A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is
Let fprime(x)=2+sin4πx192x3forallx∈Rwithf(21)=0.Ifm≤∫211f(x)dx≤M, then the possible values of mandM are (a)m=13,M=24 (b) m=41,M=21(c)m=−11,M=0 (d) m=1,M=12
Let P and Q be distinct points on the parabola y2=2x such that a circle with PQ as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle ΔOPQ is 32 , then which of the following is (are) the coordinates of P?
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 PQ be a focal chord of the parabola y2=4ax The tangents to the parabola at P and Q meet at a point lying on the line y=2x+a,a>0. Length of chord PQ is
In a triangle PQR, P is the largest angle and cosP=31. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)
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