A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence θ. The reflected (R) and transmitted (T) intensities, both as function of θ, are plotted. The correct sketch is
For a>b>c>0, if the distance between (1,1) and the point of intersection of the line ax+by−c=0 is less than 22 then,
The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side?
Three randomly chosen nonnegative integers x,yandzare found to satisfy the equation x+y+z=10.Then the probability that zis even, is:125 (b) 21 (c) 116 (d) 5536
There are five students S1, S2, S3, S4and S5in a music class and for them there are five seats R1, R2, R3, R4and R5arranged in a row, where initially the seat Riis allotted to the student Si, i=1, 2, 3, 4, 5. But, on the examination day, the five students are randomly allotted five seats.The probability that, on the examination day, the student S1gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her is403(b) 81(c) 407(d) 51
Let [x] be the greatest integer less than or equal to x˙ Then, at which of the following point (s) function f(x)=xcos(π(x+[x])) is discontinuous? (a)x=1 (b) x=−1 (c) x=0 (d) x=2
Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number in which 5 boys and 5 girls stand in such a way that exactly four girls stand consecutively in the queue. Then the value of nm is ____
PARAGRAPH XLet Sbe the circle in the xy-plane defined by the equation x2+y2=4.(For Ques. No 15 and 16)Let E1E2and F1F2be the chords of Spassing through the point P0(1, 1)and parallel to the x-axis and the y-axis, respectively. Let G1G2be the chord of Spassing through P0and having slope −1. Let the tangents to Sat E1and E2meet at E3, the tangents to Sat F1and F2meet at F3, and the tangents to Sat G1and G2meet at G3. Then, the points E3, F3and G3lie on the curvex+y=4(b) (x−4)2+(y−4)2=16(c) (x−4)(y−4)=4(d) xy=4