Match column A with their correct differentials in column B

$\begin{matrix} C o l u m n A & C o l u m n B p . & c o s x & (i) & s i n x & (v) & s i n^{2} x q . & t a n x & (i i) & c o s x & (v i) & s e c^{2} x r . & c o s e c x & (i i) & s i n x c o s x & (v i i) & - c o t x c o s e c x s . & s i n x & (i i i) & t a n x s e c x & (v i i i) & c o t x c o s e c x t . & c o t x & (i v) & - s i n x & (i x) & - c o s e c^{2} x \end{matrix}$

p - (i); q - (iii); r - (vi); s - (i); t - (viii)

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p - (ii); q - (vi); r - (vii); s - (ii); t - (vii)

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p - (iv); q - (vi); r - (vii); s - (ii); t - (ix)

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p - (ix); q - (v); r - (ix); s - (iv); t - (vi)

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Solution

The correct option is C
p - (iv); q - (vi); r - (vii); s - (ii); t - (ix)

$\frac{d c o s x}{d x}$ = -sin x

$\frac{d t a n x}{d x} = s e c^{2} x$
$\frac{d s i n x}{d x}$ = cos x
$\frac{d}{d x} (c o t x) = - c o s e c^{2} x$

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Similar questions

Q. Match column A with their correct differentials in column B

\begin{matrix} C o l u m n A & C o l u m n B p . & c o s x & (i) & s i n x & (v) & s i n^{2} x q . & t a n x & (i i) & c o s x & (v i) & s e c^{2} x r . & c o s e c x & (i i) & s i n x c o s x & (v i i) & - c o t x c o s e c x s . & s i n x & (i i i) & t a n x s e c x & (v i i i) & c o t x c o s e c x t . & c o t x & (i v) & - s i n x & (i x) & - c o s e c^{2} x \end{matrix}

Q. This section contains 1 Matrix Match type question, which has 2 Columns (Column I and Column II). Column I has four entries (A), (B), (C) and (D), Column II has four entries (P), (Q), (R) and (S). Match the entries in Column I with the entries in Column II. Each entry in Column I may match with one or more entries in Column II.

इस खण्ड में 1 मैट्रिक्स मिलान प्रकार का प्रश्न है, जिसमें 2 कॉलम (कॉलम I तथा कॉलम II) हैं। कॉलम I में चार प्रविष्टियाँ (A), (B), (C) तथा (D) हैं, कॉलम II में चार प्रविष्टियाँ (P), (Q), (R) तथा (S) हैं। कॉलम I में दी गयी प्रविष्टियों का मिलान कॉलम II में दी गयी प्रविष्टियों के साथ कीजिए। कॉलम I में दी गयी प्रत्येक प्रविष्टि का मिलान कॉलम II में दी गयी एक या अधिक प्रविष्टियों के साथ हो सकता है।

Match the Columns and choose the appropriate answer.

कॉलमों का मिलान करें और सही उत्तर चुनें।

Match the value of integration from Column-I to Column-II

कॉलम-I के समाकलनों के मान का कॉलम-II के साथ मिलान कीजिए।

	Column-I कॉलम-I		Column –II कॉलम-II
(A)	$\int e^{x} \cdot (sin x + cos x) d x$	(P)	$e^{x} cos x + c$
(B)	$\int e^{x} (cos x - sin x) d x$	(Q)	$- e^{x} sin x + c$
(C)	$\int e^{x} (- sin x - cos x) d x$	(R)	$- e^{x} cos x + c$
(D)	$\int e^{x} (sin x - cos x) d x$	(S)	$e^{x} \cdot sin x + c$

Match column B to column A

$\begin{matrix} C o l u m n A & C o l u m n B (a) s i n (90 - A) & (i) c o s A (b) t a n (90 - A) & (i i) c o s e c A (c) s e c (90 - A) & (i i i) c o t A \end{matrix}$

Q. Match column I with column II and select the correct option from the codes given below:

\begin{matrix} Column I & Column II A & Trachea & (i) & Alveolar air pO_{2} B & Respiratory centre & (i i) & ATP C & Yeast & (i i i) & Catilaginous rings D & Insects & (i v) & Medulla region E & Fish & (v) & Larynx F & Biologically useful energy & (v i) & Tracheal respiration G & 104 mm Hg & (v i i) & Ethanol H & Vocal cords & (v i i i) & Branchial respiration \end{matrix}

Q. (i) x sin x

(ii) x cos x

(iii) sin (2x − 3)

(iv)

\sqrt{\sin 2 x}

(v)

\frac{\sin x}{x}

(vi)

\frac{\cos x}{x}

(vii) x² sin x

(viii)

\sqrt{\sin (3 x + 1)}

(ix) sin x + cos x

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Match column A with their correct differentials in column B Column A Column B p.cos x(i)sin x(v)sin2xq.tan x(ii)cos x(vi)sec2xr.cosec x(ii)sinx cosx(vii)−cotx cosecxs.sin x(iii)tanx secx(viii)cotx cosecxt.cot x(iv)−sinx(ix)−cosec2x​

The correct option is C p - (iv); q - (vi); r - (vii); s - (ii); t - (ix) d cos xdx = -sin x d tan xdx= sec2x d sinxdx = cos x ddx(cot x)=−cosec2x

The correct option is C
p - (iv); q - (vi); r - (vii); s - (ii); t - (ix)

$\frac{d c o s x}{d x}$ = -sin x

$\frac{d t a n x}{d x} = s e c^{2} x$
$\frac{d s i n x}{d x}$ = cos x
$\frac{d}{d x} (c o t x) = - c o s e c^{2} x$