Ratio and Proportion, Indicies and logrithm

01) Two numbers are in the ratio 7:8, If 

      3 is added to each of them, their 

      ratio becomes 8:9. The numbers are:

      (a) 14, 16

      (b) 24, 27

      (c) 21, 24

      (d) 16, 18

02) The value of the expression :

       a^log_a^b.log_b^c.log_c^d.log_d^e

              (a) t

         (b) abcdt

         (c) (a+b+c+d+t)

        (d) None

^{03) If log}₁₀₀₀₀x = -1/4, then x given by :

     (a) 1/100

     (b) 1/10

     (c) 1/20

     (d) None of these

04) If 2^x- 2^x-1 = 4, then the value of  X^x is :

        (a) 2

        (b) 1

        (c) 64

        (d)27

05) If log [ (a + b) / 4] = 1/2 (log a+ log b)

       then :

        (a/b) + (b/a)

       (a) 12

       (b) 14

       (c) 16

       (d) 8

06) In a film shooting, A and B received money

       in a certain ratio in the same ratio. If A gets 

       Rs. 160000 and C gets Rs. 250000. Find the 

       amount received by B?

       (a) Rs. 200000

       (b) Rs. 250000

       (c) Rs. 100000

       (d) Rs. 150000

Equations Part-4

16) If (2 + √3) is a root of a quadratic

     equation x² + P_x  + q = 0 then find the 

        value of p and q.

       (a) (4, -1)

       (b) (4, 1)

       (c) (-4, 1)

       (d) (2, 3)

17) If one root of a equation is 2 + √5,

    then the quadratic equation is :

    (a) x² + 4x  -1 = 0

       (b) x^2 _ 4x -1 = 0

      (c) x² + 4x + 1 = 0

      (d) x^2 _ 4x + 1 = 0

18) The value of

         2+           1           is :

           2 +          1        

              2 +          1        

                 2 +          1        

                    2 + ...................∞

      (a) 1 + √2

     (b) 2 + √5

19) The lines 3x + 4y + 10= 0 and 

      3x + 4y + 10= 0 are _______

      (a) Parallel

      (b) Perpendicular to each other

      (c) Bisect each other

      (d) Concide with each other.

20) The value of sqrt[6 + sqrt(6 + sqrt( 6+........∞))] 

      is :

      (a) -3

      (b) 2

      (c) 3

      (d) 4

Equations Part-3

11) Find the positive value of k for which      the equations : x² + kx  + 64 = 0 and        x^{2  _} 8x  + k = 0 will have real roots:       (a) 12       (b) 16       (c) 18       (d) 22

12) If one root of the equation x^2_3x+k =0        is 2, then value of k will be         (a) -10        (b) 0        (c) 2        (d) 10

13) A man starts his job with a certain        monthly salary and earns a fixed increment       every year. If his salary was Rs. 1500 after 10        years of service, what was his starting salary         and what is the annual increment in rupees?        (a) Rs. 1300 , Rs. 50        (b) Rs. 1100 , Rs. 50        (c) Rs. 1500 , Rs. 30        (d) None

14) The value of k for which the points (k, 1),         (5 , 5) and( 10, 7) may be collinear is:

        (a) k = -5

        (b) k = 7

        (c) k = 9

        (d) k = 1

15) Roots of the equation 3x² - 14x  + k = 0         will be reciprocal of each other if:       (a) k = -3       (b) k = 0       (c) k = 3       (d) k = 14

Equations Part-2

06) The centroid of the triangle ABC is        the point (2, 3). A and B are the        points (5, 6) and (-1, 4) respectively      The coordinates of c are.      (a) (1, -2)      (b) (2, -1)       (c) (1, 2)      (d) (2, 3)

07) If X³-6x²  + 11x - 6 = 0 then find the       value of (3x - 4).      (a) (1, 2 , 3)      (b) (-1, 2 , 5)      (c) (-1, 3 , 5)      (d) (2, 3 , 5)

08) A straight line of x =15 is :      (a) Parallel to y axis      (b) Parallel to x axis      (c) A diagonal line      (d) Passes through origin

09) The equation of the straight line        through the point of intersection of       x + 2y -5 = 0 and x -3y -7 = 0       and passing through the point (1, 0)       is:      (a) x + 12y = 1      (b) x - 12y = 1      (c) x - 12y = 11

10) If roots of equation x²  + x + r = 0        are 'α' and 'β' and α³+ β³ = -6,        Find the value 'r' ?       (a)   -5                 3     (b)    7               3     (c)   -4               3     (d) 1

Equations Part-1

01) Find the equation of the line passing       through the point (1, 1) and parallel      to the line 3x + 5y +8 =0      (a) 3x + 5y +8 =0      (b) 5x + 3y +8 =0      (c) 5x + 3y -8 =0      (d) 3x + 5y -8 =002) The equation of a line which is        perpendicular to 5x - 2y =7 and      passes through the mid-point of       the line joining (2, 7) and (-4, 1)       is:     (a) 2x - 5y -18 =0     (b) 2x + 5y +18 =0     (c) 2x + 5y -18 =0     (d) None of these03) On solving sqrt[x / (1 - x)] +      [(1 - x) / x] = 2 1                               6      we get one value of x as:     (a)  4           13     (b)   1            13     (c)   2            13     (d)   3            1304) Positive value of 'k' for      which the roots of equation      12x²  + kx + 5 = 0 are in      ratio 3:2 is     (a) 5/12     (b) 12/5     (c) 5 √10              2     (d) 5√8 05) The line joining (-1, 1) and      (2, -2) and the line joining      (1, 2) and (2, k) are perpen-       dicular to each other for the       following value of k:      (a) 1      (b) 0      (c) -1      (d) 3