The mean of 100 observations is 40 and their standard deviation is 3. The sum of squares of all deviations is

**A. ** 40000

**B. ** 160900

**C. ** 160000

**D. ** 30000

**Answer : ****Option B**

**Explaination / Solution: **

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If a letter is chosen at
random from the English alphabets {*a,b,...,z*}, then the probability that
the letter chosen precedes *x*

**A. ** 12/13

**B. ** 1/13

**C. ** 23/26

**D. ** 3/26

**Answer : ****Option C**

**Explaination / Solution: **

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A solid sphere of radius x cm is melted and cast into a shape of a solid cone of same radius. The height of the cone is

**A. ** 3*x* cm

**B. ** *x* cm

**C. ** 4*x* cm

**D. ** 2*x* cm

**Answer : ****Option C**

**Explaination / Solution: **

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If sin θ + cos θ = *a*
and sec θ + cosec*θ *= *b* , then the value of *b*(*a* ^{2}
-1) is equal to

**A. ** 2a

**B. ** 3a

**C. ** 0

**D. ** 2ab

**Answer : ****Option D**

**Explaination / Solution: **

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Two persons are standing ‘x’ metres apart from each other and the height of the first person is double that of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the shorter person (in metres) is

**A. ** √2 x

**B. ** x / 2√2

**C. ** x / √2

**D. ** 2x

**Answer : ****Option B**

**Explaination / Solution: **

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If *A* is a point on
the *Y* axis whose ordinate is 8 and *B* is a point on the *X*
axis whose abscissae is 5 then the equation of the line *AB* is

**A. ** 8*x* + 5*y* = 40

**B. ** 8*x* − 5*y* = 40

**C. ** *x *=* *8

**D. ** *y* = 5

**Answer : ****Option A**

**Explaination / Solution: **

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In a given figure *ST || QR*, *PS *=* *2 cm
and *SQ* = 3 cm.
Then the ratio of the area of Δ*PQR* to the area
of Δ*PST* is

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In figure *CP* and *CQ* are tangents to a circle with
centre at *O*. *ARB *is another tangent touching the circle at* R*.
If* CP *=* *11* *cm* *and *BC* = 7 cm, then the length
of *BR* is

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The solution of 2*x*
− 1^{2} = 9 is equal to

**A. ** -1

**B. ** 2

**C. ** –1, 2

**D. ** None of these

**Answer : ****Option C**

**Explaination / Solution: **

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Which of the following can be calculated from the given matrices

,
(i) A^{2} (ii) B^{2} (iii) AB (iv) BA

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**Preparation Study Material**- Physics Vol A1 (Study/Preparation)
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