Reasoning

    Analogy
    Curator : Museum (analogy)
    Second is the place taken care of by the first.
    Analogy
    Intelligentsia : Elitist (analogy)
    The words in each pair are synonyms of each other.
    Analogy
    AERIE : EAGLE (analogy)
    An aerie is where an eagle lives; a house is where a person lives.
    Analogy
    Propensity : Tendency (analogy)
    The words in each pair are synonyms of each other.
    Analogy
    Lucknow, Patna, Bhopal, Jaipur (analogy)
    All the cities given in the question are state capitals similarly Shimla is also a capital.
    Odd Man Out
    Find the odd man out from: Lord Dalhousie, Lord Mountbattan, Lord Linlithgow & Lord Tennyson
    All except Lord Tennyson were either the Governor-General or the Viceroy of India.
    Analogy
    Typist : Typewriter :: Writer : ? (analogy)
    Typewriter is the device used by the Typist and Pen is the device used by the Writer.
    Verbal Classification
    Choose the word which is different from the rest: Anger, Grief, Humorous, Kindness, Joy
    All except Humorous are nouns, while Humorous is an adjective.
    Odd Man Out
    Find the odd man out from: Whale, Barracuda, Shark & Herring
    All except Whale are sea-fishes, while whale is a mammal.
    Verbal Classification
    Choose the word which is different from the rest: Microscope, Telescope, Periscope, Stethoscope
    All except Stethoscope are optical instruments.