Mathematics Test 143

Result

Mathematics Test 143

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
4 / -1

Fifteen coupons are numbered 1, 2, 3, ....., 15 respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupons is at most 9, is :

A
(1/15)⁷

B
(3/5)⁷

C
(8/15)⁷

D
None of these

Solution

Total coupons = 15
1 < selected coupon number < 9
i.e., 1, 2, 3, 4, 5, 6,, 7, 8, 9

∴ Probability of one selected coupon to have number

Hence, the required probability
= (3/5) x (3/5) x ....... 7 times = (3/5)⁷ (Using multiplicative principle for independent events)
Question 2
4 / -1

Find the value(s) of the parameter 'a'(a>0) for each of which the area of the figure bounded by the straight line, the parabola is the greatest

A
3^1/4

B
3^1/2

C
4^1/3

D
4^1/4

Solution
Question 3
4 / -1

A
S = 545/1088

B
S = 1056/545

C
S = 545/1056

D
S = 1088/545

Solution
Question 4
4 / -1

The parameter on which the value of the determinant

does not depend upon, is

A
a

B
p

C
d

D
x

Solution

⇒ Δ = (1 + a² - 2a cos dx) [sin (p + d)x cos px - sin px cos (p + d) x]
⇒ Δ = (1 + a2 - 2a cos dx) sin dx
Which is independent of p.
Question 5
4 / -1

If n is even positive integer, then the condition that the greatest term in the expansion of (1 + x)ⁿ may have the greatest coefficient also is

A

B

C

D

Solution
Question 6
4 / -1

The equation of the common tangent to the curves y⁡² = 8 x and xy ⁡= -1 is

A
3y = 9x + 2

B
y = 2x + 1

C
2y = x + 8

D
y = x + 2

Solution
Question 7
4 / -1

If ABC be a triangle with and AB = x such that (AB) (AC) = 1. If x varies, then the longest possible length of the angle bisector AD is

A
1/4

B
1/8

C
1/3

D
1/2

Solution

⇒ y_max = 1/2 since the minimum value of the denominator is 2 if x > 0.
Question 8
4 / -1

The locus of the midpoint of the portion of the line x cos α + y sin α = p intercepted between the axes is

A

B

C
x² + y² = 4p²

D
x² + y² = p²

Solution
Question 9
4 / -1

Find the derivative with respect to x of the function :

A

B

C

D

Solution
Question 10
4 / -1

A lady wants to select one cotton saree and one polyester saree from a textile shop. If there are 10 cotton varieties and 12 polyester varieties, in how many ways can she choose the two sarees ?

A
120

B
140

C
100

D
130

Solution

There are 10 cotton sarees. The lady can select the cotton saree in 10 different ways. Corresponding to each of the above 10 different ways, she can select the polyester saree in 12 different ways because there are 12 polyester sarees.. Hence the no. of different ways of selecting the two sarees

= 10 × 12 = 120