12th Standard Mathematics March 2026: Online Practice Test

If A is a \(3\times 3\) non-singular matrix such that \(AA^T=A^TA\) and \(B=A^{-1}A^T\), then \(BB^T=\)

If \(\rho(A)=\rho([A|B])\), then the system \(AX=B\) of linear equations is :

If z is a complex number such that \(z\in\mathbb{C}\setminus\mathbb{R}\) and \(z+\frac{1}{z}\in\mathbb{R}\), then \(|z|\) is :

The product of all four values of \(\left(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\right)^{\frac{3}{4}}\) is :

If f and g are polynomials of degrees m and n respectively and if \(h(x)=(f\circ g)(x)\), then the degree of h is :

If \(x<0\), then \(\tan^{-1}\left(\frac{1}{x}\right)\) is equal to :

The eccentricity of the circle is :

If a vector \(\vec{\alpha}\) lies in the plane of \(\vec{\beta}\) and \(\vec{\gamma}\), then

If the image of the point A(1, 2, 3) with respect to the plane \(\vec{r}\cdot(\hat{i}+2\hat{j}+4\hat{k})=38\) is A'(3, 6, 11), then the foot of the perpendicular from the point A to the given plane is :

One of the closest points on the curve \(x^2-y^2=4\) to the point (6, 0) is :

The value of 'c' satisfied by the Rolle's theorem for the function \(f(x)=x^3-3x^2,\ x\in[0,3]\) is :

The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?

Let \(A=\{(x,y)\mid a<x<b,\ c<y<d\}\subset\mathbb{R}^2\). If the function \(u:A\to\mathbb{R}^2\) is harmonic in A, then :

If \(f(x)=\int_0^x t\cos t\,dt\), then \(\frac{df}{dx}=\)

If \(f(x)=\int_1^x\frac{e^{\sin u}}{u}\,du,\ x>1\) and \(\int_1^3\frac{e^{\sin x^2}}{x}\,dx=\frac{1}{2}[f(a)-f(1)]\), then one of the possible values of a is :

The solution of the differential equation \(2x\frac{dy}{dx}-y=3\) represents :

P is the amount of certain substance left after time t. If the rate of evaporation of the substance is proportional to the amount remaining, then :

If the function \(f(x)=\frac{1}{12}\) for \(a<x<b\), represents a probability density function of a continuous random variable X, then which of the following cannot be the value of a and b?

A rod of length \(2l\) is broken into two pieces at random. The probability density function of the shorter of the two pieces is \(f(x)=\begin{cases}\frac{1}{l}, & 0<x<l\\ 0, & l\le x<2l\end{cases}\). The mean and variance of the shorter of the two pieces are respectively :

The dual of \(\neg(p\vee q)\vee[p\vee(p\wedge\neg r)]\) is :