List of practice Questions

Find the value of K for which the given system of equations has infinitely many solutions: \[ Kx + 3y = K-3 \quad \text{(1)} \] \[ 12x + Ky = K \quad \text{(2)} \]

What do you understand by irrational number? Prove that \( 5 - 3\sqrt{2} \) is an irrational number.

Assertion (A): The number \(4^n\) cannot end with the digit 0, where \(n\) is a natural number.
Reason (R): A number ends with 0 if its prime factorization contains both 2 and 5.

Assertion (A): The tangent to a circle is a special case of the secant, when the two end points of its corresponding chord coincide.
Reason (R): A tangent to a circle is a line that intersects the circle at only one point.

If the zeroes of a quadratic polynomial \( 3x^2 - kx + 12 \) are equal, then find the value of \( k \).

Find the volume of a hemisphere with radius 7 cm.

If the mid point of a line segment joining the points \( (h, 3) \) and \( (6, 5) \) is \( (4, 4) \), then find the value of h.

The distance of the point \(P(-6, 8)\) from the origin is:

In \( \triangle ABC \), \( DE \parallel BC \) such that \( \frac{AD}{DB} = \frac{3}{5} \); if \( AC = 5.6 \, \text{cm} \), then \( AE \) is equal to:

Which of the following pairs of lines in a circle cannot be parallel:

Area of a sector of a circle of radius 21 cm and the central angle 60° is:

The probability of a sure event is:

If the product of two numbers is 2880 and their H.C.F. is 12, then the value of their L.C.M. is:

A polynomial of degree three has:

What is the function of diaphragm in human respiratory system ? Where is it present in human body ?

If \[ A=\begin{bmatrix}2 & 3\\3 & 5\end{bmatrix}, \] then find the value of \[ \left|A^{2025}-3A^{2024}+A^{2023}\right|. \]

Corrective exercises should be done under a _____ advice and supervision.}

Fill in the blank with an appropriate word and complete the given sentence.
The individual ______________________ of international student mobility are well known.

Fill in the blanks with the appropriate words and complete the given sentence.
A well-known chef, started his career __________________ the age of 15 when the prodigy __________________ cooking under Eric Ripert at the iconic New York restaurant.

In 15 days, 9 women and 15 girls can reap a field. In what time could 15 women and 16 girls reap the same field, assuming 3 women can do as much work as 4 girls?

Each of these questions has a text portion followed by four alternative summaries. best captures the essence of the text.
Some decisions will be fairly obvious "no brainers". Your bank account is low, but you have a two-week vacation coming up and you want to get away to someplace warm to relax with your family. Will you accept your in-laws' offer of free use of their Florida beachfront condo? Sure. You like your employer and feel ready to move forward in your career. Will you step in for your boss for three weeks while she attends a professional development course? Of course.

The half of the average value of three number is 20. The second number is thrice the third number and first number is twice the second number. What is the sum of smallest and largest number?

If a train runs at 50 km/hr, it reaches 60 minutes earlier than its schedule time at its destination but if it runs at 8.33 m/s it reaches at its destination 300 minutes late, find the correct time for the train to complete its journey.

If the image of the point \( P(a,2,a) \) in the line \[ \frac{x}{2} = \frac{y+a}{1} = \frac{z}{1} \] is \( Q \) and the image of \( Q \) in the line \[ \frac{x-2b}{2} = \frac{y-a}{1} = \frac{z+2b}{-5} \] is \( P \), then \( a + b \) is equal to

Assertion (A) : If probability of happening of an event is \(0.2p\), \(p>0\), then \(p\) can't be more than 5.
Reason (R) : \(P(\bar{E}) = 1 - P(E)\) for an event \(E\).