The function \(f:\mathbb{R}\to[-1,1]\) defined by \(f(x)=\cos x\) is:

If \(\vec a\) is a unit vector and \((\vec x-\vec a)\cdot(\vec x+\vec a)=15\), then the value of \(|\vec x|\) is:

If \(y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots+\infty}}}\) then \(\frac{dy}{dx}\) equals to

Match List-I with List-II List-I | List-II (A) The degree of the differential equation \(\left(\frac{d^2y}{dx^2}\right)^2+\left(\frac{dy}{dx}\right)^2=x\sin\left(\frac{dy}{dx}\right)\) | (I) 4 (B) The degree of the differential equation…

If \(A\) and \(B\) square matrices of order 3 such that \(|A|=-1\), \(|B|=5\), then the value of \(|2AB|\) is :

Match List-I with List-II List-I | List-II (A) If vector \(\vec a\) and \(\vec b\) are such that \(\vec a=\lambda\vec b\) and \(|\vec a|=|\vec b|\), then | (I) \(\vec a\) and \(\vec b\) are orthogonal (B) Projection vector of \(\vec a\) on \(\vec b\) | (II) [0,12] (C) \(\vec a\)…

For the LPP: minimize \(z=6x+3y\) subject to the constraints \(4x+y\ge80\) \(x+5y\ge115\) \(3x+2y\le150\) \(x\ge0,\ y\ge0\) then the minimum value of z is

The area (in sq.units) of the region enclosed by the curve \(y=\cos x,\ \frac{-\pi}{2}\le x\le\frac{\pi}{2}\) and the \(x\)-axis is:

Let \(L_1\) and \(L_2\) be two lines, represented as, \(L_1: \vec r=\hat i+\hat j+\lambda(2\hat i-\hat j+\hat k)\) and \(L_2: \vec r=2\hat i+\hat j-\hat k+\mu(4\hat i-2\hat j+2\hat k)\), where \(\lambda\) and \(\mu\) are scalars. Then which of the following are true? (A) \(L_1\)…