Let α and β be the distinct roots of ax2 + bx + c = 0, then �

Subject

Mathematics

Class

JEE Class 12

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

11.

If the letters of word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

  • 601

  • 600

  • 602

  • 602

174 Views

12.

The value  of straight C presuperscript 50 subscript 4 space plus sum from straight r space equals 1 to 6 of straight C presuperscript 56 minus straight r end presuperscript subscript 3 space is

  • straight C presuperscript 55 subscript 4
  • straight C presuperscript 55 subscript 3
  • straight C presuperscript 56 subscript 3
  • straight C presuperscript 56 subscript 3
181 Views

13.

If A = open square brackets table row 1 0 row 1 1 end table close square brackets and I = open square brackets table row 1 0 row 0 1 end table close square brackets , then which one of the following holds for all n ≥ 1, by the principle of mathematical induction

  • An = nA – (n – 1)I

  • An = 2n-1A – (n – 1)I

  • An = nA + (n – 1)I

  • An = nA + (n – 1)I

131 Views

14.

If the coefficient of x7  open square brackets ax squared space plus open parentheses 1 over bx close parentheses close square brackets to the power of 11in equals the coefficient of x-7 inopen square brackets ax squared space minus open parentheses 1 over bx close parentheses close square brackets to the power of 11then a and b satisfy the relation

  • a – b = 1

  • a + b = 1

  • a/b =1

  • a/b =1

113 Views

Advertisement
15.

If z1 and z2 are two non-zero complex numbers such that |z1 + z2| = |z1| + |z2| then argz1 – argz2 is equal to

  • Ï€/2

  • -Ï€

  • 0

  • 0

128 Views

16. If space straight omega space equals space fraction numerator straight z over denominator straight z minus begin display style 1 third end style straight i space end fraction space and space vertical line straight omega vertical line space equals 1 comma space then space straight z space lies space on
  • an ellipse

  • a circle

  • a straight line

  • a straight line

208 Views

Advertisement

17.

Let α and β be the distinct roots of ax2 + bx + c = 0, then limit as straight x rightwards arrow straight alpha of space fraction numerator 1 minus cos space left parenthesis ax squared plus bx plus space straight c right parenthesis over denominator left parenthesis straight x minus straight alpha right parenthesis squared end fraction space is equal to

  • straight a squared over 2 left parenthesis straight alpha minus straight beta right parenthesis squared
  • 0

  • negative straight a squared over 2 left parenthesis straight alpha minus straight beta right parenthesis squared
  • negative straight a squared over 2 left parenthesis straight alpha minus straight beta right parenthesis squared


A.

straight a squared over 2 left parenthesis straight alpha minus straight beta right parenthesis squared
limit as straight x rightwards arrow straight alpha of space fraction numerator 1 minus cos space straight a space left parenthesis straight x minus straight alpha right parenthesis left parenthesis straight x minus straight beta right parenthesis over denominator left parenthesis straight x minus straight alpha right parenthesis squared end fraction space
space equals space limit as straight x rightwards arrow straight alpha of fraction numerator 2 space sin squared space open parentheses straight a begin display style fraction numerator left parenthesis straight x minus straight alpha right parenthesis left parenthesis straight x minus straight beta right parenthesis over denominator 2 end fraction end style close parentheses over denominator left parenthesis straight x minus straight alpha right parenthesis squared end fraction
space equals space limit as straight x rightwards arrow straight alpha of space fraction numerator 2 over denominator left parenthesis straight x minus straight alpha right parenthesis squared end fraction space straight x fraction numerator begin display style sin squared end style begin display style space end style begin display style open parentheses straight a fraction numerator left parenthesis straight x minus straight alpha right parenthesis left parenthesis straight x minus straight beta right parenthesis over denominator 2 end fraction close parentheses end style over denominator begin display style fraction numerator straight a squared space left parenthesis straight x minus straight alpha right parenthesis squared left parenthesis straight x minus straight beta right parenthesis squared over denominator 4 end fraction end style end fraction space straight x space fraction numerator straight a squared space left parenthesis straight x minus straight alpha right parenthesis squared left parenthesis straight x minus straight beta right parenthesis squared over denominator 4 end fraction
space equals space fraction numerator straight a squared left parenthesis straight alpha minus straight beta right parenthesis squared over denominator 2 end fraction
100 Views

Advertisement
18.

If x is so small that x3 and higher powers of x may be neglected, then fraction numerator left parenthesis 1 plus straight x right parenthesis to the power of 3 divided by 2 end exponent space minus open parentheses 1 plus begin display style 1 half end style straight x close parentheses cubed over denominator left parenthesis 1 minus straight x right parenthesis to the power of 1 divided by 2 end exponent end fraction spacemay be approximated as

  • 1 minus 3 over 8 straight x squared
  • 3 x 6 plus 3 over 8 straight x squared
  • negative 3 over 8 straight x squared
  • negative 3 over 8 straight x squared
227 Views

Advertisement
19.

If straight x space equals space sum from straight n equals space 0 to infinity of straight a to the power of straight n comma space straight y space equals space sum from straight n equals 0 to infinity of straight b to the power of straight n comma space sum from straight n equals 0 to infinity of straight c to the power of straight n where a, b, c are in A.P. and |a| < 1, |b|<1, |c|< 1, then x, y, z are in

  • G.P.

  • A.P.

  • Arithmetic − Geometric Progression

  • Arithmetic − Geometric Progression

117 Views

20.

In a triangle, ABC, let ∠C = π/2 . If r is the in radius and R is the circumradius of the triangle ABC, then 2 (r + R) equals

  • b + c

  • a+b

  • a + b + c

  • a + b + c

141 Views

Advertisement