SPSC 25 YEARS PAST PAPERS SUBJECT WISE (SOLVED)
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1/3(2x + 1)^2/3 + C
1/3(2x + 1)^3/2 + C
3(2x + 1)^3/2 + C
None of these
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Explanation
To integrate √(2x + 1), we can use the power rule of integration and the chain rule.
Let u = 2x + 1, then du/dx = 2, and du = 2dx.
∫√(2x + 1) dx = (1/2) ∫u^(1/2) du
= (1/2) (2/3) u^(3/2) + C
= (1/3) (2x + 1)^(3/2) + C
y= -x-13
y= 2x+2
y= x^2-1
None of these
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Explanation
Given:
y = 2 x^ 2 − 13 x + 5
Differentiate :
d y/ d x = 4 x − 13
For slope = − 1
4 x − 13 = − 1 x = 3
At x = 3
y = 2 ( 3 )^ 2 − 13 ( 3 ) + 5 = − 16
So the point of contact is (3, −16) .
The tangent equation:
y + 16 = − ( x − 3 )
y = − x − 13
69 years
70 years
71 years
None of these
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Explanation
Calculation: Current total age = 80 years
Three years ago, each person was 3 years younger.
Since there are three people, the total reduction in age is 3 × 3 = 9 3 × 3 = 9
So, the total of their ages three years ago is:
80 − 9 = 71 years 80 − 9 = 71 years
Parabolic
Elliptic
Hyperbolic
None of these
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Explanation
The Hessian matrix is used to determine the nature of critical points in multivariable calculus. When the Hessian matrix H is zero , the second derivative test is inconclusive, and the point is classified as parabolic .
H.M>G.M>A.M
A.M<G.M<H.M
H.M<G.M<A.M
None of these
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Explanation
Harmonic Mean (H.M) : The reciprocal of the arithmetic mean of the reciprocals of the numbers.
Geometric Mean (G.M) : The nth root of the product of the numbers.
Arithmetic Mean (A.M) : The sum of the numbers divided by the count of numbers.
A discontinues function
A continues function
Constant
None of these
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Explanation
If the differential coefficient (derivative) of a function is zero for all x x [ a , b ] [a, b] This implies the function is constant over the entire interval.
Explicit function
Even function
Implicit function
None of these
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Explanation
A function is explicit if it is solved for y y x x y y y x x x Since Y = x − 1 Y = sqrt{x} - 1 explicitly written in terms of x x x explicit function.
Coincident
Parallel
Perpendicular
None of these
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Explanation
If the correlation coefficient is 0, the two regression lines are perpendicular .
This is because a correlation coefficient of 0 indicates no linear relationship between the variables.
This causing the regression lines to be at right angles to each other.
R is division ring
If R is finite, then it is a field
R has no zero-divisor
None of these
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Explanation
An integral domain is a commutative ring with no zero-divisors, but it does not necessarily have multiplicative inverses for all nonzero elements, so it is not always a division ring. If an integral domain is finite, then it is a field (every nonzero element has a multiplicative inverse).
Semi group
Monoid
Abelian group
None of these
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Explanation
A commutative group is a group where the operation satisfies commutativity: a ⋅ b = b ⋅ a a cdot b = b cdot a Such a group is called an Abelian group, named after Niels Henrik Abel .
