A block of weight W is supported by two strings inclined at 60° and 30° to the vertical. The tensions in the strings are T1 and T2 as shown. If these tensions are to be determined in terms of W using the triangle law of forces, which of these triangles should you draw? (block is in equilibrium) :-

                                 

1.            2.  

3.            4.  

Subtopic:  Resultant of Vectors |
 64%
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The magnitude of the resultant of two vectors of magnitude 3 units and 4 units is 1 unit. What is the value of their dot product?

1.  –12 units

2.  –7 units

3.  –1 unit

4.  0

Subtopic:  Scalar Product |
 72%
From NCERT
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The value of 1x+1dx is:

1.  ln (x + 1) + C

2.  x+1-2+C

3.  1x-12+C

4.   ln (x – 1) + C

Subtopic:  Integration |
 76%
From NCERT
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If \(\vec{A} = 2\hat{i} + \hat{j} - \hat{k}\) ,  \(\vec{B} = \hat{i} + 2\hat{j} + 3\hat{k}\) , and \(\vec{C} = 6 \hat{i} - 2\hat{j} - 6\hat{k}\) , then the angle between \((\vec{A} + \vec{B})\) and \(\vec{C}\) will be

1.  30°

2.  45°

3.  60°

4.  90°

Subtopic:  Scalar Product |
 76%
From NCERT
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The maximum or the minimum value of the function y = 25x2+ 5 – 10x is:

1. ymin = 4

2. ymax = 8

3. ymin = 8

4. ymax = 4

Subtopic:  Differentiation |
 67%
From NCERT
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The unit vector perpendicular to vectors a=3i^+j^ and b=2i^-j^-5k^ is

1. ±(i^-3j^+k^)11

2. ±3i^+j^11

3. ±(2i^-j^-5k^)30

4. None of these

Subtopic:  Scalar Product |
 56%
From NCERT
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Find dydx , if y = t3+1 and  x = t2 + 3.

1. t23

2. t2

3. 3t2

4. t2

Subtopic:  Differentiation |
 85%
From NCERT
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The velocity of a body moving along the x-axis varies with x as v = (x3 - x2) m/s. Find the acceleration of the body at x = 2 m, if the acceleration is defined as a=vdvdx.

1. 132 m/s2

2. 32 m/s2

3. 8 m/s2

4. 4 m/s2

Subtopic:  Differentiation |
 72%
From NCERT
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The volume flow rate of water flowing out of a tubewell is given by Q = (3t2 - 4t +1) m3/sec. What volume of water will flow out of the tubewell in the third second if the volume flow rate is defined as Q = dVdt?

1. 10 m3

2. 17 m3

3. 36 m3

4. 34 m3

Subtopic:  Integration |
 62%
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What is the maximum value of 5sinθ – 12cosθ?

1.  12

2.  17

3.  7

4.  13

Subtopic:  Trigonometry |
 53%
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