In a triangle PQR, ∠R =π/2. If (P/2) and tan (Q/2) are the ro

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

If the cube roots of unity are 1, ω, ω2 then the roots of the equation (x – 1)+ 8 = 0, are

  • -1 , - 1 + 2ω, - 1 - 2ω2

  • -1 , -1, - 1

  • -1 , 1 - 2ω, 1 - 2ω2

  • -1 , 1 - 2ω, 1 - 2ω2

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2.

Area of the greatest rectangle that can be inscribed in the ellipse straight x squared over straight a squared plus straight y squared over straight b squared space equals space 1

  • 2ab

  • ab

  • square root of ab
  • square root of ab
178 Views

3. limit as straight n rightwards arrow infinity of space open square brackets 1 over straight n squared sec squared space 1 over straight n squared plus 2 over straight n squared space plus 2 over straight n squared sec squared 4 over straight n squared plus.....1 over straight n squared sec squared 1 close square brackets equal
  • 1 half sec space 1
  • 1 half cosec space 1
  • tan 1

  • tan 1

107 Views

4.

If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

  • 22.0

  • 20.5

  • 25.5

  • 25.5

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5.

Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of mid point of PQ is

  • y2 – 4x + 2 = 0

  • y2 + 4x + 2 = 0

  • x2 + 4y + 2 =

  • x2 + 4y + 2 =

442 Views

6.

If the coefficients of rth, (r+ 1)th and (r + 2)th terms in the binomial expansion of (1 + y)m are in A.P., then m and r satisfy the equation

  • m2 – m(4r – 1) + 4r2 – 2 = 0

  • m2 – m(4r+1) + 4r2 + 2 = 0

  • m2 – m(4r + 1) + 4r2 – 2 = 0

  • m2 – m(4r + 1) + 4r2 – 2 = 0

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7.

In a triangle PQR, ∠R =π/2. If (P/2) and tan (Q/2) are the roots of ax2 +bx+ c = 0, a ≠ 0 then 

  • a = b + c

  • c = a + b

  • b = c

  • b = c


B.

c = a + b

tan space open parentheses straight P over 2 close parentheses comma space tan space open parentheses straight Q over 2 close parentheses space are space the space roots space of space ax squared space plus bx plus space straight c space equals space 0
tan space open parentheses straight P over 2 close parentheses comma space tan space open parentheses straight Q over 2 close parentheses space equals space minus space straight b over straight a
tan space open parentheses straight P over 2 close parentheses comma space tan space open parentheses straight Q over 2 close parentheses space space equals straight c over straight a

fraction numerator tan space open parentheses straight P over 2 close parentheses comma space tan space open parentheses straight Q over 2 close parentheses space over denominator 1 minus space tan space open parentheses straight P over 2 close parentheses comma space tan space open parentheses straight Q over 2 close parentheses space end fraction space equals space tan space open parentheses straight P over 2 plus straight Q over 2 close parentheses space equals space 1
rightwards double arrow space fraction numerator negative begin display style straight b over straight a end style over denominator 1 minus begin display style straight c over straight a end style end fraction space equals space 1
rightwards double arrow negative straight b over straight a equals space straight a over straight a minus straight c over straight a rightwards double arrow space minus straight b space equals straight a minus straight c
straight c space equals straight a plus straight b
239 Views

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8.

The system of equations 
αx + y + z = α - 1, 
x + αy + z = α - 1, 
x + y + αz = α - 1 

has no solution, if α is

  • -2

  • either-2 or 1

  • not -2

  • not -2

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9.

The value of α for which the sum of the squares of the roots of the equation x2 – (a – 2)x – a – 1 = 0 assume the least value is

  • 1

  • 0

  • 3

  • 3

152 Views

10.

If roots of the equation x2 – bx + c = 0 be two consectutive integers, then b2 – 4c equals

  • – 2

  • 3

  • 2

  • 2

170 Views

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