Self Studies

General Test - 12

Result Self Studies

General Test - 12
  • Score

    -

    out of -
  • Rank

    -

    out of -
TIME Taken - -
Self Studies

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Self Studies Self Studies
Weekly Quiz Competition
  • Question 1
    4 / -1

    A train passes two persons moving at the speeds 26 m/s and 42 m/s in the opposite direction to that of the train in 9 sec and 7 sec respectively. The length of the train is:

    Solution

    Let the speed of train be ST.

    Distance = length of train(L)

    Speed(S1) of first person be 26 m/s, Speed(S2) of second person be 42 m/s

    Relative speed, person moving opposite direction,

    First person passes

    ⇒ (ST + S1) =L9

    ⇒ ST =L9 – 26 ----(1)

    Second person passes

    ⇒ (ST + S2) =L7

    ⇒ ST =L7 – 42 ----(2)

    Substitute the value of ST in equation (1)

    L9 – 26 =L7 – 42

    L7L9 = 16

    ⇒ L = 16 ×632

    ⇒ L = 504 m

    ∴ The length of the train is 504 m.

  • Question 2
    4 / -1

    Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 32 seconds respectively and they cross each other in 30 seconds. The ratio of their speed is:

    Solution

    Given:

    Two train crosses the man in 25 seconds and 32 seconds respectively.

    Two trains running in opposite direction and they crosses each other in 30 second

    When two running object moving in opposite direction their relative speed = Sum of their speed

    Let, the speed of the 1st train be x m/sec and that of the 2nd train is y m/sec

    When a train crosses a standing man it cross its won length

    1st train cross the man in 25 second

    ⇒ Length of 1st train is 25x meter

    2nd train cross the man in 32 seconds

    ⇒ Length of the 2nd train is 32y meter

    Relative speed of two trains is (x + y) m/sec

    In 30 seconds they cross each other

    ⇒ In 30 seconds the cross 30(x + y) meter

    Accordingly,

    30(x + y) = 25x + 32y

    ⇒ 30x + 30y = 25x + 32y

    ⇒ 30x - 25x = 32y - 30y

    ⇒ 5x = 2y

    xy=25

    ⇒ x : y = 2 : 5

    ∴ The ratio of the speed of two trains is 2 : 5.

  • Question 3
    4 / -1

    A train running at the speed of \(60\) km/hr crosses a pole in \(9\) sec. What is the length of the train?

    Solution

    For changing km/hr into m/sec we multiply by \(\frac{5}{18}\).

    Speed \(=\left(60 \times \frac{5}{18}\right)\) m/sec =\(\frac{50}{3}\) m/sec

    Length of the train \(=(\) Speed \(\times\) Time \()\)

    \(\therefore\) Length of the train \(=\left(\frac{50}{3} \times 9\right)\) m \(=150\) m

  • Question 4
    4 / -1

    Find the roots of equation \(a y^{2}+3 b y+c=0\), if \(3 \mathrm{~b}=\mathrm{a}+\mathrm{c}\).

    Solution

    Given,

    \(a y^{2}+3 b y+c=0\)

    Put \(3 b=a+c\)

    \(\Rightarrow a y^{2}+(a+c) y+c=0\)

    \(\Rightarrow a y^{2}+a y+c y+c=0\)

    \(\Rightarrow a y+(y+1)+c(y+1)=0\)

    \(\Rightarrow(y+1)(a y+c)=0\)

    \(\Rightarrow y=-1\) or \(y=-\frac{c}{a}\)

  • Question 5
    4 / -1

    Find a fraction with denominator \(30\) which is equivalent to \(\frac{5}{6}\).

    Solution

    Here, \(5\) times the denominator \(6\) is \(30\).

    Then for five times the numerator \(5\):

    \(\frac{5}{6}=\frac{5 \times 5}{6 \times 5}=\frac{25}{30}\)

    So, the fraction \(\frac{25}{30}\) with denominator \(30 \) is equivalent to \(\frac{5}{6}\).

  • Question 6
    4 / -1

    In a school of 750 boys, the average age of the boys is 15.4 years. The average age remains 15.3 years if 50 boys left the school. Find the average age of the students who left the school-

    Solution

    Total age of750 boys=750×15.4=11550

    Total age of700boys=700×15.3=10710

    Average age of 50boys =11550-1071050=16.8 year

  • Question 7
    4 / -1

    Looking at the number line, state which of the following statements is not true?

    NCERT Exemplar Class 7 Maths Integers Img 2

    Solution

    As we know that if a point or number is located to the right of another number, then that number is larger.

    Here B, is greater than -10 but less than 0 and A is greater than 0 but less than 10. Also, 6 is smaller than A.

  • Question 8
    4 / -1

    In what ratio must 2 varieties of coffee costing Rs. 330 and Rs. 440 per kg be mixed to get a mixture worth Rs. 363 per kg?

    Solution

    The required ratio should be

    = (440 – 363) : (363 – 330)= 77 : 33= 7 : 3

  • Question 9
    4 / -1

    Probability of getting three heads in tossing four coins is:

    Solution

    A = {HHHT, HHTH, HTHH, THHH}.So the number of favorable outcomes is n(A) = 4.

    So the probability that exactly three heads occurs P(A) = \(\frac{n(A)}{n(S)}\Rightarrow \frac{4}{16}\Rightarrow \frac{1}{4}\)

     

  • Question 10
    4 / -1

    A vertical rod \(20\) m long casts a shadow \(10\) m long on the ground. At the same time a tower casts a shadow \(50\) m long on the same ground. The height of the tower is:

    Solution

Self Studies
User
Question Analysis
  • Correct -

  • Wrong -

  • Skipped -

My Perfomance
  • Score

    -

    out of -
  • Rank

    -

    out of -
Re-Attempt Weekly Quiz Competition
Self Studies Get latest Exam Updates
& Study Material Alerts!
No, Thanks
Self Studies
Click on Allow to receive notifications
Allow Notification
Self Studies
Self Studies Self Studies
To enable notifications follow this 2 steps:
  • First Click on Secure Icon Self Studies
  • Second click on the toggle icon
Allow Notification
Get latest Exam Updates & FREE Study Material Alerts!
Self Studies ×
Open Now