Seven years ago Varun's age was five times the square of Swati's age. Three years hence Swati's age will be the two-fifth of Varun's age. Find the sum of their present ages.
For what values of \[\theta \] the equation given below is true? \[{{\tan }^{4}}\theta +{{\tan }^{6}}\theta ={{\tan }^{3}}\theta \,{{\sec }^{2}}\theta \]
Average of n numbers is a. The first number is increased by 2, second one is increased by 4, the third one is increased by 8 and so on. The average of the new number is
Divide Rs. 600 among A, B and C such that Rs. 40 more than \[\frac{2}{5}\] of A's share, Rs. 20 more than \[\frac{2}{7}\] of B's share and Rs. 10 more than \[\frac{9}{17}\] of C's share may be equal. Find the share of A.
Four numbers are in arithmetic progression. The sum of first and the last term is 8 and the product of both the middle terms is 15. The least number of the series is
In\[\Delta \,UVW,\] P is the mid-point of UW, and M is the mid-point of VW. Also PV is parallel to MN and NW = 4 cm, WM = 5 cm and MN = 3 cm. Find the length of the side UV.
The angle of elevation of the top of a tree from a point A on the ground is \[60{}^\circ \]. On walking 20 m away from its base, to a point B, the angle of elevation changes to \[30{}^\circ \]. Find the height of the tree.
In \[\Delta \,PQR,\] if \[QM\bot PR\] and \[RN\bot PQ\]intersect each other at point O, then find \[\angle QOR\] if the measure of\[\angle P=60{}^\circ .\]
In triangle \[\Delta \,PQR,\] if PV = PW, QU = QW and RV=RU and also angle \[\angle V=55{}^\circ \] and \[\angle W=55{}^\circ ,\] then find the measure of angle P in the figure shown below.
A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that \[\frac{1}{8}\] space of the cube remain unfilled. The number of marbles that the cube can accommodate is
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 4 m and 4.2 m respectively, and the height of conical part (top) is 2.8 m, then find the cost of the canvas of tent at the rate of Rs. \[500/{{m}^{2}}\](base of the tent is not covered).
Direction: Read the information given below and answer the questions that follow:
Seven army personnel A, B, C, D, E, F and G in a family are get together after a long time. Among them four are males, three females, two are married couples and three are unmarried. They are posted at different parts of the country viz.; Srinagar, Jammu, Ladakh, Bikaner, Jalandhar, Surat and Chandigarh but not necessarily in the same order. B is not married and another person who is posted at Bikaner is the most intelligent. The person who is posted at Srinagar is married to the person who is posted at Jammu, who is the least intelligent among them. D is posted at Surat and he is sitting in the leftmost corner. The person who is posted at Chandigarh is sitting in the rightmost corner. The person who is posted at Ladakh is married to C. C is the second most intelligent followed by her husband. The least intelligent is sitting on the immediate right of D, followed by the most intelligent. There are as many more intelligent persons than the person who is posted at Srinagar as there are less intelligent. In the row, followed by D there are three females sitting in succession. The person who is posted at Bikaner is a female. The person who is posted at Chandigarh is more intelligent than the person who is posted at Surat, who is more intelligent than only one person, F. Neither A nor G is a female.
Direction: Read the information given below and answer the questions that follow:
Seven army personnel A, B, C, D, E, F and G in a family are get together after a long time. Among them four are males, three females, two are married couples and three are unmarried. They are posted at different parts of the country viz.; Srinagar, Jammu, Ladakh, Bikaner, Jalandhar, Surat and Chandigarh but not necessarily in the same order. B is not married and another person who is posted at Bikaner is the most intelligent. The person who is posted at Srinagar is married to the person who is posted at Jammu, who is the least intelligent among them. D is posted at Surat and he is sitting in the leftmost corner. The person who is posted at Chandigarh is sitting in the rightmost corner. The person who is posted at Ladakh is married to C. C is the second most intelligent followed by her husband. The least intelligent is sitting on the immediate right of D, followed by the most intelligent. There are as many more intelligent persons than the person who is posted at Srinagar as there are less intelligent. In the row, followed by D there are three females sitting in succession. The person who is posted at Bikaner is a female. The person who is posted at Chandigarh is more intelligent than the person who is posted at Surat, who is more intelligent than only one person, F. Neither A nor G is a female.
Who among the following members are sitting together?
Direction: Read the information given below and answer the questions that follow:
Seven army personnel A, B, C, D, E, F and G in a family are get together after a long time. Among them four are males, three females, two are married couples and three are unmarried. They are posted at different parts of the country viz.; Srinagar, Jammu, Ladakh, Bikaner, Jalandhar, Surat and Chandigarh but not necessarily in the same order. B is not married and another person who is posted at Bikaner is the most intelligent. The person who is posted at Srinagar is married to the person who is posted at Jammu, who is the least intelligent among them. D is posted at Surat and he is sitting in the leftmost corner. The person who is posted at Chandigarh is sitting in the rightmost corner. The person who is posted at Ladakh is married to C. C is the second most intelligent followed by her husband. The least intelligent is sitting on the immediate right of D, followed by the most intelligent. There are as many more intelligent persons than the person who is posted at Srinagar as there are less intelligent. In the row, followed by D there are three females sitting in succession. The person who is posted at Bikaner is a female. The person who is posted at Chandigarh is more intelligent than the person who is posted at Surat, who is more intelligent than only one person, F. Neither A nor G is a female.
The person who is posted at Srinagar is not more intelligent than
Directions: In each question below is given a statement / allowed by two assumptions numbered and II. An assumption is something supposed or taken for granted. You have to consider the statement and the following assumptions and decide which of the assumptions in implicit in the statement.
Statement:
"Mail your grievance and confidential information to the commissioner of the police." -Request of city police to the citizens.
Assumptions:
I: All categories of people, be it the poor or the senior citizens/ might have grievances.
II: People have blind faith in the efficiency of flying squad of vigilance branch.
Directions: In each question below is given a statement / allowed by two assumptions numbered and II. An assumption is something supposed or taken for granted. You have to consider the statement and the following assumptions and decide which of the assumptions in implicit in the statement.
Statement: "Beware! Recycled coloured plastic bags contain harmful colour pigments, which on coming in contact with food particles, make food unfit for consumption, resulting in severe food poison, allergies and in extreme cases even death." ?A scientist.
Assumptions:
I: Non-biodegradable nature makes plastic bags an environmental hazard.
II: Use of plastic bags is harmful and has cascading effects on human life
Directions: Each of the questions below consists of a question and two statements numbered I and II founded by it. You have to decide whether the data provided in the statements is sufficient to answer the question.
The last Sunday of August fell on which date?
I: The first Sunday of that month fell on 5th.
II: The last day of that month was Friday.
A)
Statements I alone is sufficient to answer the question, but statement II alone is not sufficient to answer the question.
doneclear
B)
Statement II alone is sufficient to answer the question, but statement I alone is not sufficient to answer the question.
doneclear
C)
Statement either I or II is sufficient to answer the question.
doneclear
D)
Both the statements I and II taken together are not sufficient to answer the questions.
doneclear
E)
Both the statements I and II taken together are sufficient to answer the questions.
Directions: Each of the questions below consists of a question and two statements numbered I and II founded by it. You have to decide whether the data provided in the statements is sufficient to answer the question.
How many children are there between M and N?
I: M is fifteenth from the left in the row.
II: N is exactly in the middle and there are ten children towards his right.
A)
Statements I alone is sufficient to answer the question, but statement II alone is not sufficient to answer the question.
doneclear
B)
Statement II alone is sufficient to answer the question, but statement I alone is not sufficient t answer the question.
doneclear
C)
Statement either I or II is sufficient to answer the question.
doneclear
D)
Both the statements I and II taken together are not sufficient to answer the questions.
doneclear
E)
Both the statements I and II taken together are sufficient to answer the questions.
The condition of the roads in the city has deteriorated considerably during the first two months of monsoon and most of the roads have developed big pot holes. Which of the following can be a possible effect of the above cause?
A)
The municipal corporation has repaired all the roads in the city before the onset of monsoon with good quality material.
doneclear
B)
A large number of people have developed spine related injuries after regularly commuting long distances by road within the city.
doneclear
C)
The municipal corporation has been careful in choosing the contractors for repairing roads in the past.
doneclear
D)
People always complain about potholed roads during the monsoon months.
Study the following information carefully and answer the given question: In a certain code language, "only in serial order" is written as "ve pu na to" "order in the state" is written as "li ve su pu" "the logical idea only" is written as "su na ri jo" and "in idea or theory" is written as "zt jo bk pu". The code 'li ri to ve' may represent
In a given question, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and replace the question mark in the given series. 2, 9, 28, ?, 126, 217, 344.
A floral design is made on the floor in which ABCDEF is a regular hexagon. The arc \[\overset\frown{AB},\]\[\overset\frown{BC},\] \[\overset\frown{CD},\] \[\overset\frown{EF}\] and \[\overset\frown{FA}\] are the semicircles with sides of the hexagon as diameter. If each side of the hexagon is 3 cm, then find the area of the figure shown below.
In the following figure BOD is the arc of a circle with centre C having radius 42 cm. ABCD is a square and\[\Delta \,CEF\]is an isosceles right-angled triangle whose equal sides are 6 cm long. Find the area of the shaded region.
Mary finds that in the final year examination of mathematics, the question paper consists of section I, II, and III respectively. The questions of section I carries 4 marks each which contains five questions and section II and III carries 6 and 8 marks each which contains ten and five question each respectively. If she scores \[100%\] in section I and \[80%\] in section II, then find the least number of questions required by Mary to be solved correctly in the third section in order to have an average of \[90%\].
A and B are two events such that P (A) = 0.3 and\[(A\bigcup B)=0.8\]. If a and b are independent, then P(B) is
(P)
\[\frac{4}{13}\]
(B)
A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a king or a club?
(Q)
\[\frac{2}{5}\]
(C)
If A and B be two mutually exclusive events in a sample space such that \[P\,(A)=\frac{2}{5}\] and \[P\,(B)=\frac{1}{2},\] then \[P(A\bigcap \bar{B})\] is
(R)
\[\frac{5}{7}\]
(D)
A natural number is chosen at random from amongst the first 300.What is the probability that the number, so chosen is divisible by 3 or 5?
In the next Asia cup of hockey tournament 12 teams are participating and are divided into two equal groups P and Q respectively. If the team of each group will play match with each other and the top 3 teams from each group qualify for the super six slot. Then in the super six stage each team will play each other once again and top four team will be selected for the semifinal where again each team will play against each other. The top two teams will qualify for the final and they will play in the final for best of three matches. Find the number of matches to be played in then tire tournament if all of the three final matches will be compulsory to be played.
A boy is standing on the ground and flying a kite with 100 m of a string at an elevation of \[30{}^\circ \]. Another boy is standing on the roof of a 20 m high building and is flying his kite at an elevation of\[45{}^\circ \]. Both the boys are on the opposite sides of both the kites. Find the length of the string (correct the two places of decimal) that the second boy must have such that the two kites meet.
The radii of the ends of a bucket 45 cm high which is of the form a frustum of a cone are, 28 cm and 7 cm. Determine the surface area.\[\left( Take\,\,\pi =\frac{22}{7} \right)\]
In the figure as mentioned below, POQ and ROS are diameters of a circle with center O and radius 14 cm. Find the area of the shaded region. \[\left( Use\pi =\frac{22}{7} \right)\]
On dividing a number by 9, the remainder is 8. The quotient so obtained when divided by 11, leaves the remainder 9. Now the quotient so obtained when divided by 13, leaves the remainder 8. Find the remainder when the given number is divided by 1287. Also find the remainder if the number and subsequent quotients are divided by 13, 11 and 9 respectively.