List of practice Questions

Ekta, Faguni and Garima were partners in a firm sharing profits and losses in the ratio of 5 : 3 : 1. Faguni was guaranteed ₹ 25,000 as her share of profit in the firm. Any deficiency arising on that account was to be met by Ekta. The firm earned a profit of ₹ 90,000 for the year ended 31st March, 2024.
The profit credited to Faguni’s capital account was:
A and B together can complete a task in 10 days. A alone can finish it in 15 days. In how many days can B alone finish the work?
The corner points of the feasible region in graphical representation of a L.P.P. are \( (2, 72), (15, 20) \) and \( (40, 15) \). If \( Z = 1x + 9y \) be the objective function, then:
Rearrange the following words to form a meaningful sentence: 1. Always 2. You 3. Truth 4. Should 5. Speak
Find the next term in the series: 3, 6, 11, 18, 27, ?
If $\tan^{-1}(x^2 + y^2) = a^2$, then find $\frac{dy}{dx}$.
In a certain code language, "MOTHER" is coded as "OMHTRE". What will be the code for "FATHER"?
Which word does not belong to the group? Apple, Banana, Carrot, Mango
A 0.5 m long solenoid has 400 turns and carries a current of \( 3 \, \text{A} \). What is the magnetic field at the center of the solenoid?
Find the image \( A' \) of the point \( A(2,1,2) \) in the line \[ l: \mathbf{r} = 4\hat{i} + 2\hat{j} + 2\hat{k} + \lambda (\hat{i} - \hat{j} - \hat{k}). \] Also, find the equation of the line joining \( A A' \). Find the foot of the perpendicular from point \( A \) on the line \( l \).
If a line makes angles of \( \frac{3\pi}{4} \) and \( \frac{\pi}{3} \) with the positive directions of \( x \), \( y \), and \( z \)-axes respectively, then \( \theta \) is:
Differentiate \(\frac{\sin x}{\sqrt{\cos x}}\) with respect to x.
For a reaction X + Y → Z, in which both X and Y follow first order kinetics; if the concentration of X is increased 2 times and concentration of Y is increased 3 times, how does it affect the rate of reaction?
If the sum of two vectors is a unit vector, then the magnitude of their difference is:
If \( x = e^{\frac{x}{y}} \), then prove that \( \frac{dy}{dx} = \frac{x - y}{x \log x} \).
On 1st April 2023, Veebee Ltd. issued 20,000, 13% debentures of \( ₹ 100 \) each at a discount of 10% redeemable at a premium of 5% after 4 years. Total amount of interest on debentures for the year ending 31st March, 2024 will be :
If \( \mathbf{a} \) and \( \mathbf{b} \) are position vectors of two points \( P \) and \( Q \) respectively, then find the position vector of a point \( R \) in \( QP \) produced such that \[ QR = \frac{3}{2} QP. \]
If a steel rod of a radius 10 mm and length 80 cm is streched by a force of 66 kN along its length, then the longitudinal stress on the rod is nearly
OAB is sector of a circle with centre O and radius 7 cm. If length of arc \( \widehat{AB} = \frac{22}{3} \) cm, then \( \angle AOB \) is equal to
A man needs to hang two lanterns on a straight wire whose end points have coordinates A (4, 1, -2) and B (6, 2, -3). Find the coordinates of the points where he hangs the lanterns such that these points trisect the wire AB.
Let the volume of a metallic hollow sphere be constant. If the inner radius increases at the rate of 2 cm/s, find the rate of increase of the outer radius when the radii are 2 cm and 4 cm respectively.
Write the reaction of D-Glucose with the following:
(a) HCN (b) Br$_2$ water (c) (CH$_3$CO)$_2$O
The electric field at a point in space is \( 2 \times 10^3 \, \text{N/C} \) and the potential at the same point is \( 100 \, \text{V} \). What is the potential energy of a charge of \( 5 \, \mu\text{C} \) placed at that point?
Determine the values of $x$ for which the function $f(x) = \frac{x-4}{x+1}$ is an increasing or a decreasing function.
____is the process of searching for prospective employees and stimulating them to apply for jobs in the organization.