Mathematics ECAT Pre Engineering Online Test With Answers

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Mathematics ECAT Pre Engineering Online Test

Sr. # Questions Answers Choice
1 If sin x + sin2x = 1, then the value of Cos12x + 3cos10x + 3cos8x + cos6x + 2 cos4x + cos2 x-2 is equal to 0 1 2 sin<sup>2</sup>x
2 The maximum value of sinθcosθis 1 1/2 1/4 1/6
3 If cos 20°=K and cos x=2 k2-1, then the possible values of x between 0° and 360° are 140° 50° and 140° 50° and 130° 40° and 320°
4 If sinθand cosθare the roots of the equation ax2- bx + c = 0, then a, b, c satisfy the relation b<sup>2</sup>- a<sup>2</sup>= 2ac A<sup>2</sup>- b<sup>2</sup>= 2ac A<sup>2</sup>+ b<sup>2</sup>= c<sup>2</sup> B<sup>2</sup>+ a<sup>2</sup>= 2ac
5 Less then 1 Equal to 1 Greater than 1 but less then 2 Greater then or equal to 2
6 If n is add the expansion (a + x)nhas middle terms 2 3 4 5
7 The middle term of the expansion (1 + 2x)6is ______ 1st term 4th term 2nd term 5th term
8 The expansion (1 + x)-3holds when |x| &gt; 1 |x| &lt; 1 x &lt; 1 x &gt; 1
9 1st four terms of the expansion (1-x)-2are 1 + 2x + 3x<sup>2</sup>+ 4x<sup>3</sup> 3x<sup>2</sup>+ 2x + 1 1 + 3x + 4x<sup>2</sup>+ 5x<sup>3</sup> None of these
10 nC2= exists when n is ______
11 n &lt; 8/5 n &lt; 5/8 |n| &lt; 8/5 |n|&gt;8/5
12 Number of terms in the expansion of (a+x)nis n - 1 n + 1 n + 2 n + 3
13 Imaginary Rational Irrational Real numbers
14 (0.90)1/2is equal to 0.99 0.90 0.80 0.88
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16 (0.90)1/2is equal to 0.99 0.90 0.80 0.88
17 The term involving x4in the expansion of (3 - 2x)7is 120 1512 1250 15120
18 (51)4is equal to 7065201 8065201 6765201 6565201
19 72n+ 3n-1. 23n-3is divisible by 24 25 9 13
20 (2.02)4 s equal to 16 16.6496 17 18
21 When we expand (a + 2b)5then a<sup>5</sup>+ 10a<sup>4</sup>b + 40a<sup>3</sup>b<sup>2</sup>+ 80a<sup>2</sup>b<sup>3</sup>+ 80ab<sup>4</sup>+ 32b<sup>5</sup> a<sup>5</sup>+ a<sup>4</sup>b + a<sup>3</sup>b<sup>2</sup>+ a<sup>2</sup>b<sup>3</sup>+ ab<sup>4</sup>+ b<sup>5</sup> 5a<sup>5</sup>+ 4a<sup>4</sup>b + 3a<sup>3</sup>b<sup>2</sup>+ 2a<sup>2</sup>b<sup>3</sup>+ 1 ab<sup>4</sup>+ b<sup>5</sup> None
22 For every positive integers n 1+5+9+....+ (4n - 3) is n(2n - 1) (2n - 1) n - 1 n
23 3/8 7/8 1/8 None
24 <sup>n</sup>C<sub>r</sub> <sup>n+1</sup>C<sub>r+1</sub> <sup>n</sup>C<sub>r+1</sub> None
25 If (1+x-2x3)6= 1+a1x + a2x2+ a3x3+ ..... the the value of a2+ a4+ a6+ .....+a12will be 32 31 64 1024
26 The greatest integer which divides the number 101100- 1 is 100 1000 10000 100000
27 If (1+x)n=C0+ C1x +C2x2+ ......+Cnx1then C0C2+ C1C3+ C2C4+ .....+Cn-2Cn=
28 ab=-1 ab = 1 ab = 2 None
29 If the 4th term in the expansion of (px + x-1)mis 2.5 for all x∈ R, then
30 The greatest term in the expansion of (3+2x)9, when x=1 is 4th 4th and 5th 5th 6th
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