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

Advertisement

21.

The integral integral subscript 2 superscript 4 fraction numerator log space straight x squared over denominator log space straight x squared space plus space log space left parenthesis 36 minus 12 space straight x plus straight x squared right parenthesis end fraction dx  is equal to 

  • 2

  • 4

  • 1

  • 1


C.

1

straight I space equals space integral subscript 2 superscript 4 fraction numerator log space straight x squared over denominator log space straight x squared space plus space log space left parenthesis 36 minus 12 space straight x plus straight x squared right parenthesis end fraction dx
space equals space integral subscript 2 superscript 4 fraction numerator 2 space log space straight x over denominator space 2 space log space straight x space plus space log space left parenthesis 6 minus straight x squared right parenthesis end fraction dx
space equals space integral subscript 2 superscript 4 fraction numerator 2 space log space straight x space dx over denominator 2 left square bracket log space straight x space plus space log space left parenthesis 6 minus straight x right parenthesis right square bracket end fraction dx space space space.. space left parenthesis straight i right parenthesis space
equals space integral subscript 2 superscript 4 fraction numerator log space left parenthesis 6 minus straight x right parenthesis over denominator log space left parenthesis 6 minus straight x right parenthesis space plus space log space straight x end fraction dx space space space... space left parenthesis ii right parenthesis
open square brackets because space integral subscript straight a superscript straight b straight f left parenthesis straight x right parenthesis space dx space equals space integral subscript straight a superscript straight b straight f space left parenthesis straight a plus straight b minus straight x right parenthesis dx close square brackets
On space adding space eqs. space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space get
2 straight I space equals space integral subscript 2 superscript 4 fraction numerator log space straight x space plus space log space left parenthesis 6 minus straight x right parenthesis over denominator log space straight x space plus space log space left parenthesis 6 minus straight x right parenthesis end fraction dx
rightwards double arrow space 2 straight I space equals space integral subscript 2 superscript 4 space dx space equals space left square bracket straight x right square bracket subscript 2 superscript 4
2 straight I space equals space 2
straight I space equals space 1
192 Views

Advertisement
22.

The area (in sq units) of the region described by {x,y): y2 ≤ 2x and y ≥ 4x-1} is

  • 7/32

  • 5/64

  • 15/64

  • 15/64

284 Views

23.

Let y(x) be the solution of the differential equation left parenthesis straight x space log space straight x right parenthesis dy over dx space plus straight y space equals space 2 space straight x space log space straight x comma (x  ≥1). Then, y (e) is equal to 

  • e

  • 0

  • 2

  • 2

182 Views

24.

The number of points having both coordinates as integers that lie in the interior of the triangle with vertices (0,0), (0,41) and (41,0) is

  • 901

  • 861

  • 820

  • 820

378 Views

Advertisement
25.

Locus the image of the point (2,3) in the line (2x - 3y +4) + k (x-2y+3) = 0, k ε R is a 

  • straight line parallel to X - axis

  • a straight line parallel to Y- axis

  • circle of radius square root of 2

  • circle of radius square root of 2

654 Views

26.

The area (in sq units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipsestraight x squared over 9 plus straight y squared over 5 space equals space 1 space is space

  • 27/4

  • 18

  • 27/2

  • 27/2

998 Views

27.

Let O be the vertex and Q be nay point on the parabola x2 = 8y. If the point P divides the line segment OQ internally in the ratio 1:3 then the locus of P is 

  • x2= y

  • y2 =x

  • y2 =2x

  • y2 =2x

349 Views

28.

The distance of the point (1,0,2) from the point of intersection of the line fraction numerator straight x minus 2 over denominator 3 end fraction space equals space fraction numerator straight y plus 1 over denominator 4 end fraction space equals space fraction numerator straight z minus 2 over denominator 12 end fraction and the plane x-y +z = 16 is

  • 2 square root of 14
  • 8

  • 3 square root of 21
  • 3 square root of 21
169 Views

Advertisement
29.

The equation of the plane containing the line 2x-5y +z = 3, x +y+4z = 5 and parallel to the plane x +3y +6z =1 is

  • 2x + 6y + 12z = 13

  • x+3y+6z = -7

  • x+3y +6z = 7

  • x+3y +6z = 7

455 Views

30.

Let, a, b and c be three non-zero vectors such that no two of them are collinear and left parenthesis straight a space xb right parenthesis space straight x space straight c space equals space 1 third vertical line straight b vertical line vertical line straight c vertical line straight a. if θ is the angle between vectors b and  c, then a value of sin θ is

  • fraction numerator 2 square root of 2 over denominator 3 end fraction
  • fraction numerator negative square root of 2 over denominator 3 end fraction
  • 2 over 3
  • 2 over 3
220 Views

Advertisement