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Statement 1: The sum of the series 1"...

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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To solve the problem, we need to analyze both statements provided in the question. ### Step 1: Analyze Statement 1 The series given in Statement 1 is: \[ 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + \ldots + (361 + 380 + 400) \] First, we need to identify the pattern in the series. ...
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Statement-1 The sum of the series 1 +(1+ 2+4)+ (4+ 6+ 9)+(9+12+16) ...(361 +380 +400) is 8000. Statement-2 sum_(k=1)^n(k^3-(k-1)^3)=n^3for any natural number n. (1) Statement-1 is true, Statement-2 is false. (2) Statement-1 is false, Statement-2 is true. (3) Statement-1 is true, Statement-2 is true Statement-2 is a correct explanation for Statement-l (4) Statement-1 is true, Statement-2 is true Statement-2 is not a correct explanation for Statement-l.

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: (lim)_(x->0)sin^(-1){x}\ does not exist (where {.} denotes fractional part function). Statement 2: {x} is discontinuous at x=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 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

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

Statement 1: The function f(x)=[[x]]-2[x-1]+[x+2] is discontinuous at all integers. Statement 2: [x] is discontinuous at all integral values of xdot 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

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

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: 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

JEE MAINS PREVIOUS YEAR-SEQUENCES AND SERIES-All Questions
  1. In a geometric progression consisting of positive terms, each term ...

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  2. The sum of the series 1/(2!)-1/(3!)+1/(4!)-... upto infinity is (1...

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  3. The average marks of boys in a class is 52 and that of girls is 42....

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  4. The first two terms of a geometric progression add up to 12. The su...

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  5. 1+2/3+6/(3^2)+10/(3^3)+14/(3^4)+

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  6. A person is to count 4500 currency notes. Let an denote the number ...

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  7. A man saves Rs. 200 in each of the first three months of his service. ...

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  8. If 100 times the 100^(t h) term of an AP with non zero common diffe...

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  9. Statement 1: The sum of the series 1""+""(1""+""2""+""4)""+""(4""+"...

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  10. If x, y, z are in A.P. and t a n^(-1)x ,""t a n^(-1)y""a n d""t a n...

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  11. The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, .. , is...

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  12. Three positive numbers from an increasing G.P. If the middle term i...

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  13. If (10)^9+""2(11)^1(10)^8+""3(11)^2(10)^7+""ddot""+""10(11)^9=k(10)^9 ...

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  14. If m is the A.M. of two distinct real numbers l and n""(""l ,""n"">"...

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  15. The sum of first 9 terms of the series (1^3)/1+(1^3+2^3)/(1+3)+(1^3...

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  16. If the sum of the first ten terms of the series (1 3/5)^2+(2 2/5)^2+(3...

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  17. If the 2nd , 5th and 9th terms of a non-constant A.P. are in G.P...

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  18. For any three positive real numbers a , b and c ,9(25 a^2+b^2)+25(c^2...

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