The LCM of two numbers is 2079 and their HCF is 27. If one the numbers is 189, find the other.
A)
287
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B)
297
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C)
185
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D)
312
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E)
None of these
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Find the least number which is exactly divisible by 12, 15 and 21.
A)
420
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B)
680
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C)
840
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D)
780
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E)
None of these
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Find the least number which when divided by 12, 21 and 35 will leave remainder 6 in each case.
A)
426
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B)
536
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C)
436
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D)
326
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E)
None of these
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Write the decimal number \[0.\overline{57}\]in the form \[\frac{p}{q}\] in the simplest form.
A)
\[\frac{85}{43}\]
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B)
\[\frac{26}{45}\]
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C)
\[\frac{37}{45}\]
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D)
\[\frac{27}{45}\]
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E)
None of these
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Which one of the following is an irrational numbers?
A)
\[\sqrt{625}\]
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B)
\[\sqrt{1296}\]
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C)
\[\sqrt{3125}\]
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D)
\[2025\]
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E)
None of these
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The sum and the product of zeros of a quadratic polynomial are \[\frac{9}{2}\] and 2 respectively. The quadratic polynomial is
A)
\[{{x}^{2}}-9x+4\]
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B)
\[2{{x}^{2}}-9x+4\]
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C)
\[5{{x}^{2}}+9x+4\]
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D)
\[3{{x}^{2}}+9x+2\]
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E)
None of these
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If the sum of the zeros of the polynomial \[f(x)=({{k}^{2}}-14){{x}^{2}}-2x-12\] is 1, then one of the values of K is
A)
\[\sqrt{15}\]
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B)
\[-\,15\]
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C)
\[14\,\]
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D)
\[-\,4\]
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E)
None of these
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Find the quadratic polynomial whose one of the zeros is 0 and the sum of the zeros is \[\frac{12}{5}\]
A)
\[12{{x}^{2}}-5x\]
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B)
\[12{{x}^{2}}+5x\]
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C)
\[5{{x}^{2}}-12x\]
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D)
\[5{{x}^{2}}+12x\]
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E)
None of these
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Find the value of K for which the following system of linear equations has an infinite number of solutions: \[\begin{align} & kx+3y-(k-3)=0 \\ & 12x+ky-k=0 \\ \end{align}\]
A)
7
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B)
6
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C)
8
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D)
9
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E)
None of these
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Determine the value of K so that the following linear equations have no solution: \[\begin{align} & kx+4y=3 \\ & 16x+ky=6 \\ \end{align}\]
A)
-8
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B)
+ 8
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C)
4
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D)
\[-\,4\]
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E)
None of these
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The coach of a cricket team buys 3 bats and 7 balls for Rs. 1395. Later, he buys 4 bats and 5 balls for Rs. 1665. Find the cost of each bat and each ball.
A)
Rs. (500, 50)
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B)
Rs. (360, 45)
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C)
Rs. (450, 120)
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D)
Rs. (850, 150)
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E)
None of these
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The sum of two numbers is 8. If their sum is four times their difference. Find the numbers.
A)
(6, 2)
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B)
(3, 5)
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C)
(5, 3)
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D)
(2, 6)
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E)
None of these
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Solve for x: \[\frac{1}{(x-3)}-\frac{1}{(x+5)}=\frac{1}{6}\,\,(x\ne -\,5)\]
A)
6
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B)
7
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C)
\[-\,7\]
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D)
9
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E)
None of these
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If roots of the equation \[(a-b)\,{{x}^{2}}+(b-c)\,x+(c-a)=0\] are equal, then
A)
\[2b=a+c\]
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B)
\[{{b}^{2}}=ac\]
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C)
\[2a=b+c\]
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D)
\[b=ac\]
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E)
None of these
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If m times the nth term of an A.P is equal to n times its nth term. Find the value of\[\left( m+n \right)th\] term.
A)
1
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B)
0
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C)
2
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D)
n
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E)
None of these
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The sum of 5th and 9th terms of an A.P is 72 and the sum of 7th and 12th terms is 97. Find the 20th term of the progression.
A)
95
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B)
115
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C)
101
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D)
135
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E)
None of these
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The sum of first six terms of an arithmetic progression is 42. The ratio of its 10th term to its 30th term is 1: 3. Find the value of 4th term.
A)
12
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B)
8
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C)
6
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D)
10
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E)
None of these
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If \[6\tan \theta =5,\] find the value of \[\frac{6\sin \theta -2\cos \theta }{6\sin \theta +3\cos \theta }\].
A)
\[\frac{1}{6}\]
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B)
\[\frac{4}{9}\]
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C)
\[\frac{3}{8}\]
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D)
\[\frac{5}{8}\]
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E)
None of these
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In\[\Delta \,ABC,\] if \[\angle B=90{}^\circ ,\] AB = 10 cm and AC = 20 cm, then find the angle \[\angle C\].
A)
\[60{}^\circ \]
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B)
\[30{}^\circ \]
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C)
\[90{}^\circ \]
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D)
\[45{}^\circ \]
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E)
None of these
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An equilateral triangle is inscribed in a circle of radius 6 cm. Find the side.
A)
\[5\,\sqrt{3}\]
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B)
\[8\,\sqrt{3}\]
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C)
\[6\,\sqrt{3}\]
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D)
\[3\,\sqrt{3}\]
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E)
None of these
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The value of \[{{\cos }^{2}}30{}^\circ {{\cos }^{2}}45{}^\circ +4{{\sec }^{2}}60\]\[+\frac{1}{2}{{\cos }^{2}}90{}^\circ -2{{\tan }^{2}}60{}^\circ \] is
A)
\[\frac{10}{3}\]
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B)
\[\frac{83}{8}\]
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C)
\[\frac{79}{8}\]
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D)
\[\frac{59}{9}\]
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E)
None of these
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A person standing on the bank of a river. Observes that the angle subtended by a tree on the opposite bank is \[60{}^\circ \]. When he retires 20 m from the bank, he finds the angle to be \[30{}^\circ \]. Find the height of the tree.
A)
\[10\]
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B)
\[20\,\sqrt{3}\]
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C)
\[10\,\sqrt{3}\]
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D)
\[30\,\sqrt{3}\]
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E)
None of these
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Find the distance between the points \[P\,\,\left( -\,10,-\,14 \right)\] and \[Q\,\,\left( -\,4,-\,6 \right)\].
A)
8
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B)
10
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C)
12
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D)
\[-\,10\]
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E)
None of these
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For what value of P are the points \[A\left( -\,3,\,\,\text{9} \right),\] \[B\,\,\left( 2,-\,1 \right),\] \[C\,\,\left( P,-\,5 \right)\] collinear?
A)
5
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B)
6
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C)
4
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D)
2
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E)
None of these
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Two vertices of a triangles are \[\left( 3,-\,2 \right)\] and \[\left( -\,2,\text{ }1 \right)\]. If its centroid is \[\left( 1,\,\,\frac{2}{3} \right)\]. Find the third vertex.
A)
\[\left( -\,2,\text{ }3 \right)\]
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B)
(2, 3)
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C)
\[\left( 2,-\,3 \right)\]
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D)
(3, 2)
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E)
None of these
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In the adjoining figure\[DE\parallel BC\] . If AD = 1.4 cm, BD = 5.6 cm and CE = 7.2 cm. Find the value of AE.
A)
2.5 cm
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B)
2.8 cm
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C)
1.7 cm
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D)
1.8 cm
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E)
None of these
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In figure, PB and QA are perpendiculars to segment AB. If PO = 5 cm, QO = 7 cm and area of\[\Delta \,QOA=294\,\,c{{m}^{2}}\]. Find the area of\[\Delta \,POB\].
A)
\[160\,\,c{{m}^{2}}\]
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B)
\[240\,\,c{{m}^{2}}\]
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C)
\[150\,\,c{{m}^{2}}\]
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D)
\[96\,\,c{{m}^{2}}\]
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E)
None of these
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In the given figure, PT is a tangent to the circle with centre O. If OT = 7 cm and OP = 25 cm, then the length of tangent PT is
A)
30 cm
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B)
24 cm
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C)
25 cm
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D)
21 cm
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E)
None of these
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A horse is placed for grazing inside a rectangular field 40 m by 36 m. It is tethered to one corner by a rope 14 m long. On how much area can it graze?
A)
\[154\,\,{{m}^{2}}\]
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B)
\[124\,\,{{m}^{2}}\]
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C)
\[164\,\,{{m}^{2}}\]
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D)
\[282\,\,{{m}^{2}}\]
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E)
None of these
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In the adjoining figure, ABCD is a square of side 14 cm. With centres A, B, C and D four circle are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.
A)
\[48\,\,c{{m}^{2}}\]
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B)
\[42\,\,c{{m}^{2}}\]
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C)
\[36\,\,c{{m}^{2}}\]
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D)
\[56\,\,c{{m}^{2}}\]
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E)
None of these
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A hollow garden roller 63 cm wide with girth of 440 cm is made of iron 4 cm thick. The volume of iron used.
A)
\[53856\,\,c{{m}^{3}}\]
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B)
\[107712\,\,c{{m}^{3}}\]
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C)
\[117521\,\,c{{m}^{3}}\]
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D)
\[57636\,\,c{{m}^{3}}\]
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E)
None of these
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It is required to make a hollow cone 24 cm high whose base radius is 7 cm. Find the area of the sheet metal required including the base.
A)
\[467\,\,c{{m}^{2}}\]
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B)
\[764\,\,c{{m}^{2}}\]
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C)
\[704\,\,c{{m}^{2}}\]
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D)
\[568\,\,c{{m}^{2}}\]
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E)
None of these
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A frustum of a right circular cone has a diameter of base 10 cm of top 6 cm and a height of 5 cm. Find the slant height.
A)
6.385 cm
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B)
5.385 cm
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C)
4.5 cm
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D)
5.5 cm
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E)
None of these
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Find the mean of the following distribution:
Class 0-20 20-40 40-60 60-80 80-100 Frequency 7 11 10 9 13
A)
45
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B)
54
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C)
55
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D)
48
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E)
None of these
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Three unbiased coins are tossed simultaneously. Find the probability of getting at most 2 tail.
A)
\[\frac{3}{8}\]
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B)
\[\frac{7}{8}\]
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C)
\[\frac{1}{3}\]
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D)
\[\frac{1}{8}\]
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E)
None of these
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A bag contains 5 red balls, 9 white balls, 5 green balls and 8 black balls. If one ball is drawn at random. What is the probability that the ball drawn is neither red nor green?
A)
\[\frac{10}{27}\]
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B)
\[\frac{5}{27}\]
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C)
\[\frac{17}{27}\]
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D)
\[\frac{18}{27}\]
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E)
None of these
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Which one number can be placed at the question marks?
A)
4
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B)
7
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C)
6
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D)
5
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E)
None of these
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'+' means \[\div ,\] x means \[-,\] \[\div \] means x and \[-\] means +, then ______ \[8+6\times 4\div 3-4=?\]
A)
12
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B)
\[-\,12\]
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C)
\[\frac{20}{3}\]
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D)
\[-\,\frac{20}{3}\]
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E)
None of these
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Find the missing letter in the series. C4X, F9U, I16R, [?]
A)
L 25 P
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B)
L 27 P
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C)
L 25 O
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D)
M 27 Q
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E)
None of these
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Find the missing number from the given responses. 25, 50, 30, 45, 35, 40?
A)
30
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B)
35
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C)
40
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D)
45
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E)
None of these
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