List of top Mathematics Questions asked in HPBOSE Class XII

If A = \(\{a,e,i,o,u\},\) B = \(\{a,b,c\},\) then A $\cup$ B is:

\(cos\left(\frac{\pi}{2} + x\right) \) is equal to: 
 

If \( f(x) = x^2 \), find \( \frac{f(1.1) - f(1)}{1.1 - 1} \).
Find the values of the other five trigonometric functions, if \( \cos x = -\frac{1}{2} \), and \( x \) lies in the third quadrant.
Find the equation of the right bisector of the line segment joining the points \( (3,4) \) and \( (1,2) \).
Find the coordinates of the focus, axis of the parabola, the equation of the directrix, and the length of the latus rectum, if \( y^2 = 12x \).
The sum of the first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the 1st term, the common ratio, and the sum to \( n \) terms of the G.P.
Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity, and the length of the latus rectum of the ellipse: \[ \frac{x^2}{36} + \frac{y^2}{16} = 1 \]
Find the value of 'n' so that \( \frac{a^{n+1} + b^{n+1}}{a^n + b^n} \) may be the geometric mean between a and b.
The vertices of \( \triangle PQR \) are \( P(2,1) \), \( Q(-2,3) \), and \( R(4,5) \). Find the equation of the median through the vertex \( R \).
Express the given complex number in the form of \( a + ib \): \( \left( \frac{1}{3} + 3i \right)^3 \)
Using Binomial Theorem, Evaluate: \( (102)^5 \)
If \( \frac{2}{11} \) is the probability of an event, what is the probability of the event 'not A'?
Solve the given inequalities and represent the solution graphically on the number line: \[ 2(x - 1)<x + 5, \quad 3(x + 2)>2 - x \]
Find the multiplicative inverse of \( \sqrt{5} + 3i \)
Evaluate \( \left( \sqrt{3} + \sqrt{2} \right)^6 - \left( \sqrt{3} - \sqrt{2} \right)^6 \)
Solve the given inequality for real \( x \): \[ \frac{3(x - 2)}{5} \leq \frac{5(2 - x)}{3} \]
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.
How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
Verify that (0,7,10), (-1,6,6) and (-4,9,6) are the vertices of a right angled triangle.
For some constants \( a \) and \( b \), find the derivative of \( \frac{x - a}{x - b} \)
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.
Prove that \( \frac{\sin x - \sin y}{\cos x + \cos y} = \tan \frac{x - y}{2} \).
The 4th term of a G.P. is square of its second term, and the 1st term is -3. Determine its 7th term.
A collection of most dangerous animals of the world is: