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The largest natural number n such that 3...

The largest natural number n such that `3^(n) divides `66!` is

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JEE MAINS PREVIOUS YEAR-JEE MAIN 2023-Question
  1. Let [t] denote the greatest integer let. If the constant term in the e...

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  2. Let [t] denote the greatest integer let. then (2)/(pi)int((pi)/(6))^((...

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  3. The largest natural number n such that 3^(n) divides 66! is

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  4. Consider a circle C(1):x^(2)+y^(2)-4x-2y=a-5. Let its mirror image in ...

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  5. Let vec =6hati+9hatj+12hatk,vecb=ahat+11vecj-2veck-2hatk and vecc be ...

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  6. If the solution curve of the differential equation (y-2log(e)x) dx +...

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  7. let the mean and variance of 8 numbersx,y,10,12,6,12,4,8, be 9 and 9.2...

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  8. If alpha (a) is the greatest term in the sequence alpha (n)=(n^(3))/(n...

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  9. Let lambda(1),lambda (2) be the values of lambda for which the points ...

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  10. The integeral int((x/2)^x+(2/x)^x)log2x dx is equal to

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  11. Let A={1,2,3,4,5,6,7}. Then the relation R={(x,y) in A xx A : x+y=7} i...

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  12. Let A={theta in (0,2pi):(1+2i sin theta)/(1-i sintheta) "is purely ima...

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  13. Let the vectors vec u1 =hati+hatj+a hatk , vec u2=hati+b hatj+hatk and...

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  14. Let P be the plane passing through the line (x-1)/1=(y-2)/-3=(z+5)/7 a...

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  15. Let S be the set of all value of theta in [-pi,pi] for which the syste...

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  16. The negation of (p wedge (~q)) vv (~p) is equivalent to

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  17. For a,b in ZZ and abs(a-b) le 10, let the angle between the plane P:ax...

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  18. If A=[(1,5),(lamda,10)] , A^(-1)=alpha A+beta I and alpha+beta=-2, the...

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  19. Let the mean and variance of 12 observations be 9/2 and 4 respectively...

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  20. If the [robability that the random variable X takes x is given by P(X=...

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