Indian Institute of Technology Kanpur (IIT-K) 2006 JT - Question Paper

infinitely many
Solution 84: Let the ages of husband, spouse and daughter be x, y and z respectively.
Now as per ques.
x+2y+3z = 85…(i)
2x+4y+6z = 425 …(ii)
5x+10y+15z = 450…(iii)
We take formula (i) and (ii)
Here a1=1,b1=2,c1= three and d1 = 85
And a2 = 5, b2 = 10, c3 = 15 and d2 = 450
Now






 = ,








 = = ,









 = = ,












 = =
Here

















 = = ¹ so the number of possible solution is 0.
Hence the ans choice is (A).
Q.85 The determinant
4 four 4 4
3 three 3 3
2 two 2 2
1 one 1 1
1
1
1
1
x x x x
x x x x
x x x x
x x x x
+
+
+
+
equals
(A) 1+x1+x2+x3+x4 (B) x1+x2+x3+x4 (C) x1x2x3x4 (D) 1+x1x2x3x4
Solution 85 : 

4 four 4 4
3 three 3 3
2 two 2 2
1 one 1 1
1
1
1
1
x x x x
x x x x
x x x x
x x x x
+
+
+
+

  
4 four 4 4
3 three 3 3
2 two 2 2
1 two three four one two three four one two three four one two three 4
1
1
1
1 one 1 1
x x x x
x x x x
x x x x
x x x x x x x x x x x x x x x x
+
+
+
+ + + + + + + + + + + + + + + +

 
4 four 4 4
3 three 3 3
2 two 2 2
1 two three 4
1
1
1
1 one 1 1
(1 )
x x x x
x x x x
x x x x
x x x x
+
+
+
+ + + + 

 ! " ##$# 

4 four 4
3 three 3
2 two 2
1 two three 4
0 1
0 1
1 1
0 one 1 1
(1 )
x x x
x x x
x x x
x x x x
+
+
+
+ + + + 

4 four 4
1 two three four three 3 3
1
1
1 one 1
(1 )
x x x
x x x x x x x
+
+ + + + + 

 ! " ##$# 

4 4
1 two three four three 3
0 1
1 1
0 one 1
(1 )
x x
x x x x x x
+
+ + + + + 
 (1 )[1 (1 )] one two three four 4 four + x + x + x + x ´ + x - x 
 (1 ) one two three four + x + x + x + x 
 %" ""&'()
Q.86 Ms. Rao paid equated monthly installments (EMI of Rs. 25,000 every in January and February towards
her home loan, whose outstanding principal amount was Rs. 10,00,000 in December. every EMI
consists of interest on outstanding loan amount for the month and part payment of the loan amount. If

Earning:   Approval pending.