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There are 10 books in a shelf with different titles:five or these have red cover and others have green cover. In how many ways can these be arranged so that the red books are placed together ?

Let y=f(x) be the solution of the differential equation (dy)/(dx)+k/7 x tan x=1+xtanx-sinx, where f(0)=1 and let k be the minimum value of g(x) where g(x)="max"|(sqrt(193)-1)/2cosy+cos(y+(pi)/3)-x| where yepsilonR then Number of solution of the equation f(x)=2^(x)-x^(2)+x+cosx is equal to

If the tangent and normal to the hyperbola x^(2) - y^(2) = 4 at a point cut off intercepts a_(1) and a^(2) respectively on the x-axis, and b_(1) and b_(2) respectively on the y-axis, then the value of a_(1)a_(2) + b_(1)b_(2) is

If z = x + iy and if the point P in the argand plane represents z , then the locus of P satisfying the equation Amplitude of (z -1) is (pi)/(2)

Let y=f(x) be the solution of the differential equation (dy)/(dx)+k/7 x tan x=1+xtanx-sinx, where f(0)=1 and let k be the minimum value of g(x) where g(x)="max"|(sqrt(193)-1)/2cosy+cos(y+(pi)/3)-x| where yepsilonR then Area bounded by y=f(x) and its inverse between x=(pi)/2 and x=(7pi)/2 is

If z = x + iy and if the point P in the argand plane represents z , then the locus of P satisfying the equation {z in C , |z - 2| = 2 |z - 1| }

Show that x + y + 1= 0 touches the circle x^(2) + y^(2) -3x + 7y 14 = 0 and find its point of contact.

Two integers x and y are chosen one by one with replacement from 0, 1, 2,…,100. Find the probability that |x - y| le 3.

int_(0)^(1) (dx)/( x+ sqrt(x)) =……

Using elementary transformations, find the inverseof the matrices [(2,-3,3),(2,2,3),(3,-2,2)]

If the normal at any point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1meets the axes in G and g respectively. Find the ratio PG : Pg

If A=[{:(2,3),(1,-4):}],B=[{:(1,-20),(-1,3):}] then verify (AB)^(-1)=B^(-1)A^(-1)

Find the area of the parallelogram whose adjcent sides are determined by the vector.

[hati-hatj hatj -hatk hatk-hati] is equal to

Let vec(alpha)=3hat(i)+hat(j), vec(beta)=2hat(i)-hat(j)+3hat(k)and vec(beta)=vec(beta)_(1)-vec(beta)_(2), such that vec(beta)_(1) is parallel to vec(alpha) and vec(beta)_(2) is perpendicular to alpha. Find vec(beta)_(1)xx vec(beta)_(2).

From a pack of 52 cards, 3 cards are drawn successively with replacement each time. The probability of getting atleast one king is

C_1//1-C_2//2+C_3//3-C_4//4+…+(-1)^(n-1) C_n//n=

int_(2)^(3)(2-x)/(sqrt(5x-6-x^2))dx=

For j =0,1,2…nlet S _(j) be the area of region bounded by the x-axis and the curve ye ^(x)=sin xfor f pi le x le (j +1) pi The value of S_(o) is :

Number of unit squares in a chess board is

Let a die be loaded in such a way that even faces are twice likely to occur as the odd faces. What is the probability that a prime number will show up when the die is tossed?

Find the probability that in a family having 4 children, girls are in majority.

Find the equation of the circle with centre C and redius r where. C= (0,0), r= 9

Choose the correct answer: In a box containing 100 bulbs, 10 are defective. The probability that out of a﻿ sample of 5 bulbs, none is defective is

If f(x)= 2x and g(x) = (x^(2))/(2) + 1, then which of the following can be a discontinuous function?

Find the parametric equations of the cirlces (i) x^(2)+y^(2)=1 (ii) x^(2)+y^(2)-4x+6y-12=0 (iii) 4(x^(2)+y^(2))=9 (iv) 2x^(2)+2y^(2)=7 (v) (x-3)^(2)+(y-4)^(2)=8^(2)

A family consists of father, mother 2 daughter and 2 sons. In how many different ways can they sit at a around table if 2 daughter wish to sit on either

y = e^(x)(a cos x + b sin x)

Find (dy)/(dx) in the following y= sin^(-1) ((2x)/(1+ x^(2)))

ABCisa rightangledisoscelestriangleswithangleB = 90 ^@if Dis a pointon A Bso thatangleDCB= 15 ^@and ifAd = 35cm, thenCD=

A coin is tossed any number of times until a head appears. If x donotes the number of tosses till head uappear then P(x ge 3)=

Let A be a 3xx3 matrix such that A [(1,2,3),(0,2,3),(0,1,1)]=[(0,0,0),(1,0,0),(0,1,0)], then A^(-1) is :

If the position vector of A,B,C are 2i+3j+4k , i+2j, j+2kand vec(AB) = Pvec(AC) then P=

Let f(x)=x^(2)e^(-2x),x gt 0. The maximum value off(x) is

All three roots of az^3+bz^3+cz+d=0 , z being complex number. Further , assume that the origin, z_1 and z_2 form an equilateral triangle, then :

Find the value of xsqrt(6x^(4) + 4x^(2) + 2) gt -2x^(2) + 5x - 4

Let A = {a, b, c,d). If an equivalence relation R on A has exactly one equivalence class, then number of elements in R is_________

In theintermediateexaminationa candidatehasto passin eachof his6 papers . Thenumber ofwaysin withinhe can fail is

Write down the set of letters forming that word Administration?

If the system of linear equations x+2ay+az=0, x+3by+bz=0,x+4ch+cz=0 has a non zero solution then a,b,c

Minimise Z=3x+2y subject to the constraints, x+yge8………..1 3x+5yle15…………2 xge0, yge0………..3

If Z=cos phi+isin phi(AA phi in ((pi)/(3),pi)), then the value of arg(Z^(2)-Z) is equal to (where, arg(Z) represents the argument of the complex number Z lying in the interval (-pi, pi] and i^(2)=-1)

Prove that (b-c)sinA +(c-a)sinB +(a-b)sinC=0

Find the condition that the point (x,y) may lie on the line joining (1,2) and (5,-3).

A black and red dice are rolled. Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5

If y=sin^(-1)(2^(x+1)/(1+4^x))," find "(dy)/(dx).

Let a solution y=y(x) of the differential equation xsqrt(x^(2)-1) dy-ysqrt(y^(2)-1)dx=0 satisfy y(2)=(2)/(sqrt3) Statement-1, y(x)=sec(sec^(-1)x-(pi)/(6)) Statement-2 : y(x) is given by (1)/(y)=(2sqrt3)/(x)-sqrt(1-(1)/(x^(2)))

Let (1 + x)^(n) = 1 + a_(1)x + a_(2)x^(2) + ... + a_(n)x^(n). If a_(1),a_(2) and a_(3) are in A.P., then the value of n is

int_(0)^(pi//2)sin 2 x.ln(tan x)dx

Choose the correct answer: In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is