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Punjab (PTB) · Quarter book test · Free

1st Year Mathematics 4th Quarter Book Paper

40 marks · 1 hour · 28 questions. Covers: UNIT 13: Differentiation, UNIT 14: Vectors in space.

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1st Year Mathematics 4th Quarter Book Paper

1st Year · Mathematics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 40Time: 1 hour

Q1. Multiple choice questions (Attempt all · 12 × 1 = 12)

  1. The derivative of equals ......:

  2. Angle in semi circle is:

    1. 30o

    2. 45o

    3. 90o

    4. 60o

  3.  is equal to:

    1. f(0)

    2. f'(a)

    3. f'(x)

    4. f'(0)

  4. A vector with magnitude 1 is called:

    1. Null vector

    2. Unit vector

    3. Zero vector

    4. Constant vector

  5. What is the derivative of  with respect to x:

    2. 2x-1

    3. 1-2x

  6. The angle between the vectors  is:

    1. 30o

    2. 40o

    3. 60o

    4. 90o

  7.  is equal to:

    1. n(axn-1+b)

    2. n(ax+b)

    3. naxn-1

    4. na(ax+b)n-1

  8. Moment of force F about a point with position vector r will be eqal to:

    1. F x r

    2. r x F

    3. d x F

    4. F x d

    1. -xm-1

    2. -mx-m-1

    3. -xm-m+1

    4. -xm-1x

  10. Vector product of two vector is a ......:

    1. Scalar quantity

    2. Unit vector

    3. Vector quantity

    4. Null vector

  12. The dot product of vectors u and v is ......:

    1. Cos  sin 

    2. IuIIvI=cos

    3. uv cos 

    4. None

Q2. Short questions (Attempt any 8 of 12 · 8 × 2 = 16)

  1. Find from principle, the derivatives of the following expressions w.r.t their respective independent variables: (3x-2)-2

  2. Let u=3i+2j-5k, v=i-5j-k and w=-4i-j+7k. Find the following: I3v+wI.

  3. Find the derivative of the following function by definition: f(x)=c

  4. Find the moment about the point M(-2,4,6) of the force represented by , where coordinates of points A and B are (1,2,-3) and (3,-4,2) respectively.

  5. Find by definition, the derivatives w.r.t 'x' of the following function defined as:

  6. Find the vector whose magnitude is 5 and is parallel to 3i+4j-k

  7. Find derivative of with respect to x.

  8. Find a real number a so that the vectors u and v are perpendicular: u=ai+2aj-k, v=i+aj+3k

  9. Find the derivative of  at x=8 from the first principle.

  10. If u= xi + 2j + 3k, v=i+yj-3k and w=2i-3j represent the sides of a triangle. Find the values of x and y.

  11. The position of a car after t hours is given by: s(t)=2t3-3r2+t (in kilometres). Find the average velocity over the interval [1,4].

  12. Find the magnitude of the vector v and write the direction cosines of v. v= - 6i+8j

Q3. Long questions (Attempt any 3 of 4 · 3 × 4 = 12)

  1.  An electric shop sells three types of appliances. Fans, Heaters and Ovens. The monthly sales quantities are 500 units of Fans, 300 unit of Heaters and 200 units of Ovens. The profit per unit for each appliance is Rs 500 for Fans, Rs. 400 for Heater and Rs 2,000 for ovens.Calculate the total monthly profit using vector operations.

  2. Differentiate w.r.t 'x':

  3. We say that two vectors v and w in space are parallel if there is a scalar c such that v=cw. The vectors point in the same direction of c>0 and the vectors point in the opposite direction if c<0. Find a vector of length 5 in the direction opposite that of v=i-2j+3k.

  4. The position of a car traveling along a straight highway is given by x(t)=30t2-4t3, where x(t) is the distance traveled in kilometres and t is the time in hours. Determine the car's acceleration at t=3 hours.