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Engineering
106 Views   |

The function represents

• Option 1)

a simple harmonic motion with a period • Option 2)

a simple harmonic motion with a period • Option 3)

a periodic, but not simple harmonic motion with a period • Option 4)

a periodic, but not simple harmonic motion with a period It is a periodic motion but it is not  SHM Heance a periodic, but not simple harmonic motion with a period  is correct It is a periodic motion but it is not s.n Angular speed 2w   period 2= Option 1) a simple harmonic motion with a period  Incorrect option Option 2) a simple harmonic motion with a period  Incorrect option Option 3) a periodic, but not simple harmonic motion with a...
Engineering
102 Views   |

If then is equal to

• Option 1)

• Option 2)

• Option 3)

• Option 4)

As we learnt in  Formulae of Inverse Trigonometric Functions - - wherein     Squaring, we get   Option 1) Incorrect Option 2) Incorrect Option 3) Incorrect Option 4) Correct
Engineering
103 Views   |

In a triangle , i f .If   are the root of

• Option 1)

• Option 2)

• Option 3)

• Option 4)

As we learnt in  Trigonometric Equations - The equations involving trigonometric function of unknown angles are known as trigonometric equations. - wherein e.g.     Sum of roots  =                                   Similarly, product  of roots =      Divides (2) and (3) we get     Now (2a) - (5) gives, we get      Option 1) Incorrect Option 2) Incorrect Option 3) Correct Option 4) Incorrect
Engineering
120 Views   |

Let be a function defined by

then is both one­-one and onto when is the interval

• Option 1) • Option 2)

• Option 3)

• Option 4)

As we learnt in  Domains and Ranges of Inverse Trigonometric Functions - For  Domain  Range  -     Thus, range of f(x) is same as range of 2 tan-1x in the given domain. As domain is (-1,1), range of 2tan-1x will lie between Option 1) This option is incorrect Option 2) This option is incorrect Option 3) This option is correct Option 4) This option is incorrect
Engineering
110 Views   |

The differential equation representing the family of curves is a parameter, is of order and degree as follows

• Option 1)

order 1, degree 1

• Option 2)

order 1, degree 2

• Option 3)

order 2, degree 2

• Option 4)

order 1, degree 3

As we learnt in  Degree of a Differential Equation - Degree of Highest order differential coefficient appearing in it, provided it can be expressed as a polynomial equation in derivatives - wherein Degree = 2   Degree of a Differential Equation - Degree of Highest order differential coefficient appearing in it, provided it can be expressed as a polynomial equation in derivatives -...
Engineering
107 Views   |

If then the solution of the equation is

• Option 1)

• Option 2)

• Option 3)

• Option 4)

As we learnt in  Homogeneous Differential Equation - Put -     Put       Option 1) Incorrect option Option 2) Incorrect option Option 3) Incorrect option Option 4) Correct option
Engineering
101 Views   |

If the plane   passes through the midpoint of the line joining the centres of the spheres   and   then equals

• Option 1)

1

• Option 2)

–1

• Option 3)

2

• Option 4)

–2

As we learnt in General equation (cartesian form ) - -    Centre of Centre of Midpoint of   2ax-3ay+4az+6=0 passes through (1,1,1) 2a-3a+4a+6=0 a=-2 Option 1) 1 Incorrect Option   Option 2) –1 Incorrect Option   Option 3) 2 Incorrect Option   Option 4) –2 Correct Option
Engineering
101 Views   |

The distance between the line and the plane   is

• Option 1)

• Option 2)

• Option 3)

• Option 4)

As we learnt in  Angle bisector containing origin - Equation of plane bisecting the angle between the planes  containing origin is  Where       are positive   -   Distance of (2,-2,3) from x+5y+z-5=0 is Option 1) Correct Option   Option 2) Incorrect Option   Option 3) Incorrect Option   Option 4) Incorrect Option
Engineering
109 Views   |

If the angle between the line   and the plane is such that the value of   is

• Option 1)

• Option 2)

• Option 3)

• Option 4)

As we learnt in  Angle between line and Plane (vector form ) - The angle between a line and the plane is given by - wherein    Angle between line and normal to plane   Option 1) Incorrect Option   Option 2) Correct Option   Option 3) Incorrect Option   Option 4) Incorrect Option
Engineering
88 Views   |

The plane cuts the sphere   in a circle of radius

• Option 1)

1

• Option 2)

3

• Option 3)

• Option 4)

2

As we learnt in  Distance of a point from plane (Cartesian form) - The length of perpendicular from to the plane is given by    -   Centre is        Perpendicular distance from centre= Option 1) 1 Correct Option Option 2) 3 Incorrect Option Option 3) Incorrect Option Option 4) 2 Incorrect Option
Engineering
105 Views   |

The angle between the lines   and   is

• Option 1)

90º

• Option 2)

• Option 3)

30º

• Option 4)

45º

As we learnt in  Condition for perpendicularity - or -    Since Angle between the lines= Option 1) 90º Correct Option   Option 2) 0º Incorrect Option   Option 3) 30º Incorrect Option   Option 4) 45º Incorrect Option
Engineering
119 Views   |

The system of equations has no solutions , if is

• Option 1)

either –2 or 1

• Option 2)

-2

• Option 3)

1

• Option 4)

not –2.

As we learnt in

Cramer's rule for solving system of linear equations -

When   and  ,

then  the system of equations has infinite solutions.

- wherein

and

are obtained by replacing column 1,2,3 of  by   column

Option 1)

either –2 or 1

Incorrect option

Option 2)

-2

Correct option

Option 3)

1

Incorrect option

Option 4)

not –2.

Incorrect option

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Engineering
156 Views   |

If then   is a polynomial of degree

• Option 1)

0

• Option 2)

1

• Option 3)

2

• Option 4)

3

As we learnt in

Property of determinant -

If each element in a row ( or column ) of a determinant is written as the sum of two or more terms then the determinant can be written as the sum of two or more determinants

- wherein and

so degree 2.

Option 1)

0

Incorrect option

Option 2)

1

Incorrect option

Option 3)

2

Correct option

Option 4)

3

Incorrect option

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Engineering
110 Views   |

If then which one of the following holds for all , by the principle of mathematical induction

• Option 1)

• Option 2)

• Option 3)

• Option 4)

As we learnt in

Multiplication of matrices - -

now

Option 1)

Incorrect option

Option 2)

Correct option

Option 3)

Incorrect option

Option 4)

Incorrect option

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Engineering
101 Views   |

If then the inverse of is

• Option 1)

• Option 2)

• Option 3)

• Option 4)

As we learnt in

Property of inverse of a matrix -

Every invertible matrix possesses a unique inverse

-

So,

Option 1)

Incorrect option

Option 2)

Incorrect option

Option 3)

Correct option

Option 4)

Incorrect option

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Engineering
114 Views   |

A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of When the thickness of ice is 5 cm, then the rate at which the thickness of ice decreases, is

• Option 1)

• Option 2)

• Option 3)

• Option 4)

As we learnt in  Rate Measurement - Rate of any of variable with respect to time is rate of measurement. Means according to small change in time how much other factors change is rate measurement: - wherein Where dR / dt  means Rate of change of radius.     Option 1) This option is correct Option 2) This option is incorrect Option 3) This option is incorrect Option 4) This option...
Engineering
122 Views   |

If is a real­-valued differentiable function satisfying

and then equals

• Option 1)

• Option 2)

• Option 3)

• Option 4)

As we learnt in  Differentiability - Let  f(x) be a real valued function defined on an open interval (a, b) and   (a, b).Then  the function  f(x) is said to be differentiable at      if -     Since Hence Option 1) Incorrect option Option 2) Incorrect option Option 3) Correct option Option 4) Incorrect option
Engineering
134 Views   |

Suppose is differentiable at

then equals

• Option 1)

• Option 2)

• Option 3)

• Option 4)

As we learnt in  Differentiability - Let  f(x) be a real valued function defined on an open interval (a, b) and   (a, b).Then  the function  f(x) is said to be differentiable at      if -     Now so that must be finite as exists But can be finite only if and Therefore Option 1) Incorrect option Option 2) Incorrect option Option 3) Incorrect option Option 4) Correct option
Engineering
100 Views   |

let be the point (1, 0) and a point on the locus . The locus of mid point of is

• Option 1)

• Option 2)

• Option 3)

• Option 4)

As we learnt in  Parametric coordinates of parabola - - wherein For the parabola.    P(1,0) and let the Parametric Coordinate of Q be  Mid point PQ is   Hence,        and  k =2t Replace (h,k) with (x,y)   Option 1) Incorrect Option 2) Incorrect Option 3) Incorrect Option 4) Correct
Engineering
120 Views   |

The line parallel to the axis and passing through the intersection of the lines

• Option 1)

below the axis at a distance of 2/3 from it

• Option 2)

below the axis at a distance of 3/2 from it

• Option 3)

above  the axis at a distance of 2/3 from it

• Option 4)

above  the axis at a distance of 3/2 from it

As we learnt in  Line parallel to the y-axis - - wherein The line passes through the point (b,o).    Point of intersection of the lines Point of intersection is  line parallel to x- axis is below at a distance  . i.e.  Option 1) below the axis at a distance of 2/3 from it Incorrect option     Option 2) below the axis at a distance of 3/2 from it Correct option Option 3) above  the ...
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