List of top Questions asked in UP Board XII- 2026

Mention any four (4) problems of the present education system.

Achievement test measures

Mental health related program is conducted at global level by

If the child is mentally healthy, he

Factor(s) of affecting mental health is/are

Educational guidance is related to

Rorschach test is used to examine

According to Tagore, in what kind of environment should education be imparted?

Which method of waste disposal is more practical to reduce environmental pollution?

Which activity is most suitable for promoting girl education?

Upanayan Sanskar is related to which education?

If \(A=\begin{bmatrix}1&2&3\\3&-2&1\\4&2&1\end{bmatrix}\), then show that \(A^3-23A-40I=0\).

Evaluate: \(\displaystyle\int_0^\pi \frac{x\,dx}{a^2\cos^2x+b^2\sin^2x}\)

Solve the system of linear equations by Matrix Method: \(2x-3y+5z=11\), \(3x+2y-4z=-5\), \(x+y-2z=-3\).

Find the general solution of the differential equation \(x\cos\left(\dfrac yx\right)\dfrac{dy}{dx} = y\cos\left(\dfrac yx\right)+x\).

Prove that the volume of the largest right circular cone that can be inscribed in a sphere of radius \(R\) is \(\dfrac{8}{27}\) of the volume of the sphere.

Find the area bounded by the ellipse \(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\).

A family has two children. If it is known that at least one child is a boy, then find the probability of both children being boys.

If the function \(f:\left[0,\dfrac{\pi}{2}\right]\to R\) is given by \(f(x)=\cos x\) and the function \(g:\left[0,\dfrac{\pi}{2}\right]\to R\) is given by \(g(x)=\sin x\), then prove that \(f\) and \(g\) are one-one, but \(f+g\) is not one-one.

Write \(\tan^{-1}\left(\dfrac{\cos x-\sin x}{\cos x+\sin x}\right)\), \(\dfrac{-\pi}{4}<x<\dfrac{3\pi}{4}\) in the simplest form.

If \(A=\begin{bmatrix}2&3\\1&-4\end{bmatrix},\ B=\begin{bmatrix}1&-2\\-1&3\end{bmatrix}\), then find \((AB)^{-1}\).

Is the function \(f(x)=\begin{cases}x+5,&x\le1\\x-5,&x>1\end{cases}\) continuous at \(x=1\)?

Find the shortest distance between the lines \(\vec r=\hat i+\hat j-\lambda(2\hat i+\hat j+\hat k)\) and \(\vec r=2\hat i+\hat j+\hat k+\mu(3\hat i-5\hat j+2\hat k)\).

Three vectors \(\vec a, \vec b\) and \(\vec c\) satisfy the condition \(\vec a+\vec b+\vec c=0\). If \(|\vec a|=3, |\vec b|=4\) and \(|\vec c|=5\), then find the value of \(\vec a\cdot\vec b+\vec b\cdot\vec c+\vec c\cdot\vec a\).

Solve: \(\displaystyle\int \cos^2 x\, dx\)