Home
Class 12
MATHS
Let x1,""x2,"". . . . . . ,""xn be n obs...

Let `x_1,""x_2,"". . . . . . ,""x_n` be n observations, and let ` bar x` be their arithematic mean and `sigma^2` be their variance. Statement 1: Variance of `2x_1,""2x_2,"". . . . . . ,""2x_n""i s""4""sigma^2` . Statement 2: Arithmetic mean of `2x_1,""2x_2,"". . . . . . ,""2x_n""i s""4x` . (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

Statement 1: sum_(r=0)^n(r+1)^n c_r=(n+2)2^(n-1)dot Statement 2: sum_(r=0)^n(r+1)^n c_r=(1+x)^n+n x(1+x)^(n-1)dot (1) Statement 1 is false, Statement 2 is true. (2) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1 (3) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1. (4) Statement 1 is true, Statement 2 is false.

Consider the function f(x)=|x-2|+|x-5|,x in R . Statement 1: f'(4)=0 Statement 2: f is continuous in [2, 5] , differentiable in (2, 5) and f(2) = f(5) . (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

Let a, b R be such that the function f given by f(x)""=""ln""|x|""+""b x^2+""a x ,""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: a""=1/2"and"b=(-1)/4 (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

Statement 1: The sum of the series 1""+""(1""+""2""+""4)""+""(4""+""6""+""9)""+""(9""+""12""+""16)""+"". . . . . . +""(361""+""380""+""400)"" i s ""8000 . Statement 2: sum_(k=1)^n(k^3-(k-1)^3)=n^3 for any natural number n. (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

Let f(x)""=""x|x|""and""g(x)""=""sinx in x Statement 1 : gof is differentiable at x""=""0 and its derivative is continuous at that point Statement 2: gof is twice differentiable at x""=""0 (1) Statement1 is true, Statement2 is true, Statement2 is a correct explanation for statement1 (2) Statement1 is true, Statement2 is true; Statement2 is not a correct explanation for statement1. (3) Statement1 is true, statement2 is false. (4) Statement1 is false, Statement2 is true

Statement 1: An equation of a common tangent to the parabola y^2=16sqrt(3)x and the ellipse 2x^2+""y^2=""4 ""i s ""y""=""2x""+""2sqrt(3) . Statement 2: If the line y""=""m x""+(4sqrt(3))/m ,(m!=0) is a common tangent to the parabola y^2=""16sqrt(3)x and the ellipse 2x^2+""y^2=""4 , then m satisfies m^4+""2m^2=""24 . (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

Statement -1 (1/2)^7lt(1/3)^4 implies 7log(1/2)lt4log(1/3)implies7lt4 Statement-2 If axltay , where alt0 ,x, ygt0 , then xgty . (a) 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 (c) Statement -1 is true, Statement -2 is false (d) Statement -1 is false, Statement -2 is true.

Statement-1: The function F(x)=intsin^2xdx satisfies F(x+pi)=F(x),AAxinR ,Statement-2: sin^2(x+pi)=sin^2x (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

Statement-1 : lim_(x to 0) (sqrt(1 - cos 2x))/(x) at (x = 0) does not exist. Statement -2 :Right hand limit != Left hand limit i) Statement - 1 is True, Statement-2 is True, Statement-2 is a correct explanation for statement-1 ii)Statement-1 is True, Statement-2 is True, Statement-2 is Not a correct explanation for statement-1 iii)Statement-1 is True, Statement-2 is False iv)Statement -1 is False, Statement-2 is True

Consider the system of equations x-2y+3z=1;-x+y-2z=; x-3y+4z=1. Statement 1: The system of equations has no solution for k!=3. Statement2: The determinant |1 3-1-1-2k1 4 1|!=0,\ for\ k!=3. 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;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. If vec a= hat i+ hat j+ hat k ,\ vec b=2 hat i- hat j+3 hat k\ a n d...

    Text Solution

    |

  2. Radius of largest circle with center (0, 1) which can be inscribed ...

    Text Solution

    |

  3. Let x1,""x2,"". . . . . . ,""xn be n observations, and let bar x be t...

    Text Solution

    |

  4. If the variable line y=k x+2h is tangent to an ellipse 2x^2+3y^2=6, th...

    Text Solution

    |

  5. The focal chord of the parabola (y-2)^2=16(x-1) is a tangent to the ...

    Text Solution

    |

  6. If vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat k , vec c= h...

    Text Solution

    |

  7. Given three points P, Q, R with P (5, 3) and R lies on the x-axis. I...

    Text Solution

    |

  8. The value of the definite integral int (0)^(pi//2) ((1+ sin 3x)/(1+2 s...

    Text Solution

    |

  9. The minimum area of a triangle formed by any tangent to the elli...

    Text Solution

    |

  10. A number x is chosen at random from the set {1,2,3,4, ………., 100}. Defi...

    Text Solution

    |

  11. If x = (1 ^(2))/(1) =+ (2 ^(2))/( 3) + (3 ^(2))/( 5) +.....+ (1001 ^(2...

    Text Solution

    |

  12. Two numbers are selected randomly from the set S={1,2,3,4,5,6} without...

    Text Solution

    |

  13. If f(x)=x^5-5x^4+5x^3-10 has local maximum and minimum at x=p and x=q ...

    Text Solution

    |

  14. Let f(x) is a cubic polynomial with real coefficients, x in R such tha...

    Text Solution

    |

  15. Let f(x) be a function such that ("lim")(xvec0)(f(x))/x=1 and ("lim...

    Text Solution

    |

  16. Find the shortest distance between the lines (x+2)/(-4) = (y)/(1) = ...

    Text Solution

    |

  17. If the angle between the asymptotes of hyperbola (x^(2))/(a^(2))-(y^(2...

    Text Solution

    |

  18. The lengths of two opposite edges of a tetrahedron of aa n db ; the...

    Text Solution

    |

  19. Let In = int0^(npi) sinx/(1+x) dx n = 1,2,3,4. Arrange I1 , I2, I3,I4 ...

    Text Solution

    |

  20. Number of triplets of a, b & c for which the system of equations, ax -...

    Text Solution

    |