6
3
2
1
Correct answer is B
U7 = a + (7 - 1)d
= a + 6d
U3 = a + (3 - 1)d
= a + 2d
But U7 = 2(U3)
∴a + 6d = 2(a + 2d)
a + 6d = 2a + 4d
2a - a + 4d - 6d = 0
a - 2d = 0 → eqn1
Sn = n/2 (2a + (n - 1)d)
42 = 4/2 (2a + (4 - 1)d)
42 = 2(2a + 3d)
21 = 2a + 3d → eqn2
eqn1 * eqn2 0 = 2a - 4d
21 = 7d
∴d = 21/7
d = 3
Find the range of values of x for which 7x - 3 > 25 + 3x
x >7
x<7
x>-7
x<-7
Correct answer is A
7x - 3 > 25 + 3x
7x - 3x > 25 + 3
4x > 28
x > 28/4
x > 7
\(\sqrt{\frac{42W}{5L}}\)
\(\sqrt{\frac{6L}{42W}}\)
\(\frac{42W}{5L}\)
\(\frac{5L}{42W}\)
Correct answer is A
\(W\infty LD^2\\W=KLd^2\\K=\frac{W}{Ld^2}\\=\frac{140}{54}\times\left(4\frac{2}{3}\right)^2 \\=\frac{140}{54}\times\left(\frac{14}{3}\right)^2\\=\frac{140\times 9}{54\times 14\times 14}\\=\frac{5}{42}\\∴W=\frac{5}{42Ld^2}\\42W=5Ld^2\\\frac{42W}{5L}=d^2\\d=\sqrt{\frac{42W}{5L}}\)
20
35
45
60
Correct answer is C
t = time taken and N = number of men
t ∝ 1/N
t = K/N
K = Nt
K = 30 * 6
K = 180
∴t = 180/N
4 = 180/N
4N = 180
N = 180/4
45 men
A polynomial in x whose zeros are -2, -1 and 3 is
x3 - 7x + 6
x3 + 7x - 6
x3 + 7x + 6
x3 - 7x - 6
Correct answer is D
x = -2, x = -1 and x = 3
∴x+2 = 0, x+1 = 0 and x-3 = 0
Product of the factors
(x+2)(x+1)(x-3) = 0
(x2 + 3x + 2)(x-3)
x(x2 + 3x + 2) -3(x2 + 3x + 2) = 0
x3 + 3x2 + 2x - 3x2 - 9x - 6 = 0
x3 - 7x - 6 = 0