Matrix and determinant Question no. 31 If A= , then A 100 = looks_one 2 100 A looks_two 2 99 A looks_3 2 101 A looks_4 None of these Answer Option looks_two 2 99 A Solution Solution : Characteristic eqaution : (1- λ) 2 - 1 = 0 λ 2 + 1 - 2λ - 1 = 0 λ 2 - 2λ = 0 A 2 = 2A A 3 = 2A 2 = 2 2 A A 4 = 2A 3 = 2 3 A . . . . A 100 = 2 99 A Question no. 32 Matrix A= is invertible for looks_one k=1 looks_two k=0 looks_3 k=-1 looks_4 All real k Answer option looks_two k=0 Solution Solution : For Invertible , |A| ≠ 0 1(1) - k(k) ≠ 0 k 2 ≠ 1 K ≠ 1 , -1 Question no. 33 If , then values of x,y,z,w are looks_one 2,2,3,4 looks_two 2,3,1,2 looks_3 3,3,0,1 looks_4 None of these Answer option looks_one 2,2,3,4 Solution Solution : x+ y = 4 .....[1] x- y = 0 .......[2] Solve [1] and [2] x = 2 , y = 2 2...

Progression Question no. 1 What is the 15 th term of the series 3, 7 , 13 , 21 , 31 ....? looks_one 205 looks_two 225 looks_3 238 looks_4 241 Answer looks_4 241 Solution Solution : Given series is 3, 7 ,13 ,21 , 31 ..... as it is observed that given series is not in A.P. , G.P. and H.P. But difference of terms 7-3=4 , 13-7=6 , 21-13= 8 31-21 =10 are in A.P. if differences of term are in A.P. , there is formula of nth term in this type of series. t n = n 2 a + bn + c t 1 = a(1) 2 + b(1) + c =a + b + c = 3 t 2 = a(2) 2 + b(2) + c = 4a + 2b + c = 7 t 3 = a(3) 2 + b(3) + c = 9a + 3b + c = 13 solve all three equation ,find the value of a,b,c a= 1 b= 1 c= 1 now, tn = n 2 + n + 1 t 15 = (15) 2 + (15) + 1 = 225 +16 = 241 Question no. 2 If the n th term of an A.P. is 2n-1, what is the sum of upto n terms ? looks_one n 2 looks_two n 2 -1 looks_3 n 2 +1 looks_4 0.5...

differential equation Question no. 1 The degree and order respectively of the differential equation are looks_one 1,1 looks_two 1,2 looks_3 2,1 looks_4 2,2 Answer Option 1. 0 Solution very soon 16 Question no. 2 The differential equation of the curve y =sinx is looks_one looks_two ...

COMPLEX NUMBER Question no. 1 The amplitude of 0 looks_one 0 looks_two &#x03C0/2 looks_3 &#x03C0 looks_4 none of these Answer Option looks_one 0 Solution The amplitude of 0 Given : Z= 0, it means no imginary part if we assume 'zero' a small positive number it will be on +ve axis and make 0 degree angle Question no. 2 The amplitude of (1+√ 3 i)/(√ 3 +i) is looks_one &#x03C0/3 looks_two -&#x03C0/3 looks_3 &#x03C0/6 looks_4 -&#x03C0/6 Answer Option looks_3 &#x03C0/6 Solution Question no. 3 The complex number (1+2i)/(1-i) lies in which quadrant of the complex plane looks_one First looks_two Second looks_3 Third looks_4 Fourth answer Option looks_two Second Solution Question no. 4 If x= cosB + i sinB , then = looks_one cotB looks_two cot(B/2) looks_3 icot(B/2) looks_4 itan(B/2) answer Option looks_3 icot(B/2) ...