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Let S1=sum(j=1)^(10)j(j-1)^(10)Cj ,""S2=...

Let `S_1=sum_(j=1)^(10)j(j-1)^(10)C_j ,""S_2=sum_(j=1)^(10)j""^(10)C_i("andS")_"3"=sum_(j=1)^(10)j^2""^("10")"C"_"j"dot` Statement-1: `S_3=""55xx2^9` Statement-2: `S_1=""90xx2^8a n d""S_2=""10xx2^8` . (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

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Let f: R R be a continuous function defined by f(x)""=1/(e^x+2e^(-x)) . Statement-1: f(c)""=1/3, for some c in R . Statement-2: 0""<""f(x)lt=1/(2sqrt(2)), for all x in R . (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Statement-1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x""""y""+""z""=""5 . Statement-2: The plane x x""""y""+""z""=""5 bisects the line segment joining A(3, 1, 6) and B(1, 3, 4). (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Let A be a 2xx2 matrix with non-zero entries and let A^2=""I , where I is 2xx2 identity matrix. Define Tr(A) = sum of diagonal elements of A and |A| = determinant of matrix A. Statement-1: T r(A)""=""0 Statement-2: |A|""=""1 (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

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

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: 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: 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((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: 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.

RESONANCE DPP-JEE MAINS-All Questions
  1. The exponent of 12 in 100! is 97          (b)  58            (c)  48  ...

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  2. The angle of elevation of a cloud from a point 60m above a lake is 30^...

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  3. Let S1=sum(j=1)^(10)j(j-1)^(10)Cj ,""S2=sum(j=1)^(10)j""^(10)Ci("andS"...

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  4. If f(x)=A s in((pix)/2)+B ,f^(prime)sqrt(2)a n dint0^1f(x)dx=(2A)/pi, ...

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  5. A parabola has its vertex and focus in the first quadrant and axis ...

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  6. If y(t) is solution of (t+1)(dy)/(dx)-ty=1,y(0)=-1 then y(1)=

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  7. An aeroplane when flying at a height of 4000m from the ground passes ...

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  8. ((x-4)^(2005).(x+8)^(2008).(x+1))/(x^2006 (x-2)^3(x+3)^5.(x-6)(x+9)^20...

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  9. The value of (a+bomega+comega^2)/(b+comega+aomega^2)+(a+bomega+comega^...

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  10. Number of words each consisting of two vowels and two consonants which...

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  11. Number of ways in which 3 tickets can be selected from a set of 500 ...

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  12. Sum of all the 4-digit numbers which can be formed using the digits 0,...

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  13. The circle x^2+y^2=1 cuts the x-axis at Pa n dQdot Another circle with...

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  14. If lim(n to oo) sum(k=2)^(n)cos^(-1)((1+sqrt((k-1)(k+2)(k+1)k))/(k(k+...

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  15. Number of ways in which 7 people can occupy six seats, 3 seats on each...

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  16. Let C be the centre, BCB the minor axis and S the focus (ae, 0) for ...

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  17. Two non-negative integers are chosen at random, then the probability ...

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  18. Let an be the n^(t h) term of an A.P. If sum(r=1)^(100)a(2r)=alpha&su...

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  19. If variance of variables a ,2a ,2a ,3a ,3a ,3a ,dot,10 a is 54 then va...

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  20. If mean of squares of deviations of a set of n observations about -2a ...

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