List of top Questions asked in HPBOSE Class XII- 2026

Express the given complex number in the form of \( a + ib \): \( \left( \frac{1}{3} + 3i \right)^3 \)

Evaluate \( \left( \sqrt{3} + \sqrt{2} \right)^6 - \left( \sqrt{3} - \sqrt{2} \right)^6 \)

For some constants \( a \) and \( b \), find the derivative of \( \frac{x - a}{x - b} \)

The 4th term of a G.P. is square of its second term, and the 1st term is -3. Determine its 7th term.

Prove that \( \frac{\sin x - \sin y}{\cos x + \cos y} = \tan \frac{x - y}{2} \).

How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

Show that the points (-2, 3, 5), (1, 2, 3), and (7, 0, -1) are collinear OR verify that the points (0,7,10), (-1,6,6) and (-4,9,6) are the vertices of a right angled triangle.

Verify that (0,7,10), (-1,6,6) and (-4,9,6) are the vertices of a right angled triangle.

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

If \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \), \( A = \{2, 4, 6, 8\} \), and \( B = \{2, 3, 5, 7\} \), verify that \( (A \cup B)' = A' \cap B' \).

Assertion (A): The radius of a circle in which a central angle of 60 degrees intercepts an arc length of 37.4 cm (using \( \pi = \frac{22}{7} \))
Reason (R): The formula to calculate the length of an arc is \( l = Q \times r \), where \( l \) is the arc length, \( Q \) is the central angle in radians, and \( r \) is the radius of the circle.

Assertion (A): The derivative of the function \( f(x) = x^2 \) with respect to \( x \) is \( 2x \).
Reason (R): The derivative of a power function \( x^n \) is given by the formula \( \frac{d}{dx}(x^n) = nx^{n-1} \).

A collection of most dangerous animals of the world is:

Let \( A = \{1, 2\}, B = \{3, 4\} \), then the number of relations from A to B is:

The radian measure of 520° is:

Assertion (A): When a die is thrown, the event of getting a number greater than 7 is an impossible event. Reason (R): A standard die has six faces, numbered from 1 to 6.

If \( n = 5 \) and \( r = 3 \), then the value of \( ^nP_r \) is:

A person has two parents, 4 grandparents, 8 great grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.

Complex conjugate of \( 3i - 4 \) is:

The derivative of \( \sin^2 x \), w.r.t. \( x \) is:

The equation of a line in the intercept form is:

The Value of \( \lim_{x \to 0} \frac{\sin x}{x} \) is:

The vertex of the parabola \( y^2 = 4ax \) is:

1st three terms of the sequence \( a_n = 2n + 5 \) is:

How can educated unemployment be reduced in Himachal Pradesh?