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

21.

The population p(t) at time t of a certain mouse species satisfies the differential equation fraction numerator dp space left parenthesis straight t right parenthesis over denominator dt end fraction space equals space 0.5 space left parenthesis straight t right parenthesis space minus 450. if p (0) = 850, then the  time at which the population becomes zero is

  • 2 log 18

  • log 9

  • 1 half space log space 18
  • 1 half space log space 18
493 Views

22.

Let a, b ∈ R be such that the function f given by f(x) = ln |x| + bx
2+ ax, x ≠ 0 has extreme values at x = –1 and x = 2.
Statement 1: f has local maximum at x = –1 and at x = 2.
Statement 2: straight a space equals space 1 half space and space straight b space equals space fraction numerator negative 1 over denominator 4 end fraction

  • Statement 1 is false, statement 2 is true

  • Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

143 Views

23.

If: R →R is a function defined by straight f space left parenthesis straight x right parenthesis space equals space left square bracket straight x right square bracket space cos space open parentheses fraction numerator 2 straight x minus 1 over denominator 2 end fraction close parentheses straight pi where [x] denotes the greatest integer function, then f is

  • continuous for every real x

  • discontinous only at x = 0

  • discontinuous only at non-zero integral values of x

  • discontinuous only at non-zero integral values of x

165 Views

24.

Let P and Q be 3 × 3 matrices with P ≠ Q. If P3= Qand P2Q = Q2P, then determinant of(P2+ Q2) is equal to

  • -2

  • 1

  • 0

  • 0

309 Views

Advertisement
25.

Consider the function f(x) = |x – 2| + |x – 5|, x ∈ R.
Statement 1: f′(4) = 0
Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5).

  • Statement 1 is false, statement 2 is true

  • Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

154 Views

26.

Let straight a with hat on top space and space straight b with hat on top be  two unit vectors. If the vectors straight c equals space straight a with hat on top space plus 2 straight b with hat on top and straight d space equals space 5 straight a with hat on top space minus 4 straight b with hat on top are perpendicular to each other, then the angle between straight a with hat on top space and space straight b with hat on top is 

  • π/6

  • π/2

  • π/3

  • π/3

175 Views

27.

If the integral integral fraction numerator 5 space tan space straight x over denominator tan space straight x minus 2 end fraction straight d space straight x space equals space straight x
space plus space straight a space log space vertical line space sin space straight x minus space 2 space cos space straight x vertical line space plus space straight k comma  then an equal to 

  • -1

  • -2

  • 1

  • 1

121 Views

28.

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is

  • 880

  • 629

  • 630

  • 630

181 Views

Advertisement
Advertisement

29.

If g(x) = integral subscript 0 superscript straight x cos space 4 straight t space dt comma then g(x +π) equals

  • g(x)/g(π)

  • g(x) +g(π)

  • g (x) - g(π)

  • g (x) - g(π)


B.

g(x) +g(π)

C.

g (x) - g(π)

Integral straight g space left parenthesis straight x right parenthesis space equals space integral subscript 0 superscript straight x space cos space 4 straight t. dt
To find g(x+π) in terms of g(x) of g(π)
straight g left parenthesis straight x right parenthesis space equals space integral subscript 0 superscript straight x space cos space 4 straight t space dt
rightwards double arrow space straight g left parenthesis straight x plus space straight pi right parenthesis space equals space integral subscript straight t space equals 0 end subscript superscript straight t space equals space straight x plus straight pi end superscript space cos space 4 straight t space dt
equals space integral subscript 0 superscript straight x space cos space 4 straight t space dt space plus space integral subscript straight x superscript straight x plus straight pi end superscript space cos space 4 straight t space dt
equals space straight g left parenthesis straight x right parenthesis space plus straight I subscript 1
straight l subscript 1 space equals space integral subscript straight x superscript straight x plus straight pi space end superscript space cos space 4 straight t space dt
equals integral subscript 0 superscript straight pi space cos space 4 straight t space dt
space equals space straight g left parenthesis straight pi right parenthesis
straight g left parenthesis straight x plus straight pi right parenthesis space equals space straight g left parenthesis straight x right parenthesis space plus straight g left parenthesis straight pi right parenthesis
But space the space value space of space straight I subscript 1 space is space zero
rightwards double arrow space straight g left parenthesis straight x plus straight pi right parenthesis space equals space straight g left parenthesis straight x right parenthesis minus straight g left parenthesis straight pi right parenthesis

146 Views

Advertisement
30.

Let ABCD be a parallelogram such that AB with rightwards arrow on top space equals space straight q with rightwards arrow on top comma space AD with rightwards arrow on top space equals space straight p with rightwards arrow on top and ∠BAD be an acute angle. If straight r with rightwards arrow on top  is the vector that coincides with the altitude directed from the vertex B the side AD, then straight r with rightwards arrow on top is given byLet ABCD be a parallelogram such that AB = q,AD = p and ∠BAD be an acute angle. If r is the vector that coincides with the altitude directed from the vertex B to the side AD, then r is given by (1)

  • straight r with rightwards arrow on top space equals space 3 straight q with rightwards arrow on top space minus fraction numerator open parentheses straight p with rightwards arrow on top stack. straight q with rightwards arrow on top close parentheses over denominator straight p with rightwards arrow on top straight p with rightwards arrow on top end fraction straight p with rightwards arrow on top
  • straight r with rightwards arrow on top space equals negative space straight q with rightwards arrow on top space plus fraction numerator open parentheses straight p with rightwards arrow on top stack. straight q with rightwards arrow on top close parentheses over denominator straight p with rightwards arrow on top straight p with rightwards arrow on top end fraction straight p with rightwards arrow on top
  • straight r with rightwards arrow on top space equals space straight q with rightwards arrow on top space minus fraction numerator open parentheses straight p with rightwards arrow on top stack. straight q with rightwards arrow on top close parentheses over denominator straight p with rightwards arrow on top straight p with rightwards arrow on top end fraction straight p with rightwards arrow on top
  • straight r with rightwards arrow on top space equals space straight q with rightwards arrow on top space minus fraction numerator open parentheses straight p with rightwards arrow on top stack. straight q with rightwards arrow on top close parentheses over denominator straight p with rightwards arrow on top straight p with rightwards arrow on top end fraction straight p with rightwards arrow on top
645 Views

Advertisement