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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

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Let x_(1),x_(2),..,x_(n) be n observations, and let x be their arithmetic mean and sigma^(2) be the variance Statement 1 : Variance of 2x_(1),2x_(2),..,2x_(n) " is" 4sigma^(2) . Statement 2: Arithmetic mean 2x_(1),2x_(2),..,2x_(n) is 4x.

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

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Let f(x)=x|x| and g(x)=s 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) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for statement 1 (2) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for statement 1. (3) Statement 1 is true, statement 2 is false. (4) Statement 1 is false, Statement 2 is true

9, Let A be a 2 x 2 matrix with real entries. Let I be the 2 × 2 2identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A2 -1 nvo bud o malai Statement 1: If A 1 and A?-1, then det A =-1. Statement 2: If A 1 and A?-I, then tr (A)?0 A. Statement 1 is false, statement 2 is true. B. Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 . C. Statement 1 is true, statement 2 is true; statement 2 is nota correct explanation for statement 1. D. Statement 1 is true, statement 2 is false.

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

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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

RESONANCE DPP-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...

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  2. Equation of the circle touching the circle x^(2) + y^(2) -15x + 5y =0 ...

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

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

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

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  6. The value of the definite integral int0^(pi/2) ((1+sin3x)/(1+2sinx)) d...

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

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  8. if x=1^1/1+2^2/3+...1001^2/2001, y=1^1/3+2^2/5+...1001^2/2003 then ([x...

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

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

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

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  12. Find the shortest distance between the lines (x+3)/(-4) =(y-6)...

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

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

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

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

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  17. int(-pi/3)^(pi/3) [ sin^5x+ln((1+x)/(1-x))+((e^x-e^(-x))/2)]dx is

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  18. Find the coefficient of x^(50) after simplifying and collecting the li...

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  19. If x=(1+t)/(t^3),y=3/(2t^2)+2/t ,t h e nx((dy)/(dx))^3-(dy)/(dx) is eq...

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  20. A(1, 2) and B(7, 10) are two points. If P(x) is a point such that the ...

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