How many even numbers can be formed by using all the digits 2, 3, 4, 5, 6?
- A72
- B36
- C120
- D24
Question types
Model Paper 3 question types
45 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
45
Questions
6
Question groups
5
Question types
01
M.C.Q (1 Marks)
18 Q→02Assertion (A) & Reason (B) MCQ
2 Q→032 Marks Questions
7 Q→043 Marks Question
9 Q→05Case study (4 Marks)
3 Q→065 Marks Questions
6 Q→Sample Questions
Model Paper 3 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $\frac{3+2 \sin \theta}{1-2 \sin \theta}$ is a real number and $0<\theta<2 \pi$, then $\theta=$
- A$\frac{\pi}{3}$
- B$\frac{\pi}{2}$
- ✓$\pi$
- D$\frac{\pi}{6}$
Answer: C.
View full solution →If $\alpha$ and $\beta$ are acute angles satisfying $\cos 2 \alpha=\frac{3 \cos 2 \beta-1}{3-\cos 2 \beta}$, then $\alpha$ is
- A$\sqrt{2} \cot \beta$
- ✓$\sqrt{2} \tan \beta$
- C$\frac{1}{\sqrt{2}} \cot \beta$
- D$\frac{1}{\sqrt{2}} \tan \beta$
Answer: B.
View full solution →For two sets $A \cup B=A$ if
- A$A=B$
- B$A \neq B$
- C$B \subseteq A$
- D$A \subseteq B$
The solution set for $|3 x-2| \leq \frac{1}{2}$
- A$\left[\frac{5}{6}, \frac{2}{3}\right]$
- B$\left[\frac{2}{3}, \frac{2}{3}\right]$
- ✓$\left[\frac{1}{2}, \frac{5}{6}\right]$
- D$\left[\frac{5}{6}, \frac{1}{2}\right]$
Answer: C.
View full solution →Assertion $(A):$ If each of the observations $x_1, x_2, \ldots, x_n$ is increased by $a$, where $a$ is a negative or positive number, then the variance remains unchanged.
Reason $(R):$ Adding or subtracting a positive or negative number to $($or from$)$ each observation of a group does not affect the variance.
Reason $(R):$ Adding or subtracting a positive or negative number to $($or from$)$ each observation of a group does not affect the variance.
- ✓Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- BBoth $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Answer: A.
View full solution →Assertion (A): The expansion of $(1+ x )^{ n }=n_{c_0}+n_{c_1} x+n_{c_2} x^2 \ldots+n_{c_n} x^n$.
Reason (R): If $x=-1$, then the above expansion is zero.
Reason (R): If $x=-1$, then the above expansion is zero.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Find the equation of the perpendicular bisector of the line joining the points $(1, 3)$ and $(3, 1).$
View full solution →Let $A=\{(x: x \in N), B=(x: x=2 n, n \in N)\}, C=\{x: x=2 n-1, n \in N\}$ and, $D=\{x: x$ is a prime natural number$\}.$ Find: $A \cap B$.
View full solution →Find the equation of the circle which touches the lines $4 x-3 y+10=0$ and $4 x-3 y-30=0$ and whose centre lies on the line $2 x + y =0$.
View full solution →Find the equation of the parabola whose: focus is $(2,3)$ and the directrix $x-4 y+3=0$.
View full solution →Find the of derivative of the function from the first principle: $\sin x^2$.
View full solution →Let $A=\{a, e, i, o, u\}, B=\{a, d, e, o, v)$ and $C=\{e, o, t, m]$. Using Venn diagrams, verify that: $A \cap(B \cup C)=$ $(A \cap B) \cup(A \cap C)$
View full solution →Evaluate $\left[\frac{1}{1-4 i}-\frac{2}{1+i}\right]\left[\frac{3-4 i}{5+i}\right]$ to the standard form.
View full solution →If $( a + ib )=\frac{c+i}{c-i}$, where c is real, prove that $a ^2+ b ^2=1$ and $\frac{b}{a}=\frac{2 c}{c^2-1}$.
View full solution →Expand the given expression $\left(x+\frac{1}{x}\right)^6$
View full solution →Using binomial theorem, prove that $\left(2^{3 n }-7 n -1\right)$ is divisible by $49 ,$ where $n \in N$
View full solution →Ashish is writing examination. He is reading question paper during reading time. He reads instructions carefully. While reading instructions, he observed that the question paper consists of $15$ questions divided in to two parts part $I$ containing $8$ questions and part $II$ containing $7$ questions.
$i$. If Ashish is required to attempt $8$ questions in all selecting at least $3$ from each part, then in how many ways can he select these questions $(1)$
$ii$. If Ashish is required to attempt $8$ questions in all selecting $3$ from $I$ part, then in how many ways can he select these questions $(1)$
$iii.$ If Ashish is required to attempt $8$ questions in all selecting $4$ from part $I$ and $4$ from part $II,$ then in how many ways can he select these questions $(2)$
OR
If Ashish is required to attempt $8$ questions in all selecting $6$ from one section and remaining from another section, then in how many ways can he select these questions $(2)$
View full solution →$i$. If Ashish is required to attempt $8$ questions in all selecting at least $3$ from each part, then in how many ways can he select these questions $(1)$
$ii$. If Ashish is required to attempt $8$ questions in all selecting $3$ from $I$ part, then in how many ways can he select these questions $(1)$
$iii.$ If Ashish is required to attempt $8$ questions in all selecting $4$ from part $I$ and $4$ from part $II,$ then in how many ways can he select these questions $(2)$
OR
If Ashish is required to attempt $8$ questions in all selecting $6$ from one section and remaining from another section, then in how many ways can he select these questions $(2)$
For a group of $200 $ candidates, the mean and the standard deviation of scores were found to be $40$ and $15 ,$ respectively. Later on it was discovered that the scores of $43$ and $35$ were misread as $34$ and $53,$ respectively.
$i.$ Find the correct variance. $(1)$
$ii$. What is the formula of variance. $(1)$
$iii.$ Find the correct mean. $(2)$
OR
Find the sum of correct scores.$ (2)$
View full solution →| Student | English | Hindi | S.st | Science | Maths |
| Ramu | $39$ | $59$ | $84$ | $80$ | $41$ |
| Rajitha | $79$ | $92$ | $68$ | $38$ | $75$ |
| Komala | $41$ | $60$ | $38$ | $71$ | $82$ |
| Patil | $77$ | $77$ | $87$ | $75$ | $42$ |
| Pursi | $72$ | $65$ | $69$ | $83$ | $67$ |
| Gayathri | $46$ | $96$ | $53$ | $71$ | $39$ |
$ii$. What is the formula of variance. $(1)$
$iii.$ Find the correct mean. $(2)$
OR
Find the sum of correct scores.$ (2)$
Indian track and field athlete Neeraj Chopra, who competes in the Javelin throw, won a gold medal at Tokyo Olympics. He is the first track and field athlete to win a gold medal for India at the Olympics.
$i$. Name the shape of path followed by a javelin. If equation of such a curve is given by $x^2=-16 y,$ then find the coordinates of foci. $(1)$
$ii.$ Find the equation of directrix and length of latus rectum of parabola $x^2=-16 y. (1)$
$iii.$ Find the equation of parabola with Vertex $(0,0)$, passing through $(5,2)$ and symmetric with respect to $y-$ axis and also find equation of directrix.$ (2)$
OR
Find the equation of the parabola with focus $(2,0)$ and directrix $x=-2$ and also length of latus rectum. $(2)$
View full solution →$i$. Name the shape of path followed by a javelin. If equation of such a curve is given by $x^2=-16 y,$ then find the coordinates of foci. $(1)$
$ii.$ Find the equation of directrix and length of latus rectum of parabola $x^2=-16 y. (1)$
$iii.$ Find the equation of parabola with Vertex $(0,0)$, passing through $(5,2)$ and symmetric with respect to $y-$ axis and also find equation of directrix.$ (2)$
OR
Find the equation of the parabola with focus $(2,0)$ and directrix $x=-2$ and also length of latus rectum. $(2)$
Prove that: $\tan 20^{\circ} \tan 30^{\circ} \tan 40^{\circ} \tan 80^{\circ}=1$
View full solution →If $\cos x=-\frac{3}{5}$ and $x$ lies in the IIIrd quadrant, find the values of $\cos \frac{x}{2}, \sin \frac{x}{2}$ and $\sin 2 x$.
View full solution →Find the three numbers in $GP,$ whose sum is $52$ and sum of whose product in pairs is $624.$
View full solution →Evaluate : $\lim _{x \rightarrow \sqrt{10}} \frac{\sqrt{7-2 x}-(\sqrt{5}-\sqrt{2})}{x^2-10}$
View full solution →Find the derivative of $x \sin x$ from first principle.
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