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Let `vec a` and `vec b` be two vectors such that `|vec a|=1,|vec b|=4` ,and `vec a*vec b=2` .If `vec c=(2vec a timesvec b)-3vec b` and the angle between `vec b` and `vec c` is `alpha`,then `192sin^(2)alpha` is equal to___________

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JEE MAINS PREVIOUS YEAR-JEE MAIN 2024 ACTUAL PAPER-Question
  1. In the expansion of (1-x^2)(1+x)(1+3/x+3/x^2+1/x^3)^5 the sum of the c...

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  2. If alpha denotes the number of solutions of |1-i|^(x)=2^(x) and beta=(...

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  3. Let vec a and vec b be two vectors such that |vec a|=1,|vec b|=4 ,and ...

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  4. The total number of words (with or without meaning) that can be formed...

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  5. Let S=(-1,oo) and f:S rarr R be defined as f(x)=int(-1)^(x)(e^(t)-1)^(...

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  6. If the integral 525int(0)^((pi)/(2))sin2x cos^((11)/(2))x(1+Cos^((5)/(...

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  7. Let the foci and length of the latus rectum of an ellipse (x^(2))/(a^(...

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  8. Let f:R to R be a function defined by f(x)=(4^x)/(4^x+2) and M=int(f(a...

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  9. Let Q and R be the feet of perpendiculars from the point P(a,a,a) on t...

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  10. If F :(- oo, -1] rightarrow (a, b] is defined as f(x) = e^(x^3-3x+1) s...

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  11. The area of the region enclosed by the parabolas y=4x-x^(2) and 3y=(x-...

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  12. Let A(a,b),B(3,4) and C(-6,-8) respectively denote the centroid,circum...

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  13. Consider the function f:(0,oo)rarr R defined by f(x)=e^(-|log(e)x|) .I...

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  14. Let z(1) and z(2) be two complex numbers such that z(1)+z(2)=5 and z(1...

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  15. If for some m,n,^(6)C(m)+2(""^(6)C(m+1))+^(6)C(m+2)>^(8)C(3) and ^(n-1...

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  16. If a = sin^(-1) (sin 5) and b = cos^(-1) (cos 5) then value of a^2 + b...

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  17. If the mean and variance of 6 observations a, b, 68, 44, 48, 60 are 55...

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  18. Let a variable line passing through the centre of the circle x^(2)+y^(...

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  19. Let 2^("nd"),8^("th") and 44^("th") terms of a non-constant A.P. be re...

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  20. An ellipse frac{x^2}{a^2}+frac{y^2}{b^2}=1 (a> b) whose eccentircity i...

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