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Which one of the following pairs of equations has a unique solution?
Given two equations
One side of a right triangle measures 12 cm and the difference between the hypotenuse and the other side is 8 cm. The area of the triangle is
Let the hypotenuse = x cm
Then the other side is (x  8) cm
By Pythagoras theorem
(x  8)^{2} + (12)^{2} = x^{2}
⇒ x^{2} + 64  16x + 144 = x^{2}
⇒ 16x = 208
⇒ x = 208/16 = 13 cm
∴ Hypotenuse = 13cm
so the other side = (13  8) = 5cm
Area = 1/2 x 12 x 5
= 30cm^{2}
A motor boat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in 4 hrs and and 30 minutes. Determine the speed of the stream.
Let x km/hr be the speed of water
The speed of motor boat in still water is 15 km/hr, therefore, its speed downstream is (15 + x) km/hr and the speed upstream is (15  x) km/hr
Time taken for given 30 km downstream = 30/15 + x hours
Time taken for going 30 km upstream = 30/15  x hours
Since the total time is given to be 4 hours 30 minutes
or 1800 = 9(225  x^{2})
or 200  225 + x^{2} = 0
or x^{2} = 25
⇒ x = 5,  5
∴ x = 5 [as x cannot be negative so x = 5 is rejected]
Hence the speed of water = 5 km/hr
The compound interest on Rs 10000 in 2 years at 4% per annum, the interest being compounded halfyearly, is
P = 10,000
T = 2 years
R = 4% (compounded half yearly)
⇒ R% = 2 + 2 + 4/100 = 4 + 0.04
⇒ R% = 4.04%
⇒ CI = P[1 + R/100 ]T  P
⇒ CI = 10000 [1 + 4.04/100 ]^{2}  10000
⇒ CI = (104.04)^{2}  10000
⇒ CI = 10824.3216  10000
⇒ CI = Rs 824.3216
The acceleration due to gravity of a catastropic earthquake will be
Nawab Sanaullah Zehri, recently resigned before a noconfidence motion was taken against him in the provincial assembly. He belonged to which province of Pakistan?
How many such pairs of letters are there in the word MODERATE each of which has as many letters between them in the word as in the English alphabet?
There are 4 pairs in the word 'MODERATE' i.e.
(1) O and R  2 letters between them  D,E
In the alphabat series also there are 2 letters between O and R i.e. P,Q
(2) D and A  2 letters between them  E, R
In the alphabat series there are 2 letters between D and A i.e. C,B
(3) O and T  4 letters between them  DERA
In the alphabat series there are 4 letters between O and T i.e. P,Q, R, S
(4) R and T  1 letters between them  A
In the alphabat series there are 1 letter between R and T i.e. S
So the CORRECT ANSWER is More than 3 i.e. (E)
What should come in the place of question  mark (?) in the following series?
YA, CW, ?, GS, QI
If + means x, ÷ means , x means ÷ and  means +
what will be the value of 4 + 11 ÷ 5  55 = ?
Given expression : = 4 x 11  5 + 55 = 44  5 + 55 = 94
Two numbers x and y(x>y) are such that their sum is equal to three times their difference. Then the value of 3xy/2(x^{2 } y^{2}) will be
A bag contain Rs 102 in the form of rupee, 50paise and 10paise coins in the ratio 3:4:10. The number of 10paise coins is
⇒ 300x + 200x + 100x = 102 x 100
⇒ 600x = 1020 x 10
⇒ x = 17
Hence, number of 10 paisa coins are = 10(17) = 170 coins
A sum of money lent out at simple interests amounts to Rs. 720 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is :
Principal + SI for 2 years = 720 Rs. ……(I)
Principal + SI for 7 years = 1020 Rs. ……(II)
Subtracting equation (I) from (II),
S.I. for 5 years = (1020 – 720) = 300 Rs.
∴ S.I. for 2 years = 300 x 2/5 = 120 Rs
∴ Principal = (720 – 120) = 600 Rs.
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
C's 1 day's work
A's wages : B's wages : C's wages
∴ C's share (for 3 days) =
What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?
Each of the following questions consists of two sets of figures. Figures 1,2,3 and 4 constitute the Problem Set while figures A,B,C,D and E constitute the Answer Set. There is a definite relationship between figures 1 and 2. Establish a similar relationship between figures 3 and 4 by selecting a suitable figure from the Answer Set .
In the following problem, out of the five figures marked 1, 2, 3, 4 and 5, four are similar in a certain manner. However, one figure is not like the other four. Choose the figure which is different from the rest.
In the following questions, select a figure from amongst the four alternatives, which when placed in the blank space of fig. (X) would complete the pattern.
P,Q,R,S,T,V,W and Z are sitting around a circle facing the center. R is second to the left of Z who is third to the left of P. T is third to the right of W who is not an immediate neighbour of either R or Z. S is fourth to the right of Z. Q is fourth to the right of T.
Q. In which of the following pairs is the first person sitting to the immediate left of the second person?
The seating arrangement is as follows :
Study the following diagram.
Q. Which number in the above figure denotes Vegetarian Females who are not Teachers.
Find out from amongst the four alternatives as to how the pattern would appear when the transparent sheet is folded at the dotted line.
Below are the statements followed by two conclusions numbered I and II. You have to consider the statements and the following conclusions and decide which of the conclusion(s) follows the statement(s).
Statements :
a. All books are ledgers.
b. All pens are keys.
Conclusions :
I. Some ledgers are keys.
II. Some keys are books.
Above tables shows the marks obtained by 6 students in 6 different subjects. Observe the table carefully and answer the questions.
Q. What is the percentage difference between the marks gained by the student A in History and C in Hindi?
Required % = 90%  50% = 40%
Above tables shows the marks obtained by 6 students in 6 different subjects. Observe the table carefully and answer the questions.
Q. The marks obtained by B in Mathematics is how many times the percentage of marks obtained by F in Science?
Hence % of B in Maths is equal to 0.875 times of % of F in science.
Above tables shows the marks obtained by 6 students in 6 different subjects. Observe the table carefully and answer the questions.
Q. For D what is the difference between the percentage of marks in English and the average percentage of marks in all the subjects?
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