Silver (atomic weight =108 g mol−1) has a density of 10.5 g cm−3 . The number of silver atoms on a surface of area 10−12m2 can be expressed in scientific notation as y×10x . The value of x is
Let b1>1 for i=1,2,……,101. Suppose logeb1,logeb10 are in Arithmetic progression (A.P.) with the common difference loge2. suppose a1,a2……….a101 are in A.P. such a1=b1anda51=b51. If t=b1+b2+……+b51ands=a1+a2+……+a51 then
The coefficients of three consecutive terms of (1+x)n+5are in the ratio 5:10:14. Then n=___________.
Let PR=3i^+j^−2k^andSQ=i^−3j^−4k^determine diagonals of a parallelogram PQRS,andPT=i^+2j^+3k^be another vector. Then the volume of the parallelepiped determine by the vectors PT, PQand PSis5b. 20c. 10d. 30
Consider the hyperbola H:x2−y2=1 and a circle S with centre N(x2,0) Suppose that H and S touch each other at a point (P(x1,y1) with x1>1andy1>0 The common tangent to H and S at P intersects the x-axis at point M. If (l,m) is the centroid of the triangle ΔPMN then the correct expression is (A) dx1dl=1−3x121 for x1>1 (B) dx1dm=3(x12−1)x!)forx1>1 (C) dx1dl=1+3x121forx1>1 (D) dy1dm=31fory1>0
Which of the following is (are) NOT the square of a 3×3 matrix with real entries? (a)⎣⎡10001000−1⎦⎤ (b) ⎣⎡−1000−1000−1⎦⎤ (c)⎣⎡100010001⎦⎤ (d) ⎣⎡1000−1000−1⎦⎤
Let f1:R→R, f2:(−2π,2π)→R f3:(−1, e2π−2)→Rand f4:R→Rbe functions defined by