Home
Class 12
MATHS
Statement-1 Let f:[0,oo)vec[0,oo) be a f...

Statement-1 Let `f:[0,oo)vec[0,oo)` be a function defined by `y=f(x)=x^2,` then `((d^2y)/(dx^2))((d^2x)/(dy^2))=1` Statement-2 `(d^2y)/(dx^2)=-(d^2x)/(dy^2)dot((dy)/(dx))^3` Statement-1 is True, Statement-2 is True and Statement-2 is correct explanation for Statement-1 Statement-1 is True, Statement-2 is True and Statement-2 is not correct explanation for Statement-1 Statement-1 is True, Statement-2 is false Statement-2 is False, Statement-2 is true Both Statements are false

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

Statement-1: int((x^2+1)/x^2)e^((x^2+1)/x^(2))dx=e^((x^2+1)/x^(2))+C Statement-2: intf(x)e^(f(x))dx=f(x)+C (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: intsin^-1xdx+intsin^-1sqrt(1-x^2)dx=pi/2x+c Statement-2: sin^-1x+cos^-1x=pi/2 (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: 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: int(sinx)^x(xcotx+logsinx)dx=x(sinx)^x Statement-2: d/dx(f(x))^(g(x))=(f(x))^(g(x))d/dx[g(x)logf(x)] (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: intdx/(x(1+logx)^2)=-1/(1+logx)+C , Statement-2: int(f(x))^nf\'(x)dx=(f(x))^(n+1)/(n+1)+C, n+1!=0 (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: int(3-2x)/sqrt(4+2x-x^2)dx=2sqrt(4+2x-x^2)+sin^-1((x-1)/sqrt(5))+C ,Statement-2: intdx/sqrt(a^2-x^2)=x/2sqrt((a^2-x^2))+a^2/2sin^-1(x/a) (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.

Let A be a 2""xx""2 matrix Statement 1 : a d j""(a d j""A)""=""A Statement 2 : |a d j""A|""=""|A| (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

Consider the function F(x)=intx/((x-1)(x^2+1))dx Statement-1: F(x) is discontinuous at x=1 ,Statement-2: Integrand of F(x) is discontinuous at x=1 (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 (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 value of the integral int_(pi//6)^(pi//3)(dx)/(1+sqrt(tanx)) is equal to pi/6 Statement 2: int_a^bf(x)dx=int_a^bf(a+b-x)dxdot 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 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-JEE MAINS-All Questions
  1. Let f: R ->[0,pi/2) be defined by f(x)=tan^(-1)(x^2+x+a)dot Then ...

    Text Solution

    |

  2. e^(2x)-(a-1)e^x-ageq0AAx in R , then values of a which satisfy are. (...

    Text Solution

    |

  3. Statement-1 Let f:[0,oo)vec[0,oo) be a function defined by y=f(x)=x^2,...

    Text Solution

    |

  4. The solution set of the equation 4s inthetadotcostheta-2costheta-2sqrt...

    Text Solution

    |

  5. The function f(x) = sin x-x cos x is: (A).maximum or minimum for a...

    Text Solution

    |

  6. Statement-1 : If |x+3|+5=|x+8| then xgeq-3 Statement-2 : |a|+|b|=|a+b...

    Text Solution

    |

  7. The differential coefficient of sin^(-1)t/(sqrt(1+t^2))w.r.t cos^(-1...

    Text Solution

    |

  8. If x/y=(cos A)/(cos B)t h e n(x t a n A+y t a n B)/(x+y)= cot(A+B)/2 ...

    Text Solution

    |

  9. If x^2+a x+10=0 and x^2+b x-10=0 have common root, then a^2-b^2 is equ...

    Text Solution

    |

  10. If the equation sin(cot^(-1)(cot^(-1)(tan^(-1))))=lambda has a soluti...

    Text Solution

    |

  11. If P(x)=a x^2+b x+c&Q(x)=-a x^2+dx+c ,a c!=0, then the equation P...

    Text Solution

    |

  12. If f(x)=x^(11)+x^9-x^7+x^3+1 and f(sin^(-1)(sin8))=alpha,alpha is cons...

    Text Solution

    |

  13. The values of cos^2 73^0+cos^2 47^0-sin^2 43^0+sin^2 107^0 is equal t...

    Text Solution

    |

  14. If vec ar=xr hat i+yr hat j+zr hat k , where r=1,2,3 are three mutual...

    Text Solution

    |

  15. Find the equation of a straight lines which passes through the point (...

    Text Solution

    |

  16. If f(x)=max{sinx ,sin^(-1)(cosx)}, then f is differentiable everywhere...

    Text Solution

    |

  17. The equation of the circle whose diameter is the common chord of the c...

    Text Solution

    |

  18. If y=a^x^a^x^...^(((((oo))))) , then prove that (dy)/(dx)=(y^2(log)e ...

    Text Solution

    |

  19. The base B C of a A B C is bisected at the point (p ,q) & the equatio...

    Text Solution

    |

  20. Let the centre of the parallelepiped formed by vec P A= hat i+2 hat j...

    Text Solution

    |