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

61.

The angle between the lines 2x = 3y = − z and 6x = − y = − 4z is

  • 0o

  • 90o

  • 45o

  • 45o

237 Views

62.

If the plane 2ax − 3ay + 4az + 6 = 0 passes through the midpoint of the line joining the centres of the spheres

x2 + y2 + z2 + 6x − 8y − 2z = 13 and x2 + y2 + z2 − 10x + 4y − 2z = 8, then a equals

  • -1

  • 1

  • -2

  • -2

178 Views

63.

The distance between the line straight r with rightwards arrow on top space equals space 2 straight i with hat on top space minus 2 straight j with hat on top space plus 3 straight k with hat on top space plus space straight lambda space left parenthesis straight i with hat on top minus straight j with hat on top space plus 4 straight k with hat on top right parenthesis and the plane straight r with rightwards arrow on top. left parenthesis straight i with hat on top space plus 5 straight j with hat on top space plus straight k with hat on top right parenthesis space equals space 5 space is

  • 10/9

  • fraction numerator 10 over denominator 3 square root of 3 end fraction
  • 3/10

  • 3/10

104 Views

64.

For any vector straight a with rightwards arrow on top  the value of left parenthesis straight a with rightwards arrow on top space straight x straight i with hat on top right parenthesis squared space plus left parenthesis straight a with rightwards arrow on top space straight x straight j with hat on top right parenthesis squared space plus left parenthesis straight a with rightwards arrow on top space straight x straight k with hat on top right parenthesis squared is equal to

  • 3 straight a with rightwards arrow on top squared
  • straight a with rightwards arrow on top squared
  • 2 straight a with rightwards arrow on top squared
  • 2 straight a with rightwards arrow on top squared
119 Views

Advertisement
65.

If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is

  • (-1, 7/3)

  • (-1/3, 7/3)

  • (1, 7/3)

  • (1, 7/3)

112 Views

66.

Let a, b and c be distinct non-negative numbers. If the vectors straight a straight i with hat on top space plus straight a space straight j with hat on top space plus space straight c straight k with hat on top comma space space straight i with hat on top space plus straight k with hat on top space and space straight c straight i with hat on top space plus straight c straight j with hat on top space plus straight b straight k with hat on top space 

  • the Geometric Mean of a and b

  • the Arithmetic Mean of a and b

  • equal to zero

  • equal to zero

117 Views

67.

If straight a with rightwards arrow on top comma straight b with rightwards arrow on top comma space straight c with rightwards arrow on top are non -coplanar vector λ is a real number then

open square brackets straight lambda left parenthesis straight a with rightwards arrow on top space plus straight b with rightwards arrow on top right parenthesis space straight lambda squared space straight b with rightwards arrow on top straight lambda space straight c with rightwards arrow on top close square brackets space equals space open square brackets straight a with rightwards arrow on top space straight b with rightwards arrow on top space plus straight c with rightwards arrow on top straight b with rightwards arrow on top close square brackets space for

  • exactly one value of λ

  • no value of λ

  • exactly three values of λ

  • exactly three values of λ

261 Views

68.

The value of integral subscript negative straight pi end subscript superscript straight pi space fraction numerator cos squared space straight x over denominator 1 plus space straight a to the power of straight x end fraction space dx comma space straight a greater than 0 space is

  • a π

  • π/2

  • π/a

  • π/a

128 Views

Advertisement
Advertisement

69. Let space straight a with rightwards arrow on top space equals space straight i with hat on top space minus straight k with hat on top comma space straight b with rightwards arrow on top space equals space straight x straight i with hat on top space plus straight j with hat on top space plus left parenthesis 1 minus straight x right parenthesis space straight k with hat on top space and space
straight c with rightwards arrow on top space equals space straight y straight i with hat on top space plus straight x space straight j with hat on top space plus left parenthesis 1 plus straight x minus straight y right parenthesis straight k with hat on top space. Then space left square bracket straight a with rightwards arrow on top comma space straight b with rightwards arrow on top comma space straight c with rightwards arrow on top right square bracket depends on
  • only y

  • only x

  • both x and y

  • both x and y


D.

both x and y

straight a with rightwards arrow on top space equals space straight i with hat on top minus straight k with hat on top comma space straight b with rightwards arrow on top space equals space straight x straight i with rightwards arrow on top space plus straight j with rightwards arrow on top space plus left parenthesis 1 minus straight x right parenthesis straight k with hat on top space and space straight c with rightwards arrow on top space equals straight y straight i with hat on top space plus straight x straight j with hat on top space plus left parenthesis 1 plus straight x minus straight y right parenthesis straight k with hat on top
left square bracket straight a with rightwards arrow on top straight b with rightwards arrow on top straight c with rightwards arrow on top right square bracket space equals space straight a with rightwards arrow on top. space left parenthesis straight b with rightwards arrow on top straight x straight c with rightwards arrow on top right parenthesis
straight b with rightwards arrow on top space straight x straight c with rightwards arrow on top space equals space open vertical bar table row cell straight i with hat on top end cell cell straight j with hat on top end cell cell straight k with hat on top end cell row straight x 1 cell 1 minus straight x end cell row straight y straight x cell 1 plus straight x minus straight y end cell end table close vertical bar
space equals space straight i with hat on top space left parenthesis 1 plus space straight x minus straight x minus straight x squared right parenthesis minus space straight j with hat on top space left parenthesis straight x plus straight x squared minus xy minus straight y plus xy right parenthesis space plus straight k with hat on top space left parenthesis straight x squared minus straight y right parenthesis
straight a with rightwards arrow on top. left parenthesis straight b with rightwards arrow on top straight x straight c with rightwards arrow on top right parenthesis space equals space 1
which does not depend on x and y.
99 Views

Advertisement
70.

Three houses are available in a locality. Three persons apply for the houses. Each applies to one house without consulting others. The probability that all the three apply for the same house is 

  • 2/9

  • 1/9

  • 8/9

  • 8/9

152 Views

Advertisement