In the mac. Arthur process of extraction
let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from the two planes P1:x+2y−z+1=0 and P2:2x−y+z−1=0, Let M be the locus of the feet of the perpendiculars drawn from the points on L to the plane P1. Which of the following points lie(s) on M?
Let Sbe the circle in the xy-plane defined by the equation x2+y2=4.(For Ques. No 15 and 16)Let Pbe a point on the circle Swith both coordinates being positive. Let the tangent to Sat Pintersect the coordinate axes at the points Mand N. Then, the mid-point of the line segment MNmust lie on the curve(x+y)2=3xy(b) x2/3+y2/3=24/3(c) x2+y2=2xy(d) x2+y2=x2y2
Ifα=∫01(e9x+3tan(−1)x)(1+x212+9x2)dxwherηn−1takes only principal values, then the value of ((log)e∣1+α∣−43π)is
The following integral ∫4π2π(2cosecx)17dxis equal to(a)∫0log(1+2)2(eu+e−u)16du(b)∫0log(1+2)2(eu+e−u)17du(c)∫0log(1+2)2(eu−e−u)17du(d)∫0log(1+2)2(eu−e−u)16du
If 2x−y+1=0 is a tangent to the hyperbola a2x2−16y2=1 then which of the following CANNOT be sides of a right angled triangle? (a)a,4,2 (b) a,4,1(c)2a,4,1 (d) 2a,8,1
For 3×3matrices MandN,which of the following statement (s) is (are) NOT correct ?NTMNis symmetricor skew-symmetric, according as mis symmetric or skew-symmetric.MN−NMis skew-symmetric for all symmetric matrices MandN˙MNis symmetric for all symmetric matrices MandN(adjM)(adjN)=adj(MN)for all invertible matrices MandN˙
Let f:[0,2]→R be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1Let:F(x)=∫0x2f(t)dtforx∈[0,2]I˙fFprime(x)=fprime(x) . for all x∈(0,2), then F(2) equals (a)e2−1 (b) e4−1(c)e−1 (d) e4