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KVPY Exam Pattern, KVPY Questions with Answers Page 35

(#M40026980) KVPY QUESTION Mental Ability Keep an EYE

Let H be the orthocenter of an acute - angled triangle ABC and O be its circumcenter. Then HA + HB+ HC

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(#M40026979) KVPY QUESTION Mental Ability Keep an EYE

A purse contains 4 copper coins and 3 silver coins. A second purse contains 6 copper coins and 4 silver coins. A
purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin

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(#M40026978) KVPY QUESTION Mental Ability Keep an EYE

Let Σ=
=
n
k 1
Sn k denote the sum of the first n positive integers. The numbers S1, S2, S3,…S99 are written on 99
cards. The probability of drawing a card with an even number written on it is

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(#M40026977) KVPY QUESTION Mental Ability Keep an EYE

Let [x] and {x} be the integer part and fractional part of a real number x respectively. The value of the integral [x]{x}dx is

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(#M40026976) KVPY QUESTION Mental Ability Keep an EYE

Let f : R → R be the function f(x) = (x – a1)(x–a2)+(x–a2)(x–a3) + (x– a3) (x–a1) with a1, a2, a3 ∈ R. Then f(x) > 0 if
and only if –
(A) At least two of a1, a2, a3 are equal (B) a1 = a2 = a3
(C) a1, a2, a3 are all distinct (D) a1, a2, a3 , are all positive and distinct

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(#M40026975) KVPY QUESTION Mental Ability Keep an EYE

Let n be a natural number and let 'a' be a real number. The number of zeros of x^2n+1 – (2n + 1) x + a = 0 in the
interval [–1, 1] is –

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(#M40026974) KVPY QUESTION Mental Ability Keep an EYE

The mid- point of the domain of the function f (x) =sqrt( 4 − 2x + 5) for real x is

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(#M40026973) KVPY QUESTION Mental Ability Keep an EYE

The value of sec9° – sec27° – sec63° + sec81° is

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(#M40026972) KVPY QUESTION Mental Ability Keep an EYE

The value of sec81° – sec63° – sec27° + sec9° is

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(#M40026971) KVPY QUESTION Mental Ability Keep an EYE

The value of cosec9° – cosec27° – cosec63° + cosec81° is

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