The length, breadth and height of a room are m 25 cm, 6 m 75 cm and 4 m 50 cm respectively. Determine the longest rod which can measure the dimension of the room exactly.
A)
75 cm
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B)
70 cm
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C)
69 cm
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D)
65 cm
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E)
None of these
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A circular field has a circumference of 360 km. Three cyclists start together and can cycle 48 km, 60 km and 72 km a day round the field, they will meet again at the same starting point after:
A)
32 days
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B)
28 days
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C)
30 days
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D)
35 days
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E)
None of these
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There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field, while Ravish takes 12 minutes for the same. If they both start from the same point and at the same time and went in the same direction, then after how many minutes will they meet again at the starting point?
A)
30 minutes
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B)
24 minutes
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C)
36 minutes
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D)
42 minutes
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E)
None of these
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Five years ago mother was seven times as old as her daughter and five years hence mother will be three times the age of her daughter. Find the present age of mother.
A)
40 years
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B)
50 years
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C)
30 years
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D)
36 years
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E)
None of these
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Find the largest number which exactly divides 282 and 1247 and leaves remainder 6 and 5 respectively.
A)
154
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B)
276
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C)
142
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D)
138
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E)
None of these
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If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:
A)
\[\frac{155}{301}\]
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B)
\[\frac{301}{155}\]
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C)
\[\frac{11}{120}\]
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D)
\[\frac{120}{11}\]
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E)
None of these
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If and \[\alpha \] are \[\beta \] the roots of the polynomial \[f\,\,\left( y \right)={{y}^{2}}-p\,\,\left( y+1 \right)-c,\] such that \[(\alpha +1)\,\,(\beta +1)=0\] then find the value of c.
A)
2
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B)
\[-\,1\]
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C)
0
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D)
1
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E)
None of these
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When we divide\[(9{{x}^{4}}-4{{x}^{2}}+4)\]by\[(3{{x}^{2}}+x-1),\] then the quotient is:
A)
\[2{{x}^{2}}+x\]
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B)
\[3{{x}^{2}}-1\]
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C)
\[2x+1\]
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D)
\[3{{x}^{2}}-x\]
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E)
None of these
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If the product of roots of f(t)\[f\,(t)=a{{t}^{3}}-6{{t}^{2}}+11t-6\] is 4, then a is equal to:
A)
\[\frac{3}{2}\]
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B)
\[\frac{-\,3}{2}\]
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C)
\[\frac{2}{3}\]
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D)
\[\frac{-\,2}{3}\]
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E)
None of these
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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
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B)
Rs. 6
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C)
Rs. 2
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D)
Rs. 4
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E)
None of these
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On selling a T.V at 5% gain and a refrigerator at 10% gain, a shopkeeper gains Rs. 2000. But if he sells the T.V at 10% gain and the refrigerator at 5% loss, he gains Rs. 1500 on the transaction. Find the actual price of the refrigerator.
A)
Rs. 10000
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B)
Rs. 15000
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C)
Rs. 7500
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D)
Rs. 9000
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E)
None of these
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The sum of a two - digit number and the number formed by interchanging the digit is 132. If 12 is added to the number, the new number becomes 5 times the sum of the digits. Find the number.
A)
46
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B)
48
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C)
45
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D)
43
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E)
None of these
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Ten years ago, father was twelve times as old as his son and ten years hence, he will be twice as old as his son will be. Find present age of father.
A)
20 years
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B)
35 years
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C)
39 years
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D)
34 years
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E)
None of these
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Form the polynomial whose zeroes are\[\frac{4+\sqrt{2}}{2},\]\[\frac{4-\sqrt{2}}{2}\].
A)
\[2{{x}^{2}}-8x+7\]
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B)
\[2{{x}^{2}}+8x+7\]
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C)
\[2{{x}^{2}}-8x-7\]
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D)
\[2{{x}^{2}}+8x-7\]
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E)
None of these
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The sum of two numbers a and b is 15, and the sum of their reciprocals is\[\frac{3}{10}\]. Find a and b.
A)
a = 5, b = 10 or a = 10, b = 5
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B)
a =11, b = 4 or a = 4, b = 11
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C)
a = 9, b = 6 or a = 6, b = 9
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D)
a = 12, b = 3 or a = 3, b =12
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E)
None of these
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The hypotenuse of a right - angled triangle is \[3\sqrt{5\,}cm\]. If smallest side is tripled and larger side is doubled, the new hypotenuse will be 15 cm. Find the length of larger side.
A)
6 cm
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B)
9 cm
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C)
5 cm
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D)
10 cm
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E)
None of these
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If 10th term of an A.P. is 52 and 16th term is 82. Find the 32nd term.
A)
160
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B)
175
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C)
162
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D)
169
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E)
None of these
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If \[\frac{{{c}^{n+1}}+{{d}^{n+1}}}{{{c}^{n}}+{{d}^{n}}}\] is the arithmetic mean between c and d, then find the value of n.
A)
1
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B)
2
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C)
0
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D)
3
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E)
None of these
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Which term of the A.P. 3, 15, 27, 39....will be 132 more than its 54th term?
A)
56th term
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B)
65th term
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C)
63th term
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D)
69th term
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E)
None of these
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The sum of 4th and 8th term of an A.P. is 24 and sum of 6th and the 10th term is 44. Find the sum of first three terms of this A.P.
A)
8
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B)
\[-\,24\]
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C)
18
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D)
24
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E)
None of these
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Find the area of the shaded region from the figure given below: \[\left( Take\,\pi =\frac{22}{7} \right)\]
A)
\[0.6125\,\,c{{m}^{2}}\]
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B)
\[0.8173\,\,c{{m}^{2}}\]
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C)
\[0.5625\,\,c{{m}^{2}}\]
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D)
\[0.4785\,\,c{{m}^{2}}\]
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E)
None of these
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Three sphere whose radii is 3 cm, 4 cm and 5 cm are melted to form a big sphere. Then what is the radius of the big sphere.
A)
6 cm
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B)
7 cm
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C)
8 cm
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D)
9 cm
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E)
None of these
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Find the area of the shaded region in the figure given below:
A)
\[94.73\,\,c{{m}^{2}}\]
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B)
\[96.85\,\,c{{m}^{2}}\]
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C)
\[103.84\,\,c{{m}^{2}}\]
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D)
\[101.75\,\,c{{m}^{2}}\]
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E)
None of these
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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)
\[231.43\,\,c{{m}^{2}}\]
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B)
\[254.34\,\,c{{m}^{2}}\]
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C)
\[190.93\,\,c{{m}^{2}}\]
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D)
\[63.585\,\,c{{m}^{2}}\]
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E)
None of these
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Find the values of p and q so that the polynomial\[f(x)=p{{x}^{3}}+2{{x}^{2}}-19x+q\] is divisible by\[{{x}^{2}}+x-6\].
A)
p = 3, q = 6
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B)
p = 6, q = 3
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C)
p = 4, q = 5
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D)
p = 5, q = 6
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E)
None of these
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In a given \[\Delta \,ABC,\] \[DE\parallel BC\] and \[\frac{AD}{DB}=\frac{3}{5}.\] If AC= 5.6 cm, then find AE.
A)
2.1 cm
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B)
2.4 cm
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C)
1.2 cm
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D)
3.1 cm
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E)
None of these
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In the following figure, if \[DE\parallel BC\] then x is equal to:
A)
9 cm
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B)
8 cm
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C)
4 cm
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D)
6 cm
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E)
None of these
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In the given figure, \[AB\parallel CD\]. If \[OA=3x-19,\] \[OB=x-4,\] \[OC=x-3\] and OD = 4, then find x.
A)
10 or 9
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B)
11 or 8
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C)
14 or 5
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D)
8 or 5
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E)
None of these
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In the given figure, find the length of VX, if WM = 11 cm and WV = 7 cm.
A)
8 cm
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B)
6 cm
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C)
4 cm
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D)
2 cm
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E)
None of these
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If a circle is inscribed in a quadrilateral PQRS, then find which one of the following is correct?
A)
\[PQ+SR=QR+PS\]
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B)
\[PQ-SR=QR+PS\]
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C)
\[PQ+SR=QR-PS\]
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D)
\[PQ-SR=QR-PS\]
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E)
None of these
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Find the radius of incircle inscribed in a right triangle whose base and altitude are 7 cm and 24 cm respectively.
A)
1 cm
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B)
2 cm
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C)
3 cm
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D)
4 cm
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E)
None of these
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In the figure given below find the correct value of x, if O is the centre of the circle?
A)
\[70{}^\circ \]
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B)
\[100{}^\circ \]
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C)
\[120{}^\circ \]
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D)
\[85{}^\circ \]
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E)
None of these
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In the figure given below, O is the centre of the circle and \[\angle PQR=30{}^\circ \]. Find the value of y.
A)
\[100{}^\circ \]
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B)
\[120{}^\circ \]
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C)
\[150{}^\circ \]
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D)
\[80{}^\circ \]
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E)
None of these
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The value of \[[\operatorname{cosec}\,\,(75{}^\circ +q)-sec\,\,(15{}^\circ -q)-\]\[tan\,\,(55{}^\circ +q)+cot\,\,(35{}^\circ -q)]\] is equal to:
A)
\[-\,1\]
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B)
0
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C)
1
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D)
\[\frac{3}{2}\]
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E)
None of these
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If tan A = 1 and \[\text{tan}\,\text{B}\,=\sqrt{3},\]find \[cos\,A\,cos\,B-\sin \,\,A\,\,\sin B\].
A)
\[\frac{1+\sqrt{3}}{2}\]
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B)
\[\frac{1-\sqrt{3}}{2\,\sqrt{2}}\]
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C)
\[\frac{\sqrt{3}}{2\,\sqrt{2}}\]
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D)
\[\frac{2}{\sqrt{3}}\]
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E)
None of these
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If \[\sin \alpha +{{\sin }^{2}}\alpha +{{\sin }^{3}}\alpha =1,\] then the value of \[{{\cos }^{6}}\alpha -4{{\cos }^{4}}\alpha +8{{\cos }^{2}}\alpha \] is:
A)
2
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B)
4
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C)
\[-\,2\]
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D)
0
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E)
None of these
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\[\frac{\sin \alpha }{1-\cot \alpha }+\frac{\cos \alpha }{1-\tan \alpha }\] in its simplest form is equal to:
A)
0
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B)
1
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C)
\[\sin \alpha +\cos \alpha \]
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D)
\[\sin \alpha -\cos \alpha \]
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E)
None of these
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A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of \[30{}^\circ \] with the ground. The distance between the foot of the tree to the point where the top touches the ground is 8 m. What is the height of the tree?
A)
\[8\,\sqrt{3\,}m\]
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B)
\[2\,\sqrt{5\,}m\]
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C)
\[5\,\sqrt{2\,}m\]
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D)
\[3\,\sqrt{2\,}m\]
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E)
None of these
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Find the coordinates of the point which divides the line segment joining the points \[A\,\,\left( 5,-2 \right)\] and B (3, 8) in the ratio 1 : 2.
A)
\[\left( \frac{13}{3},\frac{4}{3} \right)\]
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B)
\[\left( \frac{13}{2},2 \right)\]
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C)
\[\left( \frac{13}{4},\frac{4}{3} \right)\]
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D)
\[\left( \frac{13}{2},\frac{4}{3} \right)\]
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E)
None of these
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Find the value of 'k' for which the points A (1, 2), B (3, k) and C (4, 5) are collinear.
A)
\[\frac{1}{2}\]
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B)
\[\frac{14}{3}\]
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C)
\[\frac{1}{3}\]
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D)
4
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E)
None of these
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