MCQOPTIONS
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MCQOPTIONS
This section includes 8666 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 101. |
If \[{{\sec }^{2}}\theta =\frac{4}{3}\], then the general value of \[\theta \]is [MP PET 1988] |
| A. | \[2n\pi \pm \frac{\pi }{6}\] |
| B. | \[n\pi \pm \frac{\pi }{6}\] |
| C. | \[2n\pi \pm \frac{\pi }{3}\] |
| D. | \[n\pi \pm \frac{\pi }{3}\] |
| Answer» C. \[2n\pi \pm \frac{\pi }{3}\] | |
| 102. |
The amplitude of \[{{e}^{{{e}^{-i\theta }}}}\]is equal to [RPET 1997] |
| A. | \[\sin \theta \] |
| B. | \[-\sin \theta \] |
| C. | \[{{e}^{\cos \theta }}\] |
| D. | \[{{e}^{\sin \theta }}\] |
| Answer» C. \[{{e}^{\cos \theta }}\] | |
| 103. |
For \[A=133{}^\circ ,\ 2\cos \frac{A}{2}\]is equal to [DCE 2001] |
| A. | \[-\sqrt{1+\sin A}-\sqrt{1-\sin A}\] |
| B. | \[-\sqrt{1+\sin A}+\sqrt{1-\sin A}\] |
| C. | \[\sqrt{1+\sin A}-\sqrt{1-\sin A}\] |
| D. | \[\sqrt{1+\sin A}+\sqrt{1-\sin A}\] |
| Answer» D. \[\sqrt{1+\sin A}+\sqrt{1-\sin A}\] | |
| 104. |
What is the acute angle between the lines represented by the equations \[y-\sqrt{3}x-5=0\] and \[\sqrt{3}x-x+6=0?\] |
| A. | \[30{}^\circ \] |
| B. | \[45{}^\circ \] |
| C. | \[60{}^\circ \] |
| D. | \[75{}^\circ \] |
| Answer» B. \[45{}^\circ \] | |
| 105. |
A bag contains 3 red, 7 white and 4 black balls. If three balls are drawn from the bag, then the probability that all of them are of the same colour is |
| A. | \[\frac{6}{71}\] |
| B. | \[\frac{7}{81}\] |
| C. | \[\frac{10}{91}\] |
| D. | None of these |
| Answer» D. None of these | |
| 106. |
The solution of the differential equation \[\frac{dy}{dx}=\sec x(\sec x+\tan x)\]is |
| A. | \[y=\sec x+\tan x+c\] |
| B. | \[y=\sec x+\cot x+c\] |
| C. | \[y=\sec x-\tan x+c\] |
| D. | None of these |
| Answer» B. \[y=\sec x+\cot x+c\] | |
| 107. |
If \[a+b+c=0\] and \[p\ne 0,\] the lines \[ax+(b+c)y=p,\] \[bx+(c+a)y=p\] and \[cx+(a+b)y=p\] |
| A. | Do not intersect |
| B. | Intersect |
| C. | Are concurrent |
| D. | None of these |
| Answer» B. Intersect | |
| 108. |
If the line \[\frac{x}{a}+\frac{y}{b}=1\] passes through the points (2, -3) and (4, -5), then \[(a,\ b)\]= |
| A. | (1, 1) |
| B. | (- 1, 1) |
| C. | (1, - 1) |
| D. | (- 1, - 1) |
| Answer» E. | |
| 109. |
Equation of the tangent to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]which is perpendicular to the straight line \[y=mx+c\]is |
| A. | \[y=-\frac{x}{m}\pm a\sqrt{1+{{m}^{2}}}\] |
| B. | \[x+my=\pm \text{ }a\text{ }\sqrt{1+{{m}^{2}}}\] |
| C. | \[x+my=\pm a\sqrt{1+{{(1/m)}^{2}}}\] |
| D. | \[x-my=\pm a\sqrt{1+{{m}^{2}}}\] |
| Answer» C. \[x+my=\pm a\sqrt{1+{{(1/m)}^{2}}}\] | |
| 110. |
The only value of x for which \[{{2}^{\sin x}}+{{2}^{\cos x}}>{{2}^{1-(1/\sqrt{2})}}\] holds, is |
| A. | \[\frac{5\pi }{4}\] |
| B. | \[\frac{3\pi }{4}\] |
| C. | \[\frac{\pi }{2}\] |
| D. | All values of x |
| Answer» B. \[\frac{3\pi }{4}\] | |
| 111. |
The probabilities of two events A and B are given as \[P(A)=0.8\] and \[P(B)=0.7.\] What is the minimum value of \[P(A\cap B)?\] |
| A. | 0 |
| B. | 0.1 |
| C. | 0.5 |
| D. | 1 |
| Answer» D. 1 | |
| 112. |
If \[\mathbf{a}=2\mathbf{i}+4\mathbf{j}-5\mathbf{k}\] and \[\mathbf{b}=\mathbf{i}+2\mathbf{j}+3\mathbf{k}\], then \[|\mathbf{a}\times \mathbf{b}|\] is [UPSEAT 2002] |
| A. | \[11\sqrt{5}\] |
| B. | \[11\sqrt{3}\] |
| C. | \[11\sqrt{7}\] |
| D. | \[11\sqrt{2}\] |
| Answer» B. \[11\sqrt{3}\] | |
| 113. |
In a triangle \[ABC,\,\,2{{a}^{2}}+4{{b}^{2}}+{{c}^{2}}=4ab+2ac,\] then\[\cos B\] is equal to |
| A. | 0 |
| B. | \[\frac{1}{8}\] |
| C. | \[\frac{3}{8}\] |
| D. | \[\frac{7}{8}\] |
| Answer» E. | |
| 114. |
In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple as well as orange juice. Then, which of the following is/are true? I. 150 students were taking at least one juice. II. 225 students were taking neither apple juice nor orange juice. |
| A. | Only I is true |
| B. | Only II is true |
| C. | Both I and II are true |
| D. | None of these |
| Answer» C. Both I and II are true | |
| 115. |
The area enclosed between the curve \[y={{\log }_{e}}(x+e)\]and the co-ordinate axes is [AIEEE 2005] |
| A. | 3 |
| B. | 4 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 116. |
Assuming that the sums and products given below are defined, which of the following is not true for matrices [Karnataka CET 2003] |
| A. | \[A+B=B+A\] |
| B. | \[AB=AC\]does not imply \[B=C\] |
| C. | \[AB=O\]implies \[A=O\]or \[B=O\] |
| D. | \[(AB{)}'={B}'{A}'\] |
| Answer» D. \[(AB{)}'={B}'{A}'\] | |
| 117. |
Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity \[\vec{u}\] and the other from rest with uniform acceleration\[\vec{f}\]. Let \[\alpha \] be the angle between their directions of motion. The relative velocity of the second particle w.r.t. the first is least after a time |
| A. | \[\frac{u\,\,\cos \,\,\alpha }{f}\] |
| B. | \[\frac{u\,\,\sin \,\,\alpha }{f}\] |
| C. | \[\frac{f\,\,\cos \,\,\alpha }{u}\] |
| D. | \[u\,\,\sin \,\,\alpha \] |
| Answer» B. \[\frac{u\,\,\sin \,\,\alpha }{f}\] | |
| 118. |
Which of the following is true for matrix \[AB\] [RPET 2003] |
| A. | \[{{(AB)}^{-1}}={{A}^{-1}}{{B}^{-1}}\] |
| B. | \[{{(AB)}^{-1}}={{B}^{-1}}{{A}^{-1}}\] |
| C. | \[AB=BA\] |
| D. | All of these |
| Answer» C. \[AB=BA\] | |
| 119. |
Two aeroplane I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is |
| A. | 0.2 |
| B. | 0.7 |
| C. | 0.06 |
| D. | 0.14 |
| Answer» E. | |
| 120. |
The probability that a man can hit a target is \[\frac{3}{4}\]. He tries 5 times. The probability that he will hit the target at least three times is [MNR 1994] |
| A. | \[\frac{291}{364}\] |
| B. | \[\frac{371}{464}\] |
| C. | \[\frac{471}{502}\] |
| D. | \[\frac{459}{512}\] |
| Answer» E. | |
| 121. |
Abhay speaks the truth only 60%. Hasan rolls a die blindfolded and asks abhay to tell him if the outcome is a prime abhay says, YES what is the probability that he outcome is really prime? |
| A. | 0.5 |
| B. | 0.75 |
| C. | 0.6 |
| D. | None of these |
| Answer» D. None of these | |
| 122. |
Find the range of \[f(x)=sgn({{x}^{2}}-2x+3).\] |
| A. | \[\{1,-1\}\] |
| B. | \[\{1\}\] |
| C. | \[\{-1\}\] |
| D. | None of these |
| Answer» C. \[\{-1\}\] | |
| 123. |
If k is a scalar and I is a unit matrix of order 3, then \[adj(k\,I)=\] [MP PET 1991; Pb. CET 2003] |
| A. | \[{{k}^{3}}I\] |
| B. | \[{{k}^{2}}I\] |
| C. | \[-{{k}^{3}}I\] |
| D. | \[-{{k}^{2}}I\] |
| Answer» C. \[-{{k}^{3}}I\] | |
| 124. |
The domain of the function\[f(x)=\sqrt{{{x}^{14}}-{{x}^{11}}+{{x}^{6}}-{{x}^{3}}+{{x}^{2}}+1}\] is |
| A. | \[(-\infty ,\infty )\] |
| B. | \[[0,\infty )\] |
| C. | \[(-\infty ,0]\] |
| D. | \[R\backslash [0,1]\] |
| Answer» B. \[[0,\infty )\] | |
| 125. |
The equation \[2{{\cos }^{2}}\left( \frac{x}{2} \right).{{\sin }^{2}}x={{x}^{2}}+\frac{1}{{{x}^{2}}},\]\[0\le x\le \frac{\pi }{2}\] has |
| A. | one real solution |
| B. | no solution |
| C. | more than one real solution |
| D. | None of these |
| Answer» C. more than one real solution | |
| 126. |
A bag contains 4 white and 3 red balls. Two draws of one ball each are made without replacement. Then the probability that both the balls are red is |
| A. | \[\frac{1}{7}\] |
| B. | \[\frac{2}{7}\] |
| C. | \[\frac{3}{7}\] |
| D. | \[\frac{4}{7}\] |
| Answer» B. \[\frac{2}{7}\] | |
| 127. |
If \[\overrightarrow{A}=3\mathbf{i}+\mathbf{j}+2\mathbf{k}\] and \[\overrightarrow{B}=2\mathbf{i}-2\mathbf{j}+4\mathbf{k}\] and q is the angle between \[\overrightarrow{A}\] and \[\overrightarrow{B},\] then the value of \[\sin \theta \] is |
| A. | \[\frac{2}{\sqrt{7}}\] |
| B. | \[\sqrt{\frac{2}{7}}\] |
| C. | \[\frac{4}{\sqrt{7}}\] |
| D. | \[\frac{3}{\sqrt{7}}\] |
| Answer» B. \[\sqrt{\frac{2}{7}}\] | |
| 128. |
The general solution of the trigonometric equation \[\tan \theta =\cot \alpha \] is [MP PET 1994] |
| A. | \[\theta =n\pi +\frac{\pi }{2}-\alpha \] |
| B. | \[\theta =n\pi -\frac{\pi }{2}+\alpha \] |
| C. | \[\theta =n\pi +\frac{\pi }{2}+\alpha \] |
| D. | \[\theta =n\pi -\frac{\pi }{2}-\alpha \] |
| Answer» B. \[\theta =n\pi -\frac{\pi }{2}+\alpha \] | |
| 129. |
If \[\frac{\pi }{2}<\alpha <\pi ,\,\text{ }\pi <\beta <\frac{3\pi }{2};\] \[\sin \alpha =\frac{15}{17}\] and \[\tan \beta =\frac{12}{5}\], then the value of \[\sin (\beta -\alpha )\] is [Roorkee 2000] |
| A. | -0.773755656108597 |
| B. | -0.0950226244343891 |
| C. | 21/221 |
| D. | 171/221 |
| Answer» E. | |
| 130. |
Square matrix \[{{[{{a}_{ij}}]}_{n\times n}}\]will be an upper triangular matrix, if |
| A. | \[{{a}_{ij}}\ne \]0, for \[i>j\] |
| B. | \[{{a}_{ij}}\ne \], for \[i>j\] |
| C. | \[{{a}_{ij}}=\]0, for \[i<j\] |
| D. | None of these |
| Answer» C. \[{{a}_{ij}}=\]0, for \[i<j\] | |
| 131. |
The lines \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] are perpendicular to each other, if [MP PET 1996] |
| A. | \[{{a}_{1}}{{b}_{2}}-{{b}_{1}}{{a}_{2}}=0\] |
| B. | \[{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}=0\] |
| C. | \[a_{1}^{2}{{b}_{2}}+b_{1}^{2}{{a}_{2}}=0\] |
| D. | \[{{a}_{1}}{{b}_{1}}+{{a}_{2}}{{b}_{2}}=0\] |
| Answer» C. \[a_{1}^{2}{{b}_{2}}+b_{1}^{2}{{a}_{2}}=0\] | |
| 132. |
O is the origin and A is the point (3, 4). If a point P moves so that the line segment OP is always parallel to the line segment OA, then the equation to the locus of P is |
| A. | \[4x-3y=0\] |
| B. | \[4x+3y=0\] |
| C. | \[3x+4y=0\] |
| D. | \[3x-4y=0\] |
| Answer» B. \[4x+3y=0\] | |
| 133. |
If \[|\mathbf{a}\,.\,\mathbf{b}|\,=3\] and \[|\mathbf{a}\times \mathbf{b}|\,=4,\] then the angle between a and b is |
| A. | \[{{\cos }^{-1}}\frac{3}{4}\] |
| B. | \[{{\cos }^{-1}}\frac{3}{5}\] |
| C. | \[{{\cos }^{-1}}\frac{4}{5}\] |
| D. | \[\frac{\pi }{4}\] |
| Answer» C. \[{{\cos }^{-1}}\frac{4}{5}\] | |
| 134. |
The equation of the line passing through the point (1, 2) and perpendicular to the line \[x+y+1=0\] is [MNR 1981] |
| A. | \[y-x+1=0\] |
| B. | \[y-x-1=0\] |
| C. | \[y-x+2=0\] |
| D. | \[y-x-2=0\] |
| Answer» C. \[y-x+2=0\] | |
| 135. |
\[\tan \frac{2\pi }{5}-\tan \frac{\pi }{15}-\sqrt{3}\tan \frac{2\pi }{5}\tan \frac{\pi }{15}\] is equal to |
| A. | \[-\sqrt{3}\] |
| B. | \[\frac{1}{\sqrt{3}}\] |
| C. | 1 |
| D. | \[\sqrt{3}\] |
| Answer» E. | |
| 136. |
D is a point on AC of the triangle with vertices A \[(2,3)\], \[B(1,-3)\], \[C(-4,-7)\] and BD divides ABC into two triangles of equal area. The equation of the line drawn though B at right angles to BD is |
| A. | \[y-2x+5=0\] |
| B. | \[2y-x+5=0\] |
| C. | \[y+2x-5=0\] |
| D. | \[2y+x-5=0\] |
| Answer» B. \[2y-x+5=0\] | |
| 137. |
The number of roots of the equation \[\log (-2x)\] \[=2\log (x+1)\] are [AMU 2001] |
| A. | 3 |
| B. | 2 |
| C. | 1 |
| D. | None of these |
| Answer» C. 1 | |
| 138. |
If \[A=\left[ \begin{matrix} 1 & 2 & 3 \\ 5 & 0 & 7 \\ 6 & 2 & 5 \\ \end{matrix} \right]\]and \[B=\left[ \begin{matrix} 1 & 3 & 5 \\ 0 & 0 & 2 \\ \end{matrix} \right]\], then which of the following is defined |
| A. | AB |
| B. | \[A+B\] |
| C. | \[{A}'{B}'\] |
| D. | \[{B}'{A}'\] |
| Answer» D. \[{B}'{A}'\] | |
| 139. |
Area bounded by the curve \[{{x}^{2}}=4y\] and the straight line \[x=4y-2\] is [SCRA 1986; IIT 1981; Pb. CET 2003] |
| A. | \[\frac{8}{9}\] sq. unit |
| B. | \[\frac{9}{8}\] sq. unit |
| C. | \[\frac{4}{3}\] sq. unit |
| D. | None of these |
| Answer» C. \[\frac{4}{3}\] sq. unit | |
| 140. |
The solution of the equation \[x+\frac{1}{x}=2\] will be [MNR 1983] |
| A. | 2, -1 |
| B. | 0, -1, \[-\frac{1}{5}\] |
| C. | \[-1,-\frac{1}{5}\] |
| D. | None of these |
| Answer» E. | |
| 141. |
If \[{{\log }_{2}}x+{{\log }_{x}}2=\frac{10}{3}={{\log }_{2}}y+{{\log }_{y}}2\] and \[x\ne y,\] then \[x+y=\] [EAMCET 1994] |
| A. | 2 |
| B. | 65/8 |
| C. | 37/6 |
| D. | None of these |
| Answer» E. | |
| 142. |
A straight line cuts off an intercept of 2 units on the positive direction of x-axis and passes through the point (-3, 5). What is the foot of the perpendicular drawn from the point (3, 3) on this line? |
| A. | \[(1,3)\] |
| B. | \[(2,0)\] |
| C. | \[(0,2)\] |
| D. | \[(1,1)\] |
| Answer» E. | |
| 143. |
The equations of the tangents to the circle \[{{x}^{2}}+{{y}^{2}}=36\]which are inclined at an angle of \[{{45}^{o}}\]to the x-axis are |
| A. | \[x+y=\pm \sqrt{6}\] |
| B. | \[x=y\pm 3\sqrt{2}\] |
| C. | \[y=x\pm 6\sqrt{2}\] |
| D. | None of these |
| Answer» D. None of these | |
| 144. |
The adjacent sides AB and AC of a triangle ABC are represented by the vectors \[-2\hat{i}+3\hat{j}+2\hat{k}\] and \[-4\hat{i}+5\hat{j}+2\hat{k}\] respectively. The area of the triangle ABC is |
| A. | 6 square units |
| B. | 5 square units |
| C. | 4 square units |
| D. | 3 square units |
| Answer» E. | |
| 145. |
If \[F(x)=\int_{{{x}^{2}}}^{{{x}^{3}}}{\log t\,dt,\,\,(x>0),}\] then \[{F}'(x)=\] [MP PET 2001] |
| A. | \[(9{{x}^{2}}-4x)\log x\] |
| B. | \[(4x-9{{x}^{2}})\log x\] |
| C. | \[(9{{x}^{2}}+4x)\log x\] |
| D. | None of these |
| Answer» B. \[(4x-9{{x}^{2}})\log x\] | |
| 146. |
The equation of the tangent to the curve \[(1+{{x}^{2}})y=2-x,\] where it crosses the x-axis, is [Kerala (Engg.) 2002] |
| A. | \[x+5y=2\] |
| B. | \[x-5y=2\] |
| C. | \[5x-y=2\] |
| D. | \[5x+y-2=0\] |
| Answer» B. \[x-5y=2\] | |
| 147. |
A circle passes through the origin and has its centre on \[y=x\]. If it cuts \[{{x}^{2}}+{{y}^{2}}-4x-6y+10=0\] orthogonally, then the equation of the circle is [EAMCET 1994] |
| A. | \[{{x}^{2}}+{{y}^{2}}-x-y=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}-6x-4y=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-2x-2y=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}+2x+2y=0\] |
| Answer» D. \[{{x}^{2}}+{{y}^{2}}+2x+2y=0\] | |
| 148. |
Two tangents drawn from the origin to the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]will be perpendicular to each other, if |
| A. | \[{{g}^{2}}+{{f}^{2}}=2c\] |
| B. | \[g=f={{c}^{2}}\] |
| C. | \[g+f=c\] |
| D. | None of these |
| Answer» B. \[g=f={{c}^{2}}\] | |
| 149. |
The area of the parallelogram whose diagonals are \[\frac{3}{2}\mathbf{i}+\frac{1}{2}\mathbf{j}-\mathbf{k}\] and \[2\mathbf{i}-6\mathbf{j}+8\mathbf{k}\] is [UPSEAT 2002] |
| A. | \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=bc+ca+ab\] |
| B. | \[5\sqrt{2}\] |
| C. | \[({{a}^{2}}+ab,\,{{b}^{2}}+ab,\,-ab)\] |
| D. | \[(-bc,\,{{b}^{2}}+bc,\,{{c}^{2}}+bc),\] |
| Answer» B. \[5\sqrt{2}\] | |
| 150. |
If the lines \[ax+by+c=0\], \[bx+cy+a=0\] and \[cx+ay+b=0\] be concurrent, then [IIT 1985; DCE 2000, 02] |
| A. | \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}+3abc=0\] |
| B. | \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-abc=0\] |
| C. | \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc=0\] |
| D. | None of these |
| Answer» D. None of these | |