
question_answer1) Find the largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively.
A) 11 done
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B) 19 done
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C) 17 done
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D) 21 done
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E) None of these done
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question_answer2) In a school, there are two sections A and B in which 32 students are in section A and 36 students are in section B. What is the minimum number of books required for their class library so that they can be distributed equally among students of section A or section B.
A) 280 done
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B) 290 done
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C) 288 done
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D) 295 done
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E) None of these done
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question_answer3) A rectangular field is 1872 cm long and 1320 cm broad. It is to be paved with square tiles of the same size. Find the least possible numbers of such tiles.
A) 4250 done
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B) 4290 done
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C) 4225 done
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D) 4195 done
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E) None of these done
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question_answer4) If \[\alpha \] and \[\beta \] are the zeroes of the polynomial\[f(x)={{x}^{2}}px+q,\]then find the value of\[{{\alpha }^{2}}+{{\beta }^{2}}\].
A) \[{{p}^{2}}+q\] done
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B) \[{{p}^{2}}2q\] done
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C) \[{{p}^{2}}+{{q}^{2}}\] done
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D) \[{{p}^{2}}5q\] done
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E) None of these done
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question_answer5) If \[\alpha \] and \[\beta \] are roots of the polynomial\[p(s)=3{{s}^{2}}6s+4,\] then find the value of\[\frac{\alpha }{\beta }+\frac{\beta }{\alpha }+2\,\,\left( \frac{1}{\alpha }+\frac{1}{\beta } \right)+3\alpha \beta \].
A) 8 done
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B) 2 done
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C) 6 done
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D) 0 done
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E) None of these done
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question_answer6) If 5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46, find the cost of one pen.
A) Rs. 5 done
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B) Rs. 6 done
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C) Rs. 2 done
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D) Rs. 4 done
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E) None of these. done
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question_answer7) Solve: \[\frac{x}{a}+\frac{y}{b}=a+b\] and \[\frac{x}{{{a}^{2}}}+\frac{y}{{{b}^{2}}}=2\]
A) \[x={{a}^{2}}\,\,and\,\,y={{b}^{2}}\] done
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B) \[x=1\,\,and\,\,y=ab\] done
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C) \[x=a\,\,and\,\,y={{b}^{2}}\] done
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D) \[x={{a}^{2}}\,\,and\,\,y=b\] done
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E) None of these done
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question_answer8) For what value of a will the equations \[x+2y+7=0\] and \[2x+ay+14=0\] represent coincident lines?
A) 4 done
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B) 5 done
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C) 0 done
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D) 2 done
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E) None of these done
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question_answer9) If twice the son's age in years is added to the father's age, the sum becomes 70. But if twice the father's age is added to the son's age, the sum is 95. Find the age of son.
A) 15 years done
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B) 20 years done
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C) 17 years done
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D) 12 years done
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E) None of these done
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question_answer10) The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, area is increased by 67 square units. The length and breadth of the rectangle are respectively:
A) 15 units and 9 units done
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B) 17 units and 9 units done
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C) 20 units and 7 units done
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D) 17 units and 5 units done
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E) None of these done
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question_answer11) The sum of a number and its reciprocal is\[2\,\,\frac{1}{30}\]. Find the number.
A) \[\frac{5}{6}\,\,or\,\,\frac{6}{5}\] done
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B) \[\frac{7}{6}\,\,or\,\,\frac{6}{7}\] done
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C) \[\frac{1}{4}\,\,or\,4\] done
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D) \[\frac{3}{4}\,\,or\,\,\frac{4}{3}\] done
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E) None of these done
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question_answer12) One  fourth of a herd of camels were seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the number of camels.
A) 24 done
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B) 49 done
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C) 36 done
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D) 64 done
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E) None of these done
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question_answer13) A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B alone to finish the work.
A) 25 days done
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B) 27 days done
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C) 32 days done
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D) 30 days done
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E) None of these done
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question_answer14) If mth term of an A.P. is \[\frac{1}{n}\] and nth term is \[\frac{1}{m}\] then find its (mn)th term:
A) 2 done
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B) \[\,1\] done
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C) 0 done
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D) 1 done
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E) None of these done
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question_answer15) In a garden  bed there are 23 rose plants in the first row, twenty  one in the second row, nineteen in the third row and so on. There are five plants in the last row. How many rows are there?
A) 10 done
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B) 12 done
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C) 14 done
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D) 9 done
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E) None of these done
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question_answer16) Find the 31st term of A.P., if its 11th term is 38 and the 16th term is 73.
A) 182 done
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B) 178 done
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C) 181 done
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D) 183 done
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E) None of these done
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question_answer17) What will be the A.P look like whose 3rd term is 16 and 7th term exceeds the 5th term by 12?
A) 4, 8, 12, 16....... done
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B) 3, 6, 9, 12...... done
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C) 2, 4, 6, 8...... done
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D) 4, 10, 16, 22...... done
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E) None of these done
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question_answer18) The radii of two spheres are in the ratio 1 : 2. Find the ratio of their surface areas.
A) 1 : 4 done
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B) 2 : 3 done
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C) 5 : 4 done
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D) 6 : 1 done
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E) None of these done
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question_answer19) A chord AB of a circle of radius 9 cm makes a right angle at the centre of the circle. Find the area of major segment of the circle.
A) \[231.43\,c{{m}^{2}}\] done
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B) \[254.34\,c{{m}^{2}}\] done
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C) \[190.93\,c{{m}^{2}}\] done
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D) \[63.585\,c{{m}^{2}}\] done
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E) None of these done
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question_answer20) In a bullet gun powder is to be filled into a metallic enclosure. The metallic enclosure is made up of a cylindrical base and a conical top, each having a radius of 5 cm. If the ratio of the height of the cylindrical part to that of the conical part is 3 : 2, then the ratio of their volumes will be:
A) 3 : 4 done
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B) 9 : 2 done
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C) 7 : 8 done
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D) 9 : 11 done
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E) None of these done
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question_answer21) In the adjoining figure, ABCD is a square of side 14 cm. With centres A, B, C and D four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.
A) \[48\,c{{m}^{2}}\] done
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B) \[42\,c{{m}^{2}}\] done
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C) \[36\,c{{m}^{2}}\] done
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D) \[56\,c{{m}^{2}}\] done
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E) None of these done
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question_answer22) If \[\Delta \,ABC\sim \Delta \,QRP\] and AB = 6 cm, BC = 4 cm, AC = 8 cm, QR = 6 cm, then PQ + QR is equal to:
A) 9 cm done
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B) 14 cm done
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C) 7.5 cm done
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D) 12 cm done
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E) None of these done
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question_answer23) A vertical stick 12 m long casts a shadow 8 m long on the ground. At the same time, a tower casts the shadow 40 m long on the ground. Find the height of the tower.
A) 55 m done
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B) 51 m done
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C) 60 m done
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D) 62 m done
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E) None of these done
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question_answer24) From the figure given below find the length of QR, if\[\Delta \,ABR\sim \Delta \,PQR\].
A) 4.1 cm done
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B) 4.5 cm done
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C) 5.3 cm done
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D) 6.4 cm done
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E) None of these done
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question_answer25) If angle subtended by two tangents at the centre with the radii drawn through their point of contacts is \[130{}^\circ \], then find the angle subtended between these tangents outside the circle.
A) \[55{}^\circ \] done
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B) \[50{}^\circ \] done
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C) \[45{}^\circ \] done
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D) \[65{}^\circ \] done
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E) None of these done
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question_answer26) Two circles intersect at M and N. IMNK and MNLJ are the quadrilaterals inscribed in the two circles as shown in the figure given below. If \[\angle I=95{}^\circ ,\] and \[\angle K=65{}^\circ ,\] then the values of x and y are respectively:
A) \[65{}^\circ \,\,and\,\,135{}^\circ \] done
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B) \[85{}^\circ \,\,and\,\,115{}^\circ \] done
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C) \[55{}^\circ \,\,and\,\,145{}^\circ \] done
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D) \[75{}^\circ \,\,and\,\,125{}^\circ \] done
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E) None of these done
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question_answer27) In a right angled triangle ABC, \[\angle B\]is right angle side AB is half of the hypotenuse. AE is parallel to median BD and CE is parallel to BA. What is the ratio of length of BC to that of EC?
A) \[\sqrt{2}:1\] done
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B) \[\sqrt{3}:2\] done
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C) \[\sqrt{5}:\sqrt{3}\] done
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D) \[\sqrt{3}:4\] done
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E) None of these done
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question_answer28) If \[\cos \,(\alpha +\beta )=0\] and \[\sin \,(\alpha \beta )=\frac{1}{2},\] then find the value of\[\frac{\cos 2\beta }{\sin \,(\alpha /2)}\].
A) 0 done
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B) 1 done
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C) \[\,1\] done
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D) 4 done
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E) None of these done
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question_answer29) If \[\sin \,A+{{\sin }^{2}}\text{A}=1,\] then \[(co{{s}^{2}}A+{{\cos }^{4}}A)\] is equal to:
A) 1 done
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B) \[\frac{1}{2}\] done
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C) 2 done
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D) 3 done
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E) None of these done
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question_answer30) If q is an acute angle such that \[{{\tan }^{2}}q=\frac{8}{7},\] then the value of \[\frac{(1+sin\theta )(1sin\theta )}{(1+cos\theta )(1cos\theta )}\] is:
A) \[\frac{7}{8}\] done
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B) \[\frac{8}{7}\] done
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C) \[\frac{7}{4}\] done
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D) \[\frac{64}{49}\] done
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E) None of these done
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question_answer31) The shadow of a tower standing on a level ground is found to be 40 m longer when Sun's altitude is \[30{}^\circ \] than when it was \[60{}^\circ \]. What is the height of the tower?
A) \[15\,\sqrt{3}m\] done
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B) \[20\,\sqrt{3}m\] done
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C) \[20\,\sqrt{3}m\] done
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D) \[18\,\sqrt{3}m\] done
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E) None of these done
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question_answer32) Find the lengths of the median AD of the \[\Delta \,ABC\]whose vertices are A (7, 3), B (5, 3) and \[C\,\,\left( 3,1 \right),\] where D is the midpoint of the side BC.
A) \[\sqrt{5}\] done
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B) \[\sqrt{6}\] done
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C) \[\sqrt{13}\] done
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D) 3 done
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E) None of these done
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question_answer33) Find the angle between the lines \[x+2y=1\]and \[x+4y=2\].
A) 1 done
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B) \[\frac{1}{\sqrt{3}}\] done
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C) \[{{\tan }^{1}}\left( \frac{2}{9} \right)\] done
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D) \[\sqrt{3}\] done
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E) None of these done
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question_answer34) If the point (x, y) is equidistant from (4, 3) and (0, 3), then the value of x is:
A) 2 done
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B) 4 done
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C) 5 done
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D) 3 done
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E) None of these done
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question_answer35) If \[\sum{{{f}_{i}}{{x}_{i}}=35,}\] \[\sum{{{f}_{i}}=4p63}\] and mean = 7, then p is equal to:
A) 12 done
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B) 13 done
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C) 14 done
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D) 17 done
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E) None of these done
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question_answer36) What is the median of the following distribution:
x  1  2  3  4  5  6  7  8  9 
f  8  10  11  16  20  25  15  9  6 
A) 5 done
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B) 6 done
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C) 4 done
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D) 2 done
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E) None of these done
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question_answer37) There are twenty books in a library numbered 61 to 80 on their cover page. What is the probability of getting a book having a multiple 8 or a prime number on its cover page?
A) \[\frac{1}{5}\] done
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B) \[\frac{2}{5}\] done
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C) \[\frac{3}{80}\] done
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D) \[\frac{1}{10}\] done
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E) None of these done
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question_answer38) There are fifteen horses in a stable, of which 5 are black, 2 are red, 6 are white and 2 are of mixed colors. All the black and mixed color horses are hybrid. If one horse is chosen at random, find that it is a hybrid horse.
A) \[\frac{9}{15}\] done
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B) \[\frac{1}{5}\] done
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C) \[\frac{7}{15}\] done
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D) \[\frac{1}{3}\] done
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E) None of these done
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question_answer39) Katherine studies in a senior secondary school. A math test was conducted as a part of monthly routine and she scores 50 marks, getting 4 marks for each correct answer and losing 2 marks for each wrong answer. Had she been awarded 5 marks for each correct answer and deducted 3 marks for each wrong answer, she would have scored 60 marks. The total number of questions in the test was
A) 25 done
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B) 5 done
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C) 15 done
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D) 20 done
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E) None of these done
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question_answer40) If \[\alpha ,\] \[\beta ,\] \[\gamma \] are the roots of the equation\[{{z}^{3}}4z+2=0,\] then the value of \[(\alpha 3)\]\[(\beta 3)\]\[(\gamma 3)\] is given by:
A) \[\,9\] done
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B) \[\,14\] done
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C) \[\,12\] done
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D) \[\,17\] done
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E) None of these done
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