List of practice Questions

A drone is flying at a height of 100 m above the ground. It observes on its right two stationary cars on a highway at angles of depression 45° and 30°. On the basis of above information, answer the following questions: Find the distance between the two cars.
Form a quadratic equation, one of whose zero is \( 2 + \sqrt{5} \) and the sum of zeros is 4.
The A.P. \( 8, 10, 12, \ldots \) has 60 terms. Find the sum of the last 20 terms.
Find the area of a circle with maximum area that can be inscribed in a square of side 7 cm.
If \( \sin A + \cos A = \sqrt{2} \), find the value of \( \sin A \cos A \).
Two coins are tossed simultaneously, what is the probability of getting at least one head?
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.