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FORMULA QUIZ : CLASS 12 : 28 dec 2022

Total questions: 48

Worksheet time: 24mins

Name
Class
Date
1.

 If,   a → ⊥ b →, thenIf,\ \ \ \overrightarrow{a\ }\ \perp\ \overrightarrow{b\ },\ then  

a)

  a → =  b →\ \overrightarrow{a\ }\ =\ \ \overrightarrow{b\ }  

b)

  a → ∥ b →\ \overrightarrow{a\ }\ \parallel\ \overrightarrow{b\ }  

c)

  a → .  b → = 0\ \overrightarrow{a\ }\ .\ \ \overrightarrow{b\ }\ =\ 0  

d)

  a → , b → = 5\ \overrightarrow{a\ }\ ,\ \overrightarrow{b\ }\ =\ 5  

2.

If a line makes  α, β ,  and ,  γ , \alpha,\ \beta\ ,\ \ and\ ,\ \ \gamma\ ,\    
angle with x, y and z axes then - 

a)

 sin⁡2α+ sin⁡2β+ sin⁡2γ = 1\sin^2\alpha+\ \sin^2\beta+\ \sin^2\gamma\ =\ 1  

b)

 sin⁡2α+ sin⁡2β+ sin⁡2γ = 2\sin^2\alpha+\ \sin^2\beta+\ \sin^2\gamma\ =\ 2  

c)

 cos⁡2α+ cos⁡2β+ cos⁡2γ = 2\cos^2\alpha+\ \cos^2\beta+\ \cos^2\gamma\ =\ 2  

d)

 cos⁡2α+ cos⁡2β+ cos⁡2γ = 1\cos^2\alpha+\ \cos^2\beta+\ \cos^2\gamma\ =\ 1  

3.

 ∫cosec⁡ x cot⁡ x dx = \int_{ }\operatorname{cosec}\ x\ \cot\ x\ dx\ =\   

a)

cosec x + C

b)

 - cosec x+ C

c)

 cot⁡ x + c\cot\ x\ +\ c  

d)

 - cot x + C

4.

For - any - matrix A,  A(adj A)=A\left(adj\ A\right)=  

a)

 ∣A∣ I\left|A\right|\ I  

b)

 ∣A∣2\left|A\right|^2  

c)

 ∣adj A∣\left|adj\ A\right|  

d)

 ∣adj A∣2\left|adj\ A\right|^2  

5.

If for any matrix A , A' = - A , then

a)

A is symmetric

b)

A is skew symmetric

c)

A is invertible

d)

A is singular

6.

 ∫ dxxx2−1  =\int\ \frac{dx}{x\sqrt{x^2-1\ }}\ =  

a)

 sin⁡−1x + c\sin^{-1}x\ +\ c  

b)

 cos⁡ −1 x + c\cos\ ^{-1}\ x\ +\ c  

c)

 sec⁡ −1 x + c\sec\ ^{-1\ }x\ +\ c  

d)

 tan⁡−1x + C\tan^{-1}x\ +\ C  

7.

 Pr⁡ojection − of   a →, on  b → \Pr ojection\ -\ of\ \ \overrightarrow{\ a\ },\ on\ \overrightarrow{\ b\ }\   


a)

 a →. b →∣b →∣\frac{\overrightarrow{a\ }.\ \overrightarrow{b\ }}{\left|\overrightarrow{b\ }\right|}  

b)

 a →. b →∣a →∣\frac{\overrightarrow{a\ }.\ \overrightarrow{b\ }}{\left|\overrightarrow{a\ }\right|}  

c)

 a → ∣b →∣\frac{\overrightarrow{a\ }\ }{\left|\overrightarrow{b\ }\right|}  

d)

  b →∣a →∣\frac{\ \overrightarrow{b\ }}{\left|\overrightarrow{a\ }\right|}  

8.

 Unit − vector  ⊥   to,    bothUnit\ -\ vector\ \ \perp\ \ \ to,\ \ \ \ both  
 a →  and  b → is\overrightarrow{a\ }\ \ and\ \ \overrightarrow{b\ }\ is  

a)

 a →∣a →∣\frac{\overrightarrow{a\ }}{\left|\overrightarrow{a\ }\right|}  

b)

 a → × b →∣a → × b →∣\frac{\overrightarrow{a\ }\ \times\ \overrightarrow{b\ }}{\left|\overrightarrow{a\ }\ \times\ \overrightarrow{b\ }\right|}  

c)

 ∣a → × b →∣\left|\overrightarrow{a\ }\ \times\ \overrightarrow{b\ }\right|  

d)

 1∣a → × b →∣\frac{1}{\left|\overrightarrow{a\ }\ \times\ \overrightarrow{b\ }\right|}  

9.

 (a,b)∈R ⟹ ( b, a) ∈ R,  then\left(a,b\right)\in R\ \Longrightarrow\ \left(\ b,\ a\right)\ \in\ R,\ \ then  


a)

 R is symmetric

b)

R is transitive

c)

R is equivqalence

d)

None of these

10.

 ∫tan⁡x dx =    \int\tan x\ dx\ =\ _{\ \ \ }^{ }  

a)

cot x

b)

  − log⁡ cos⁡ x\ -\ \log\ \cos\ x  

c)

 coeec2xcoeec^2x  

d)

sec x tanx

11.

 A'  - is  - transpose - of  matrix,  then

a)

( AB)' = A'B'

b)

(AB)' = AB

c)

(AB)' = - AB

d)

(AB)' = B'A'

12.

 ddxcot⁡x =\frac{d}{dx}\cot x\ =  

a)

 cosec⁡2x\operatorname{cosec}^2x  

b)

 − cosec⁡2x-\ \operatorname{cosec}^2x  

c)

cosecx . cotx

d)

sec x.  tanx

13.

 Matrix − A = A n×n ,   then Matrix\ -\ A\ =\ A\ _{n\times n}\ ,\ \ \ then\   

 ∣adj A∣= \left|adj\ A\right|=\   

a)

 ∣A∣\left|A\right|  

b)

 ∣A∣n\left|A\right|^n  

c)

 ∣A∣n−1\left|A\right|^{n-1}  

d)

 II  

14.

bijective function is -

a)

One - one function

b)

Onto function

c)

One one and onto both

d)

None of these

15.

 ddx(ax)=\frac{d}{dx}\left(ax\right)=  

a)

 axlog⁡aa^x\log a  

b)

 axlog⁡a\frac{a^x}{\log a}  

c)

a

d)

x

16.

A  and  B,   are -  independent,   then

a)

P(A∩B)= P(A)P(B)P\left(A\cap B\right)=\ \frac{P\left(A\right)}{P\left(B\right)}

b)

P(A∩B)= P(A).P(B)P\left(A\cap B\right)=\ P\left(A\right).P\left(B\right)

c)

P(A∩B)= P(A)+P(B)P\left(A\cap B\right)=\ P\left(A\right)+P\left(B\right)

d)

P(A+B)= P(A) + P(B)P\left(A+B\right)=\ P\left(A\right)\ +\ P\left(B\right)

17.

 sin⁡−1(2x1+x2)=\sin^{-1}\left(\frac{2x}{1+x^2}\right)=  

a)

 2sin⁡−1 x2^{ }\sin^{-1\ }x  

b)

 2tan⁡−1 x2^{ }\tan^{-1\ }x  

c)

 2cot⁡−1 x2^{ }\cot^{-1\ }x  

d)

 2sec⁡−1 x2^{ }\sec^{-1\ }x  

18.

 log⁡ab=\log_ab=  

a)

1

b)

 log⁡ealog⁡eb\frac{\log_ea}{\log_eb}  

c)

 log⁡eblog⁡ea\frac{\log_eb}{\log_ea}  

d)

0

19.

   p(x)(x−a)(x−b)2 =\ \frac{p\left(x\right)}{\left(x-a\right)\left(x-b\right)^2}\ =  

a)

 A(x−a)+B(x−b)\frac{A}{\left(x-a\right)}+\frac{B}{\left(x-b\right)}  

b)

 A(x−a)+B(x−b)2\frac{A}{\left(x-a\right)}+\frac{B}{\left(x-b\right)^2}  

c)

 A(x−a)+B(x−b)+c(x−b)2\frac{A}{\left(x-a\right)}+\frac{B}{\left(x-b\right)}+\frac{c}{\left(x-b\right)^2}  

d)

 A(x−a)+Bx+ c(x−b)2\frac{A}{\left(x-a\right)}+\frac{Bx+\ c}{\left(x-b\right)^2}  

20.

 ddxtan⁡x\frac{d}{dx}\tan x  

a)

secx .tan x

b)

 sec⁡2x\sec^2x  

c)

 cosec⁡x. cot⁡ x\operatorname{cosec}x.\ \cot\ x  

d)

 − cosec⁡2x-\ \operatorname{cosec}^2x  

21.

 By, Bayes′−theorem, P(E1A)=By,\ Bayes'-theorem,\ P\left(\frac{E_1}{A}\right)=  

a)

 P(A)P(AE1)P(A)P(AE1)+P(E2)P(AE2)\frac{P\left(A\right)P\left(\frac{A}{E_1}\right)}{P\left(A\right)P\left(\frac{A}{E_1}\right)+P\left(E_2\right)P\left(\frac{A}{E_2}\right)}  

b)

 P(A)P(E1A)P(A)P(E1A)+P(E2)P(AE2)\frac{P\left(A\right)P\left(\frac{E_1}{A}\right)}{P\left(A\right)P\left(\frac{E_1}{A}\right)+P\left(E_2\right)P\left(\frac{A}{E_2}\right)}  

c)

 P(E1)P(AE1)P(E1)P(AE1)+P(E2)P(AE2)\frac{P\left(E_1\right)P\left(\frac{A}{E_1}\right)}{P\left(E_1\right)P\left(\frac{A}{E_1}\right)+P\left(E_2\right)P\left(\frac{A}{E_2}\right)}  

d)

 P(E1)P(AE1)P(E1)P(AE1)−P(E2)P(AE2)\frac{P\left(E_1\right)P\left(\frac{A}{E_1}\right)}{P\left(E_1\right)P\left(\frac{A}{E_1}\right)-P\left(E_2\right)P\left(\frac{A}{E_2}\right)}  

22.

 Matrix,   A  = An×n , Matrix,\ \ \ A\ \ =\ A_{n\times n}\ ,\   

  then   ∣kA∣\ then\ \ \ \left|kA\right|  

a)

 k∣A∣k\left|A\right|  

b)

 kn∣A∣k^n\left|A\right|  

c)

 kn−1∣A∣k^{n-1}\left|A\right|  

d)

 II  

23.

 ∫sin⁡x dx = \int_{ }\sin x\ dx\ =\   

a)

- cos x+ C

b)

cos x + C

c)

cot x + C

d)

 sec⁡ x .tan⁡ x + C\sec\ x\ .\tan\ x\ +\ C  

24.

 ∫ dxx2−a2=\int\ \frac{dx}{x^2-a^2}=  

a)

 12alog⁡∣x−ax+a∣+C\frac{1}{2a}\log\left|\frac{x-a}{x+a}\right|+C  

b)

 12alog⁡∣x+ax−a∣+C\frac{1}{2a}\log\left|\frac{x+a}{x-a}\right|+C  

c)

 1atan⁡−1(xa)+C\frac{1}{a}\tan^{-1}\left(\frac{x}{a}\right)+C  

d)

 sin⁡−1(xa)+C\sin^{-1}\left(\frac{x}{a}\right)+C  

25.

 If (a, a)∈ R,    then  − R  − is If\ \left(a,\ a\right)\in\ R,\ \ \ \ then\ \ -\ R\ \ -\ is\   

a)

Reflexive

b)

Symmetric

c)

Transitive

d)

None of these

26.

  ( Am×n)  × (B p×q ) \ \left(\ A_{m\times n}\right)\ \ \times\ \left(B_{\ p\times q\ }\right)\   is
possible  if

a)

m = q

b)

n = q

c)

n = m

d)

n = p 

27.

 If , f′′(x) > 0 , thenIf\ ,\ f''\left(x\right)\ >\ 0\ ,\ then  

a)

f is maximum

b)

f is increasing

c)

f is minimum

d)

f is decreasing

28.

 ∫ex[ f(x) + f′(x)] dx =\int_{ }e^x\left[\ f\left(x\right)\ +\ f'\left(x\right)\right]\ dx\ =  

a)

 ex+ Ce^x+\ C  

b)

 f(x)+Cf\left(x\right)+C  

c)

 exf′(x) +Ce^xf'\left(x\right)\ +C  

d)

 exf(x)+Ce^xf\left(x\right)+C  

29.

 a →∣a →∣ is\frac{\overrightarrow{a\ }}{\left|\overrightarrow{a\ }\right|}\ is  

a)

 Pr⁡ojection   \Pr ojection\ \ \   

 of   a ,→    on     b →of\ \ \ \overrightarrow{a\ ,}\ \ \ \ on\ \ \ \ \ \overrightarrow{b\ }  

b)

 Vector ,  ⊥  to   a →Vector\ ,\ \ \perp\ \ to\ \ \ \overrightarrow{a\ }  

c)

 unit   −  vector , along ,  a  → unit\ \ \ -\ \ vector\ ,\ along\ ,\ \ \overrightarrow{a\ \ }\   

d)

 angle −  between,   a →  and   b  →angle\ -\ \ between,\ \ \ \overrightarrow{a\ }\ \ and\ \ \ \overrightarrow{b\ \ }  



30.

 If , dydx+Py =Q ,  then −If\ ,\ \frac{dy}{dx}+Py\ =Q\ ,\ \ then\ -  
Integrating factor is -

a)

 ∫P dx\int P\ dx  

b)

 ∫Q dx\int_{ }Q\ dx  

c)

 e∫Pdxe^{\int_{ }Pdx}  

d)

 e∫Q dxe^{\int Q\ dx}  

31.

 ∫abf(x) dx∫baf(x) dx =\frac{\int_a^bf\left(x\right)\ dx}{\int_b^af\left(x\right)\ dx}\ =  

a)

0

b)

1

c)

-1

d)

2

32.

If for every element y of codomain there exists an element

x in domain such that f(x) = y, then

a)

f is one one

b)

f is onto

c)

f is transpose

d)

f is continuous

33.

Unit - matrix , may also be called

a)

Null matrix

b)

Row matrix

c)

Column matrix

d)

Scalar matrix

34.

 ∫sec⁡ x dx = \int_{ }\sec\ x\ dx\ =\   

a)

log tanx + c

b)

 cosec⁡2x+C\operatorname{cosec}^2x+C  

c)

 log⁡(tan⁡x)+C\log\left(\tan x\right)+C  

d)

 log⁡(sec⁡ x+ tan⁡x) +C\log\left(\sec\ x+\ \tan x\right)\ +C  

35.

 We  solve ∫ (ax+b)ax2+bx+ cdx , byWe\ \ solve\ \int_{ }\ \frac{\left(ax+b\right)}{\sqrt{ax^2+bx+\ c}}dx\ ,\ by  

a)

Applying - partial - fractions

b)

 applying −  product − ruleapplying\ -\ \ product\ -\ rule  

c)

 Nr = A  .ddx (ax2+ bx+c) +  BNr\ =\ A\ \ \frac{.d}{dx}\ \left(ax^2+\ bx+c\right)\ +\ \ B  

d)

 putting : ax2+ bx+c= tputting\ :\ ax^2+\ bx+c=\ t  

36.

direction ratios of - P and Q are (a, b, c ) and


(p, q, r),  then , the direction ratios, of PQ are - 

a)

(p+a, q+b, r+c)

b)

(p/a, q/b, r/c)

c)

(p - a, q - b, r - c)

d)

None of these

37.

Row matrix has how many rows -

a)

1

b)

2

c)

3

d)

4

38.

 Matrix  −    A Matrix\ \ -\ \ \ \ A\   


  is  −    invertible  −      if\ is\ \ -\ \ \ \ invertible\ \ -\ \ \ \ \ \ if  

a)

 ∣A∣ =0\left|A\right|\ =0  

b)

 ∣A∣= I\left|A\right|=\ I  

c)

 ∣A∣≠0\left|A\right|\ne0  

d)

None of these

39.

 ddx(log⁡ x)=\frac{d}{dx}\left(\log\ x\right)=  

a)

1

b)

x

c)

 1x\frac{1}{x}  

d)

0

40.

Plane - passing - through - point  −(x1, y1, z1)-\left(x_1,\ y_1,\ z_1\right)  is

a)

 A(x− x1)+ B (y − y1)A\left(x-\ x_1\right)+\ B\ \left(y\ -\ y_1\right)  


 +C (z−z1)= 0+C\ \left(z-z_1\right)=\ 0  

b)

 xa+yb+zc=1\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1  

c)

 x− x1a= y− y1b= z−z1c\frac{x-\ x_1}{a}=\ \frac{y-\ y_1}{b}=\ \frac{z-z_1}{c}  

d)

none of these

41.

 tan⁡−1(x+y1−xy)=\tan^{-1}\left(\frac{x+y}{1-xy}\right)=  

a)

 tan⁡−1x− tan⁡−1y\tan^{-1}x-\ \tan^{-1}y  

b)

 2tan⁡−1x+ 2tan⁡−1y2\tan^{-1}x+\ 2\tan^{-1}y  

c)

 tan⁡−1x+ tan⁡−1y\tan^{-1}x+\ \tan^{-1}y  

d)

 tan⁡−1(x+y )\tan^{-1}\left(x+y\ \right)  

42.

while -  dealing  with - homogeneous -  differential 
- equation  we -

a)

evalute -  integrating - factor

b)

 put ,  y = vx

c)

 arrange -  in the form ,  f(x) dx  =  g(y) dy 

d)

None - of - these

43.

If A  ,B , C, D  are vertices of a parallelogram, then its area is

a)

 ∣AB→×CD→∣\left|\overrightarrow{AB}\times\overrightarrow{CD}\right|  

b)

 12∣AB→×CD→∣\frac{1}{2}\left|\overrightarrow{AB}\times\overrightarrow{CD}\right|  

c)

 ∣AB→×AC→∣\left|\overrightarrow{AB}\times\overrightarrow{AC}\right|  

d)

 12∣AB→×AC→∣\frac{1}{2}\left|\overrightarrow{AB}\times\overrightarrow{AC}\right|  

44.

 OB→− OA →=\overrightarrow{OB}-\ \overrightarrow{OA\ }=  

a)

 BA→\overrightarrow{BA}  

b)


 AB →\overrightarrow{AB\ } 

c)

 ∣AA→∣\left|\overrightarrow{AA}\right|  

d)

0

45.

 ddx(axlog⁡ea)= \frac{d}{dx}\left(\frac{a^x}{\log_ea}\right)=\   

a)

 axa^x  

b)

 axlog⁡ea\frac{a^x}{\log_ea}  

c)

 axlog⁡eaa^x\log_ea  

d)

0

46.

Vector - equation -  of - plane, passing through


03 - non - collinear - points 
 a →, b → and c  → is −\overrightarrow{a\ },\ \overrightarrow{b\ }\ and\ \overrightarrow{c\ \ }\ is\ -  

a)

 ( r → − a→). [ (b → − a →)×(c → − a →)]\left(\ \overrightarrow{r\ }\ -\ \overrightarrow{a}\right).\ \left[\ \left(\overrightarrow{b\ }\ -\ \overrightarrow{a\ }\right)\times\left(\overrightarrow{c\ }\ -\ \overrightarrow{a\ }\right)\right]  

= 0

b)

  r → [ (b → − a →)×(c → − a →)]= 0 \ \overrightarrow{r\ }\ \left[\ \left(\overrightarrow{b\ }\ -\ \overrightarrow{a\ }\right)\times\left(\overrightarrow{c\ }\ -\ \overrightarrow{a\ }\right)\right]=\ 0\   

c)

 ( r → − a→)= 0 \left(\ \overrightarrow{r\ }\ -\ \overrightarrow{a}\right)=\ 0\   

d)

 ( r → − a→). [ (b → + a →)×(c → + a →)]= 0 \left(\ \overrightarrow{r\ }\ -\ \overrightarrow{a}\right).\ \left[\ \left(\overrightarrow{b\ }\ +\ \overrightarrow{a\ }\right)\times\left(\overrightarrow{c\ }\ +\ \overrightarrow{a\ }\right)\right]=\ 0\   

47.

 Area,   between  Area,\ \ \ between\ \   

 x = f(y),  and,  y =a,  andx\ =\ f\left(y\right),\ \ and,\ \ y\ =a,\ \ and  
 y = b, is −y\ =\ b,\ is\ -  

a)

 ∫ab dy\int_a^b\ dy  

b)

 ∫abxdy\int_a^bxdy  

c)

 ∫aby dx\int_a^by\ dx  

d)

 ∫abdx\int_a^bdx  

48.

 y − y1 = − 1(dydx)(x1, y1) ( x − x1)y\ -\ y_{1\ }=\ -\ \frac{1}{\left(\frac{dy}{dx}\right)_{\left(x_1,\ y_1\right)}}\ \left(\ x\ -\ x_1\right)  


 represents represents\   

a)

 Tangent − at  − (x1,y1)Tangent\ -\ at\ \ -\ \left(x_1,y_1\right)  

b)

 max⁡imummin⁡imum − at  − (x1,y1)\frac{\max imum}{\min imum}\ -\ at\ \ -\ \left(x_1,y_1\right)   

c)

 increasin⁡gdecreasin⁡g −  at −  (x1,y1)\frac{increa\sin g}{decrea\sin g}\ -\ \ at\ -\ \ \left(x_1,y_1\right)  

d)

 Normal −  at  −  (x1,y1)Normal\ -\ \ at\ \ -\ \ \left(x_1,y_1\right)  

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