IOE Examination [30 marks]

                  Tribhuvan University Institute of Engineering Entrance Examination Board 

                                        BE/B.Arch. Online Entrance Examination

                      IOE FREE EXAM   [30 questions]  

                                          Time: 45min 

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1. All of the following statements are correct except
   
   1.   The total length of an astronomical telescope is the sum of the focal lengths of its two lenses
   2.   The image formed by the astronomical telescope is always erect because the effect of the combination of the two lenses is divergent
   3.   The magnification of an astronomical telescope can be increased by decreasing the focal length of the eye-piece
   4.   Final image formed by astronomical telescope is inverted, not erect.
2. The ratio of resolving power of telescope, when lights of wavelength 4400
   A°and 5500 A°are used is
   1.   5:4
   2.   9:1
   3.   4:5
   4.   16:25
3. The frequency of vibration of a rod is 200Hz. If the velocity of sound in air is 340m/s, the wave length of the sound produced is
   1.   1.7m
   2.   13.6m
   3.   3.4m
   4.   6.8
4. Which of the following transitions in hydrogen atoms emit photons of highest frequency?
   
   1.   n=1 to n=2
   2.   n=2 to n=1
   3.   n=2 to n=6
   4.   n=6 to n=2
5. The escape velocity of a particle of mass m varies as
   1.   m²
   2.   m⁰
   3.   m¹
   4.   m³
6. An iron bar of length 10 m is heated from 0°C to 100°C. If the coefficient of linear thermal expansion of iron is 10 * 10–6 /°C, the increase in the length of bar is
   1.   0.5cm
   2.   1cm
   3.   2.0cm
   4.   1.5cm
7. If two cells are connected in series opposition in an electrical circuit, when does current flow? Assume only conductors are present.
   1.   Size of cells is different
   2.   Magnitude of emf of cells is same
   3.   Magnitude of emf of cells is different
   4.   Always works irrespective of nature of cells
8. If the direction of the initial velocity of the charged particle is perpendicular to the magnetic field, the orbit of charged particle will be
   
   1.   a cycloid
   2.   a straight line
   3.   a helix
   4.   a circle
9. In β- decay,a
   1.   neutron converts into a proton emitting antineutrino.
   2.   proton converts into a neutron emitting neutrino.
   3.   neutron converts into a proton emitting neutrino.
   4.   proton converts into a neutron emitting antineutrino.
10. The potential difference across the Coolidge tube is 20 kV and 10 mA current flows through the voltage supply. Only 0.5% of the energy carried by the electrons striking the target is converted into X-rays. The power carried by the X-ray beam is P. Then
    1.   P=2 W
    2.   P=0.1 W
    3.   P=1 W
    4.   P=10 W
11. A point (x, y, z) moves parallel to z-axis. Which of the three variable x, y, z remain fixed
    1.   x
    2.   y and z
    3.   x and y
    4.   z and x
12. If in a ΔABC,
    cosA/a= cosB/b=cosC/c , then the triangle is?
    1.   Right angled
    2.   Obtuse angled
    3.   Isosceles
    4.   Equilateral
13. The volume V and depth x of water in a vessel are connected by the relation V=5x−x²/6 and the volume of water is increasing at the rate of 5cm³/sec , when x=2cm . The rate at which the depth of water is increasing, is
    1.   (5/18)cm/sec
    2.   (5/16)cm/sec
    3.   (1/4)cm/sec
    4.   None of these
14. If tangent to circle x²+y²=4 at (2,0) is tangent to ellipse x²/a²+y²/b²=1 , then the value of a is
    1.   1
    2.   −2
    3.   4
    4.   -4
15. The area bounded by y=log⁡x , the ordinates y=0,y=2 and y axis is :
    
    1.   e²−e
    2.   e²−1
    3.   e²−2
    4.   e²−2e
16. The sum can be found of a infinite G.P. whose common ratio is r,
    
    1.   For all values of r
    2.   Only for 0<r<1
    3.   For only positive value of r
    4.   Only for −1<r<1(r≠0)
17. The function y=x²/1−x² has a local minima at:
    1.   x=1
    2.   x=0
    3.   x=2
    4.   no minima
18. Angles made by the lines represented by the equation xy+y=0 with axis are
    
    1.   0∘ and 30∘
    2.   30∘ and 60∘
    3.   0∘ and 90∘
    4.   30∘and 90∘
19. In ΔABC , if 2s=a+b+c then the value of s(s−a)/bc−(s−b)(s−c)/bc
    
    1.   sinA
    2.   cosA
    3.   tanA
    4.   None of these
20. If the foci and vertices of an ellipse be (±1,0) and (±2,0) , then the minor axis of the ellipse is :
    
    1.   2√5
    2.   2√3
    3.   2
    4.   4
21. Which one of the following nitrate will leave behind a metal on strong heating ?
    1.   Ferric nitrate
    2.   Silver nitrate
    3.   Copper nitrate
    4.   Manganese nitrate
22. Benzene reacts with sulphuric acid to give :
    
    1.   Hydrogen gas
    2.   Sulphur dioxide
    3.   Carboxylic acid
    4.   Sulphonic gas
23. In which of the following, Aufbau principle is violated?
    
    1.   A
    2.   B
    3.   C
    4.   D
24. Starch paper is used to test for the presence of
    1.   Oxidising agent
    2.   iodine
    3.   Iodine ion
    4.   Reducing agent
25. A quick supply of Cl₂gas may be made by reacting crystals of KMnO4 with a concentrated solution of
    1.   Potassium chloride
    2.   Hydrochloric acid
    3.   Sodium chloride
    4.   Bleaching powder
26. The conjugate base of (NH₂)−IS
    
    1.   NH3
    2.   NH²−
    3.   NH+⁴
    4.   N−3
27. The most stable oxidation state of iron is
    
    1.   +2
    2.   +3
    3.   -3
    4.   -2
28. On adding solid potassium cyanide to water
    
    1.   pH will increase
    2.   pH will decrease
    3.   Electrical conductance will not change
    4.   pH will not change
29. 0.16 g of dibasic acid required 25 ml of decinormal NaOH solution for complete neutralisation. The molecular weight of the acid will be
    
    1.   256
    2.   128
    3.   32
    4.   64
30. Dissociation of H3PO4 occurs in ____________ stages
    
    1.   1
    2.   3
    3.   4
    4.   2