Construction - Class 10 - MCQ - by Dr Rajesh Kumar Thakur

Construction

1   1.      To divide a line segment PQ in the ratio of m : n, draw a ray PX such that                               

         a) m + n           b) m – n            c) mn               d) m/n

2  2.      To divide a line segment internally in the ratio of m : n, the condition on m and n is -      

      a) m and n are real numbers                    b) m and n are rational numbers                    

         c) m and n are positive integers           d) m and n are irrationals

3  3.      When a triangle is constructed, similar to given triangle with scale factor k, and the constructed triangle is inside the given triangle then -                                                     

        a) k = 1            b) k > 1             c) k < 1             d) k = 0

4  4.     From an external point P, to construct tangents to a circle centered at O, OP is joined and then another circle is drawn, taking M as centre and OM as radius the point M is the point of intersection of OP and -                                                                                      

     a) perpendicular bisector of OP                        b) M and O coincide                         

       c) M and P coincide                                         d) the circle        

     5.      To draw a pair of tangents to a circle which are inclined to each other at an angle of 60 degree, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be -                                                                            

       a) 130⁰             b) 120⁰            c)140⁰              d) 150⁰

    6.      To divide a line segment AB in the ratio of 5: 7, first a ray AX is drawn so that                                                                                

         a) 8                  b) 10                c) 12                d) 14

     7.      To construct a triangle similar to a given triangle ABC with its sides 3/7 of the corresponding sides of triangle ABC, first draw a ray BX such that 1

, B₂ , --- B₁₀ on BX at equal distances and next step is to join -                                                          

              a) join B₁₀ to C                                     b) join B₃ to C                                                  

            c) join B₄ to C                                      d) join B₇ to C 

    8.      To construct a triangle similar to a given triangle ABC with its sides 5/3 of the corresponding sides of triangle ABC, a ray BX is drawn such that CBX is an acute angle and X is on the opposite side of A with respect to BC. What is the minimum number of points to be located at equal distances on ray BX?                                                                 

        a)3                   b) 4                  c)5                   d)6

   9.      To draw a pair of tangents to a circle which are inclined to each other at an angle of 45 degree, what should be the angle between two radii?                                                     

         a)130⁰             b) 135⁰             c) 90⁰               d)110⁰

   

1  10.  How many tangents can be drawn from a point lying inside a circle?                             

     a) 0                  b)1                   c)2                   d) 4

          Dr Rajesh Kumar Thakur

Arithmetic Progression - class 10 - - by Dr Rajesh Kumar Thakur / Mr K Bhanumoorthy

Arithmetic Progression

1.       A sequence where the difference between two consecutive number always remain same is called -                                                                                                                                                                                            a) Arithmetic progression                        b) Geometric Progression                                            c) Harmonic Progression                               d) None of these

    2.       If a is the first term, d be the difference of an AP then the nth term of AP is given by -                       a) a + nd                                                                b ) a + ( n – 1) d                    

  c) a + 3d                                                               d) n²d

    3.       If the first term is – 5, common difference is 7, find the 15^th number of the given sequence.          a) 89                      b) 93                      c) 101                    d)213

4.       Find the 10^th term from the end of the AP: 4, 9, 14, --- 254?                                                                          

A) 129                    b) 89                      c)209                     d) 176

5.       Find the middle number of the AP 7, 13, 19, … 241?                                                                                      

    a) 121                    b) 126                    c) 234                    d) a and b both

6.       If the m^th term of an AP is 1/n and n^th term be 1/m then what will be the mn^th term

a)       1                      b) 4                        c) 7                         d)10

    7.       The 6^th and 17^th term of an AP are 19 and 41 respectively, find the 40^th term?                                   

    A) 46                      b) 78                      c) 87                       d) 93

8.       If 2x, x + 10, 3x + 2 are in AP then find the value of x                                                                                        

a) 6                         b) 11                      c) 14                       d) 8

9.       If the first three terms of an AP are 3y – 1, 3y + 5 and 5y + 1 then find y                                                   

a) – 3                     b) 5                        c) 9                         d) 2

  10.   If k, 2k – 1 and 2k + 1 are three consecutive terms of an AP then find the value of k?                          a) 2                         b) 3                        c) 5                         d) 7

11.   In an AP, if d = - 4, n = 7 and nth term = 4 then what is the value of a?                                                       a) 6                         b) 7                        c) 20                       d)28

     12.   The 21^st term of an AP whose first two terms are -3 and 4 is ---                                                                   a) 17                      b) 137                    c) 143                    d) -143

13.   The famous mathematician associated with the finding the sum of the first 100 natural number is -                                                                                                                                                                         a) Pythagoras                                    b) Newton                                                                                           c) Gauss                                               d) Euclid

14.   The sum of first 16 terms of the AP 10, 6, 2--- is                                                                                                

  a) -320                  b) 120                    c) -352                   d) -400

15.   If the sum of n terms of an AP is 2n² + 5n, then its nth term is -                                                                    a) 4n – 3                                 b) 3n – 4                                   c) 4n + 3                               d) 3n + 4

Dr Rajesh Kumar Thakur

Contributed By : - Mr K Bhanumoorthy

Application of Trignometry

Application of Trigonometry

1   1.      The line drawn from the eye of an observer to a point in the object where the person is viewing is called -                                                                                                                   

    a) horizontal line                                 b) line of sight                                              

   c) vertical line                                     d) parallel line

          

   2   The angle formed by the line of sight with the horizontal line when the object is above the horizontal level is called the -                                                                           

               a) angle of elevation                           b) angle of depression                        

               c) alternate angle                                d) vertical opposite angle

   3.     The angle formed by the line of sight with the horizontal when the object is below the horizontal level is called --                                                                                                     

      a) angle of elevation                           b) angle of depression                         c) alternate angle                                d) vertical opposite angle

    

   4 .      A ladder is 100√3 m high. Find the angle of elevation of its top from a point 100m away from its foot.                                                                                                                                    a) 30⁰                   b) 45⁰                         c) 60⁰                                d) 90⁰

   5.      A ladder makes an angle of 60 deg. with the ground when placed against a wall. If the foot of the ladder is 2m away from the wall, then the length of the ladder is-              a) 4m               b) 4√3 m                      c) 4/√3m          d) 6m

   6.      The ratio of the length of a rod and its shadow is 1 : √3. What is the angle of elevation of the sun?                                                                                                                                a) 30⁰                   b) 45⁰                   c) 60⁰                                d) 90⁰ 

   7.      If the angles of elevation of the top a tower from two points distant a and b from the base and in the same straight line with it are complementary then the height of the tower is -                                                                                                                             

      a) ab                b) a√b              c) a/√3m            d)a

   8.      If the angles of elevation of the top a tower from two points distant 4m and 9m from the base and in the same straight line with it are complementary then the height of the tower is -                                                                                                                              

      a) 4m               b) 6m               c) 9m                        d) 12m 

    9.      The angle of depression of a car parked on the road from the top of a 150m high tower is 30⁰. The distance of the car from the tower is -                                                                    

       a) 50m             b)50√3m          c) 150√2m       d) 100m

   10.  From a light house the angle of depression of two ships on opposite sides of the light house are observed to be 30⁰ and 45⁰. If the height of the light house is h metres, what is the distance between the ships?                                                                                      

       A) (√3 + 1)m                b) (√3 – 1)m                        c) √3 m            d) 24m   

        

   11.  A kite is flying at a height of 60m above the ground. The string attached to kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60 deg. find the length of the string assuming that there is no slack in the string?          

     a)40m              b) 60√3m                     c) 60m             d) 40√3m

   12.  A tree 12m high is broken by the wind in such a way that its top touches the ground and makes an angle of 60 deg. with the ground. At what height from the bottom the tree is broken?                                                                                                             

       A) 5m              b) 5.569m                    c) 6m                         d) 6.5m

   13.  When we raise our hand to look at the object, the angle formed by the line of sight with horizontal is known as -                                                                                                       

      a) angle of elevation                                       b) angle of depression        

      c) acute angle                                                 d) obtuse angle

   14.   When the length of the shadow of a pillar is equal to its height, the elevation at source of sight is -                                                                                                                      

              a) 30⁰               b) 45⁰                               c) 60⁰               d) 90⁰             

    15. A ladder is 10m long. It touches a wall at height of 5m. the angle  made by it with the horizontal line is -                                                                                                               

     a) 30⁰               b) 45⁰                          c) 60⁰               d) 90⁰

   16.  The tops of two poles of height 10m and 18m are connected with wire. If wire makes an angle of 30⁰ with horizontal, then length of wire is -                                                  

       a) 10m             b) 12m             c) 16m             d) 18m

   17.  A ladder leans against wall at point B (window end) from a ground level and makes an angle horizontally at 52°. height of ladder is 15 m. When same ladder leans above point B at point A (window start) and makes an angle of 85° horizontally. distance between point A and point B is-                                                                                      

       a) 12.4m                      b) 3.12m                      c) 4m               d) 5m

1   18.  Height of a light house is 65 m. angles of elevation and depression of top and foot of a radar mast are 52° and 30° respectively. height of radar mast is -                               

         a) 109m                       b) 209m               c) 109.9m        d) 209.9m

1   19.  A tower subtends an angle of 30 deg. at a point on the same level as its foot. At a second point h meters above the first, the depression of the foot of the tower is 60 degree. What is the height of the tower?                                                                                 

   a)h meter                                b) h/2 meter                          c) h/3 meter                            d) h/4 meter

   

     20. The angle of elevation of a cloud from a point h metre above a lake is The angle of depression of its reflection in the lake is 45 degree. What is the height of cloud?                   

    a) h tan(45 + a)                      b) h tan(30 + a)                                                              

c   c) h tan(45  - a)                       d) h cot(45 +a)

           Dr Rajesh Kumar Thakur