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

Q.114 What is the digit in the units place of 10251?
(A) two (B) four (C) six (D) 8
Solution 114: C:"&(




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A # 5 '
  
  
  

 
 
 8 8
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Q. 115 In D PQR, m ÐQPR=45°, m ÐPQR=60° and PR =15 QS is a median and T is the mid-point of QS.
PT extended meets QR at U. Then QU equals
(A) five cm (B) six cm (C) 7.5 cm (D) 10cm
Q.116 The number of distinct real number x for which four 2
8
x - x
is a positive integer is
(A) three (B) four (C) five (D) 8
Solution 116: 06-"1"  """)
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-"+:+" 
4 2
8
x - x
"-"+ 
""
+--"+:1"++C*C" 
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+-"+-"+:1  ""+"")
Q.117 The minimum attainable value of the function
f(x, y) = x2 +1 + (x - y)2 + four + (12 - y)2 + four is
(A) 12 (B) 13 (C) three + 148 (D) four + 145
Q.118 In a right-angled triangle LIPQR with PQ ¹ QR , M is a point on its hypotenuse PR. L and N are feet
of the perpendiculars from M on PQ and QR respectively. LN will be minimized when
(A) D PQM and D PQR are similar (B) M is the mid-point of PR
(C) m Ð PQM = m ÐMQR = 45° (D) PM : MR = PQ :QR
Q.119 In D PQR, QR = QR and m ÐQPR=20°. S is a point on PR such that m ÐSQR = 60° and T is a point
on PQ such that mÐTRQ = 50°. Then m ÐSTR equals
(A) 60° (B) 70° (C) 80° (D) 90°
Q.120 The number of ordered triplets (x, y, z) such that x, y, z are primes and xy +1 = z is
(A) (B) one (C) two (D) infinitely many

Earning:   Approval pending.