & \text{if } x=±1\end{cases}$
The number of points of discontinuity of f(x, y) is equal to _________.

How many fonts have been used to write the letter Q in the image shown below?

Let $\vec{a}=\hat{i}+2 \hat{j}+\lambda \hat{k}, \vec{b}=3 \hat{i}-5 \hat{j}-\lambda \hat{k}, \vec{a} \cdot \vec{c}=7,2 \vec{b} \cdot \vec{c}+43=0, \vec{a} \times \vec{c}=\vec{b} \times \vec{c}$. Then $|\vec{a} \cdot \vec{b}|$ is equal to

A fully filled water tank OABCD has a circular arc (AB) of radius 10 m at the bottom as shown in the following figure. The height BC is 10 m. The length OA and CD are 5 m and 15 m, respectively. The density of the water is $\rho$ kg/m³ and the acceleration due to gravity is $g$ m/s². The magnitude of the resultant hydrostatic force per unit width acting on AB in N/m lies between

Let $A$ be the area bounded by the curve $y=x|x-3|$, the $x$-axis and the ordinates $x=-1$ and $x=2$ Then $12 A$ is equal to _____

What is double fertilization? Explain.