Differentiation Test 48

Result

Differentiation Test 48

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Weekly Quiz Competition

Question 1
1 / -0

Let $$g(x)$$ be a continuous function for all $$x$$, and $$f(x)=f(\alpha)+(x-\alpha).g(x)\ \forall \ x\ =\epsilon \ R$$. Then;

A
$$f(x)$$ is necessarily differentiable at $$x=\alpha$$

B
$$f(x)$$ is not necessarily differentiable at $$x=\alpha$$

C
$$f(x)$$ is not necessarily continuous at $$x=\alpha$$

D
$$None\ of\ these$$

Solution
Question 2
1 / -0

The number of 5 letter words formed using letters of word "CALCULUS" is

A
$$280$$

B
$$15$$

C
$$1110$$

D
$$56$$

Solution
Question 3
1 / -0

Find the missing number, if a certain rule is followed
$$1$$ $$9$$ ?
$$2$$ $$12$$ $$14$$
$$3$$ $$117$$ $$105$$
either row-wise or column-wise.

A
$$7$$

B
$$8$$

C
$$11$$

D
$$9$$

Solution
Question 4
1 / -0

Direction: In a given question, one number is missing in the series. you have to understand the pattern of the series and insert the number
JN 28 27 GP
CE 12 45 TU
LR ? ? MS

A
$$34, 36$$

B
$$35, 35$$

C
$$30, 32$$

D
$$30, 41$$
Question 5
1 / -0

Fill in the missing values.
J V R B
Z 18 24 22 14
L 11 17 15 7
? 9 15 13 5
T 15 21 ? 11

A
X and $$29$$

B
P and $$15$$

C
H and $$19$$

D
F and $$12$$

Solution
Question 6
1 / -0

The number of the three digits numbers having only two consecutive digits identical is:

A
153

B
160

C
180

D
161

Solution
Question 7
1 / -0

Area of a triangle whose vertices are $$(a\cos \theta ,b\sin \theta ),(-a\sin \theta ,b\cos \theta)$$ and $$(-a\cos \theta ,-b\sin \theta )$$ is-

A
$$ab\sin \theta \cos \theta $$

B
$$a\cos \theta \sin \theta$$

C
$$\frac 12ab$$

D
ab

Solution
Question 8
1 / -0

Let A(-4, 0) & B(4,0). Then the number of points C=(x,y) on the circle $${x^2} + {y^2} = 16$$ lying in first quadrant $$(x,y \geqslant 0)$$ such that the area of the triangle whose vertices are A,B,C is a integer is

A
14

B
15

C
16

D
None of these
Question 9
1 / -0

Area of the triangle formed by the tangents at the points $$\left( {4,6} \right),\left( {10,8} \right)$$ and $$\left( {2,4} \right)$$ on the parabola $${y^2} - 2x = 8y - 20,$$is (in sq. units)

A
4

B
2

C
1

D
8

Solution
Question 10
1 / -0

The area of the triangle inscribed in the parabola $$y^2$$ = $$4x$$ , the ordinates of whose vertices are 1 , 2 and 4 is :

A
7/2

B
5/2

C
3/2

D
3/4