Explore topic-wise InterviewSolutions in .

Examine for the rational roots of x^8 - 3x + 1=0

Statement-1 : cos.(pi)/(7)cos.(2pi)/(7)cos.(4pi)/(7)=-(1)/(8) Statement-2 : costhetacos2thetacos2^(2)thetaunderset(cos2^(n-1)theta)(............)=-(1)/(2^(n))" if "theta=(pi)/(2^(n)-1)

Show that each of the given three vectors is a unit vector. (1)/(7)(2hati+3hatj+6hatk),(1)/(7)(3hati-6hatj+2hatk),(1)/(7)(6hati+2hatj-3hatk)Also , show that they are mutually perpendicular to each other.

The nummber of tangents to x^(2)//9-y^(2)//4=1 throught (6,2) is

Solve for x: - tan^(-1)("x"+1)+tan^(-1)("x"-1)=tan^(-1) (8/31)

The term independent of x in the expansion of (3/2x^(2) - 1/(3x))^(9) is

{:(,"Hyperbola",,"Foci "),(I,((x-1) ^(2) )/(16) - ((y-2)^(2) )/(9) =1,,(a) ("1,-1")("-9,-1")),(II,((x+2)^(2) )/(9) - ((y-3) ^(2) )/(27) =1 ,,(b) ("6,2") ("-4,2")),(III,((x+1)^(2) )/(25) -((y+2)^(2) )/(16)= 1 ,,(c) ("4,3") ("-8,3")),(IV,9x^(2) -4y(2) =8","(2","-) ,,(d) (-1pm sqrt (41) ","-2)):}

int_(0)^(log5)(e^(x)sqrt(e^(x)-1))/(e^(x)+3)dx=

Using integration, find the area of the following region: R={(x,y):x^2leyle|x|}

int_(0)^(pi//2) (200 sinx + 100 cosx)/(sinx + cosx) dx is equal to

Find the scalar product of the following pairs of vectors and the angle between them. 2hati-3hatj+6hatk and 2hati-3hatj-5hatk

If A=[{:(3,1),(7,5):}] and A^2+xI=yA then find X and Y. Hence find A^(-1)

If vecaxxvecb = vecbxxvecc ne vec0, prove that veca+vecc = mvecb, where m is a scalar.

Findtheareaof theregionboundedby thecirclesx^2+ y^2 = 16 and(x+4)^2 +y^2=16

int(1)/(sin^(2)x cos^(2)x)dx=

Find the maximum sum of the A.P. 40 +38+36+34+32+……………

If (1,3) and (2,k)are conjugate points with respect to the circlex^(2) + y^(2) = 35, then find k .

Find the area of the region{(x,y):0 le y le x^(2)+1,0 le y le x + 1,0 le x le 2}.

Volume of a tetrahedron is k area of one face) (length of perpendicular from the opposite vertex upon it). where k is :

If (x_(1),y_(1)) and (x_(2),y_(2)) are ends of focal chord of y^(2)=4ax then x_(1)x_(2)+y_(1)y_(2) =

Let "c" be the circle with centre at (1,1) and radius =1. If 'T' is the circle centred at (0,y) passing thorugh origin and touching the circle 'C' externally , then the radius of 'T'is equalto:

If x = r cos theta, u = r sin theta then (del theta)/(del x) is:

Findthe arealyingabovex-axisand includedbetweenthe circlex^2+y^2 = 8xand insideof theprarabolay^2= 4x .

Evaluate the following integrals. int(x)/(x^(2) + 1) dx

If int (1)/( 2 + sin^(2) x )dx = k.tan^(-1) ( l tan x ) + C then (k, l )=

obtain the equation of hyperbola in each of the following cases: foci at (0,+-sqrt2) and vertices (0,+-1)

Differentiate sin (cos (x^2)) with respect to x.

Lines vecr=veca_1+tvecb_1 and vecr=veca_2+svecb_2 are parallel iff:

A regular polygon has 20 sides How many triangles can be drawn by using the vertices, but not using the sides?

{:(,"Equation of the curve ",,"Nature of the curve "),(I,x=2 (cos t+sin t)y=5(cost-sint )",", ,(a) ("Parabola")),(II,x=3( cosh theta +sin h theta )y=(4cos h theta -sin h theta )",",,(b) ("elipse")),(III,x=sin ^(2) t y=2cos t "," ,,(c) (hyperbola)) :}

Consider, f(x)=(x+2a)(x+a-4)(a in R), g(x)=k(x^(2)+x)+3k+x(k in R) and h(x)=(1-sin theta)x^(2)+2(1-sin theta)x-3 sin theta ( theta in R-(4n+1)(pi)/(2), n in I) If f(x) lt 0 for -1 le x le 1, then 'a' satisfies

Consider, f(x)=(x+2a)(x+a-4)(a in R), g(x)=k(x^(2)+x)+3k+x(k in R) and h(x)=(1-sin theta)x^(2)+2(1-sin theta)x-3 sin theta ( theta in R-(4n+1)(pi)/(2), n in I) If g(x) gt-3 for all real x, then the values of k are given by

If [veca, vecb, vec c]=1, then the value of (veca*(vecb xx vec c))/((vec c xx veca)*vecb)+(vecb*(vec cxx vec a))/((veca xx vecb)*vec c)+(vec c*(veca xx vecb))/((vec c xx vecb)*veca) is

Consider, f(x)=(x+2a)(x+a-4)(a in R), g(x)=k(x^(2)+x)+3k+x(k in R) and h(x)=(1-sin theta)x^(2)+2(1-sin theta)x-3 sin theta ( theta in R-(4n+1)(pi)/(2), n in I) If the quadratic equation h(x)=0 has both roots complex, then theta belongs to

If 12 x -4ygt 8 and 2/3 x + 6y ge 14 form a system of inequalities, which of the following graphs shows the solution set for the system ?

A ray of light passes through a prism whose refracting angle is 5^(@) and dispersive power is 0.03. The refractive index for the mean ray in a spectrum is 1.62. The mean deviation and angle of dispersion respectively are

A, B, C, D, E, F in that order, are the vertices of a regular hexagon with centre orgin. If the position vectors of the vertices A and B are respectively, 4hati+3hatj-hatk and -3hati+hatj+hatk, then DE is equal to

The plane 2x – 3y + 6z - 11 = 0 makes an angle sin^(-1)alpha with X- axis. The value of alpha is equal to …............

Verify Lagrange 's mean value theorem for the function f(x) = x+ (1)/(x), 1 le x le 3

If the curves (x ^(2))/(4) + (y ^(2))/(9) =1 and (x ^(2))/(16) -(y ^(2))/(k)=1 cut each other orthogonally, then k =

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and﻿ P(EcapF) = 0.2, find P(E|F) and P(F|E)﻿.

A line of fixed length (a+b) moves so that its ends are always on two perpendicular straight lines fixed. Prove that a marked point on the line , which divides this line in to portions of lengths a and b describes an ellipse when a=8 , b=12.

In a box containing 15 identical bulbs, 5 are defective. If 5 bulbs are drawn at random from the box with replacement, find the probability that (i) none is defective (ii) only one of them is defective (iii) atleast one of them is defective

9 different pens and 3 different books are distributed randomly to 3 students giving 4 things to each. Find the probability that every student must receive atleast one book.

The probability distribution of X is (# #TRG_MAT_MCQ_XII_P2_C08_E02_005_Q01.png" width="80%"> Then P(X is odd)=

Let w(x,y)=xy+(e^(y))/(y^(2)+1) for all (x,y)inRR^(2). Calculate (del^(2)w)/(delydelx)and(del^(2)w)/(delxdely)

If A is an invertible matrix of order 2 then find |A^(-1)|

Distance of the point (2,5,-3) from the plane vec r.(6hat i-3 hat j+2 hat k)=4 is

A delegation of four friends is to be selected from a group of 12 friends .The number of ways,the delegationbe selected if two particular friends redused to be together and two other particular friends wish to be together only in the delegation is

If [veca, vecb, vec c]=1, then the value of (veca(vecb xx vec c))/((vec c xx veca)vecb)+(vecb(vec cxx vec a))/((veca xx vecb)vec c)+(vec c(veca xx vecb))/((vec c xx vecb)veca) is

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(EcapF) = 0.2, find P(E|F) and P(F|E).